Turbulent Diffusion

It is established for the first time that the spatial distribution of breaking waves on the ocean surface is a multifractal process. This result is based on an analysis of airborne visible and near-infrared imagery of the ocean surface under a limited range of wind speed and fetch. A detailed study of the optical spectra of the images and the cumulative probability structure of the prevalent background shows that the lower-intensity reflective areas follow a Rayleigh probability distribution. By contrast, the higher-intensity pixels associated with the scattered light from foam and breaking waves demonstrate scaling characteristics in both the optical spectra and the cumulative probability distributions. It is demonstrated that the degree to which the whitecaps are singularities on a dark background is described by a Lipschitz exponent c•, which uniquely tags each breaking wave. This identification process, called "fractal" or "singularity filtering", leads to a critical condition c• = 1 tentatively associated with the crossover from active entraining whitecaps to passively dissipating foam. The multifractal representation associated with the degree of singularity is simply a restatement that the imagery is composed of a continuum of sets, where each set consists of those breaking waves at a particular phase in their existence. The fractal spectrum of the image above a threshold is shown to be representable by a fractal generator. Physically, the fractal generator models the energy exchange in a breaking wave field as a flux of energy input from the atmosphere to the wave field cascaded over scales of the order of a kilometer to meters. If the energy flux is further parameterized in terms of the receiving area, an assumption similar to closure techniques used in classical turbulence models, the empirical results symmetrically span Phillips's basic arguments for the energy flux terms controlling a wind-driven sea. 16,179 16,180 KERMAN AND BERNIER: MULTIFRACTAL BREAKING WAVES ! . Ii . i Figure 1. (a), Field of breaking waves observed using a line scanner on board an aircraft flying at about 500 m over the Bay of Fundy. Field of view about 250m 2, resolution was about 0.5m, and optical wavelength was 0.95/•m. (b), Image thresholded to remove reflective Rayleigh component. (c), Image of asubsets (a) 1) identified with nonentraining (foam) areas. (d), Image of a subsets, a < 1, identified with entraining (breaking wave) areas. qualitative way what is observed about breaking waves, even at the risk of stating in some cases the obvious. When the field is imaged either by standard photography [Ross and Cardone, 1974; Smith, 1981; Kennedy and Snyder, 1983] or with side-scanning techniques from underneath the surface [Thorpe and Hall, 1983; Thorpe and Humphties, 1980] or from the air (Figure la) [Kerman and Szeto, 1994], several features of the spatial field of breaking waves are evident. The first feature of breaking waves is their distinct isolated nature: the fact that they are born, mature, and die almost always without affecting or being mod-16,182 K••AN AND BERNIER: MULTIFRACTAL BREAKING WAVES

A novel experimental technique to measure static pressure fluctuation was applied in order to evaluate velocity-pressure correlation in a turbulent mixing layer. The developing region of the mixing layer was found to be out of equilibrium state, indicating the oscillatory velocity fluctuation due to vortex shedding and remarkable production of turbulence. The contribution of pressure-related terms in the transport equation of the Reynolds stress is found to be well captured by the present method. A simple model for pressure diffusion by Lumley gave a satisfactory approximation when the flow approached the self-similar state. However, the analogy between pressure diffusion and turbulent diffusion becomes weaker when the flow exhibits characteristics which are not found in the equilibrium state.

A new theoretical model for mid-latitude mesosphere and lower thermosphere at equinox conditions has been developed by including new values of various characteristic atmospheric parameters. A value of the eddy diffusion coefficient was deduced compatible with others reported in the literature and we discuss its effect upon the concentration of the different constituents. Photodissociation processes were handled with a detailed division of the different regions of the solar spectrum, mainly in the Schumann-Runge bands, allowing an exact computation of the diurnal O('D) and O,('AJ altitude profiles produced by solar radiation. The model includes CO, CO,, NZ and oxygen and hydrogen compounds. Our results compare well with recent experimental altitude profiles of minor compounds at mesospheric levels. The altitude profiles have been tested to reproduce various nightglow features, such as the Infrared Atmospheric System of O,('A,) in 1.27 pm and the atomic oxygen green line. The resulting profiles are in line with results obtained using rocket borne instrumentation.

Profiles of currents, density, and microstructure were obtained in the Pacific Ocean on and near the equator at 140øW in late 1984 as pa• of the Tropic Heat program. During a 4•-day time series on the equator, the shear zone above the core of the undercurrent had very low mean Richardson numbers, Ri, between Va and «. Average turbulent dissipation rates, e, were high in this zone, = 10 -7 Wkg -1, and varied by a factor of 100 between minima in the early afternoon and maxima at night. The signal reached to 90 m, well into the stratified zone. Eddy coefficients, K, were low at high Ri, and gradually increased as Ri decreased, until they rose dramatically near Ri =Va. The observed K (Ri) relations are specific to time, location, and temporal and spatial resolution of the data.

A mathematical scheme is developed to simulate the vertical turbulent dispersion of air pollution that is absorbed or deposited to the ground. The scheme is an exact analytical solution of the atmospheric diffusion equation, without any restriction to the vertical profile of wind speed and eddy diffusivities, and taking into account the dry deposition by a boundary condition of a nonzero flux to the ground. The performances of the solution, with a proper parameterization of the vertical profiles of the wind and eddy diffusivities, were evaluated against the dataset from the Hanford (Washington) diffusion experiment, in which two tracers (one depositing and one nondepositing) were released simultaneously. In addition, the solution derived in this work is compared with four different models, with deposition at the ground, found in the literature.

The results of an analysis of velocity fluctuations in the plasma sheet of the Earth&#x27;s magnetotail measured onboard INTERBALL Tail Probe satellite are presented. The hodographs of the velocity in directions (Y, Z) and correlation functions are presented for a number of passages when the satellite was in the plasma sheet for a long time. The turbulent diffusion coefficients are calculated. A comparison of the obtained diffusion coefficients with those predicted theoretically in [1] is carried out. It is shown that the results of observations confirm theoretical predictions.

The results of an analysis of velocity fluctuations in the plasma sheet of the Earth&#x27;s magnetotail measured onboard INTERBALL Tail Probe satellite are presented. The hodographs of the velocity in directions (Y, Z) and correlation functions are presented for a number of passages when the satellite was in the plasma sheet for a long time. The turbulent diffusion coefficients are calculated. A comparison of the obtained diffusion coefficients with those predicted theoretically in [1] is carried out. It is shown that the results of observations confirm theoretical predictions.

Vehicle particle emissions are studied extensively because of their health effects, contribution to ambient PM levels and possible impact on climate. The aim of this work was to obtain a better understanding of secondary particle formation and growth in a diluting vehicle exhaust plume using 3-d information of simulations together with measurements. Detailed coupled computational fluid dynamics (CFD) and aerosol dynamics simulations have been conducted for H 2 SO 4 -H 2 O and soot particles based on measurements within a vehicle exhaust plume under real conditions on public roads. Turbulent diffusion of soot and nucleation particles is responsible for the measured decrease of number concentrations within the diesel car exhaust plume and decreases coagulation rates. Particle size distribution measurements at 0.45 and 0.9 m distance to the tailpipe indicate a consistent soot mode (particle diameter D p $50 nm) at variable operating conditions. Soot mode number concentrations reached up to 10 13 m À3 depending on operating conditions and mixing.

The paper describes the implementation and applicability of the Large eddy simulation (LES) technique for simulating turbulent flows. The LES approach is implemented in the in-house RANS research code Spider-3D. The Spider-LES code is validated by studying the unsteady flow over a backward-facing step (BFS). The LES simulation over the BFS is carried out at a Reynolds number of 5100 based on the inlet free-stream velocity. Finite-volume discretization schemes for the non-linear convective terms and sub-grid stress (SGS) models used for LES approach are discussed in the present study. To investigate mesh dependency, two types of grid resolution are studied. The results computed from Spider-LES are validated against DNS reference data by Le et al. The mean longitudinal, vertical velocity profile and the turbulence intensities compare satisfactory with the DNS data at the normalized coordinates X * = (x − X r ) /X r . The reattachment length X r in the longitudinal direction, varies from 7.2h to 7.4h with different SGS models used as compared to the DNS value of 6.28h.

The emergence of methods allowing the simplification of detailed chemical kinetics enables detailed modeling of turbulent diffusion flames. One of these methods, the “Intrinsic Law-Dimensional Manifolds” (ILDM) method and its application to the computation of turbulent reactive flows are described here. A CFD solver and a Monte-Carlo code solving the transport equation of the scalar joint pdf are coupled and

An analytical technique to solve the Eulerian advection-diffusion equation for nonstationary conditions and passive contaminant within the Planetary Boundary Layer is analysed in this paper. The approach produces comparable results when considering the most important quantity in air-pollution application, that is the ground level concentration distribution. This is a promising result as this computer-based technique may be used for quantitative and qualitative estimations of contaminant distribution.

Pressure Diffusion flame Flame structure Flamelet approach Radiation a b s t r a c t A numerical study of hydrogen turbulent diffusion flame structure is carried out in the pressure range of 1e10 atm with a special emphasis on mixing. The investigation is conducted under constant volumetric fuel and air flows. Mixing is characterized by mixture fraction, its variance and the scalar dissipation rate. The flow field and the chemistry are coupled by the flamelet assumption. Mixture fraction and its variance are transported by computational fluid dynamic (CFD). Computational predictions are analysed at two radial stations (the first one represent the near-field region and the second one the far-field region). The computational results indicate a deterioration of mixing with pressure rise.

After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the Lévy flight superdiffusion as a self-similar Lévy process. The condition of self-similarity converts the infinitely divisible characteristic function of the Lévy process into a stable characteristic function of the Lévy motion. The Lévy motion generalizes the Brownian motion on the base of the α-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. This leads to the Kolmogorov's equation for arbitrary Markovian processes. As particular case we obtain the fractional Fokker-Planck equation for Lévy flights. Some results concerning stationary probability distributions of Lévy motion in symmetric smooth monostable potentials, and a general expression to calculate the nonlinear relaxation time in barrier crossing problems are derived. Finally we discuss results on the same characteristics and barrier crossing problems with Lévy flights, recently obtained with different approaches.

This work deals with the formulation and numerical implementation of a two-dimensional mathematical and numerical model describing open channel hydrodynamics, sediment and/or scalar transport and riverbed evolution in curved channels. It is shown that a well balanced 2D model can predict flow features, sediment and scalar concentration, and bed elevation with an accuracy that is suitable for practical river engineering. The term ''balanced" implies that important physical processes are modeled with a similar degree of complexity and exhaustiveness. The starting point of the model formulation is the assumption of self-similarity of vertical velocity profiles (horizontal velocities in the longitudinal and transverse directions), that are scaled by shear velocity and streamline curvature, both resolved by the model. The former is scaled by a bed-resistance coefficient that must be estimated or calibrated -as usualon a application-specific basis, and the latter is computed by a new, grid-based but grid orientation independent, scheme that acts on the discrete solution. All processes, including bottom shear, momentum dispersion, scalar dispersion, turbulent diffusion, bed load, and suspended load, are modeled using physically based, averaged values of empirical or semi-empirical constants, and consistently with the assumed velocity profiles (and bed-generated turbulence). Bed deformation modeling can be implemented with either an equilibrium or non-equilibrium formulation of the Exner equation, depending on the adaptation length scale, which must be taken under consideration if significantly larger than the length scale of the spatial discretization. The governing equations are solved by high-resolution, unstructured-grid Godunov method, which is elsewhere tested and shown to be reliable and second-order accurate. Application of the model to laboratory test cases, using standard parameter values and previously reported bed-resistance coefficients, gives results comparable to many 2D and 3D models previously applied to the same cases, most part of which benefit from case-specific parameter tuning. There are obviously intrinsic limits to the descriptive ability of 2D models in river modeling, but the results of this study point to the utility and cost-effectiveness of a well-designed 2D model.

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10 12 . The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k-e, k-x, k-x-SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 ]. The k-x-SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10 9 -10 12 .

In this paper (Part I) we derive the basic equations governing the model, discuss the treatment of meteorological variables (inversion height, wind field, and turbulent eddy diffusivity), present a kinetic mechanism for photochemical smog, and describe the technique employed for ...

Abstrac~Effects of flow direction, nonlinear drag and the corrected lift force on particle deposition rate in turbulent pipe flow is studied. A digital simulation technique is used and the trajectories of particles of different sizes are analyzed. The experimental data for the mean flow field and the intensities of fluctuation velocity components are used in the analysis, and the effects of turbulent diffusion and Brownian dispersion are included in the computational model. The instantaneous turbulent fluctuation is simulated as a continuous Gaussian random vector field and the Brownian force is modeled as a Gaussian white-noise random process. Ensembles of particle trajectories are evaluated and statistically analyzed. It is shown that the simulation results for the deposition velocity are in reasonable agreement with the model predictions, the available experimental data, and the recent simulation results for channel flows. It is shown that the downward gas flow in a vertical pipe enhances the particle deposition rate, while the upward flow reduces it. © 1997

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Moreover, large eddies are able to mix scalar quantities in a manner that is counter to the local gradient. We present a general solution of a two-dimension steady state advection-diffusion equation, considering non-local turbulence closure using the General Integral Laplace Transform Technique. We show some examples of applications of the new solution with different vertical diffusion parameterisations.

Soot formation is compared in turbulent diffusion flames burning a commercial Diesel and two Diesel surrogates containing n-decane and a-methylnaphthalene. A burner equipped with a high-efficiency atomisation system has been specially designed and allows the stabilisation of liquid fuels flames with similar hydrodynamics conditions. The initial surrogate composition (70% n-decane, 30% a-methylnaphthalene) was previously used in the literature to simulate combustion in Diesel engines. In this work, a direct comparison of Diesel and surrogates soot tendencies is undertaken and relies on soot and fluorescent species mappings obtained respectively by Laser-Induced Incandescence (LII) at 1064 nm and Laser-Induced Fluorescence at 532 nm. LIF was assigned to soot precursors and mainly to high-number ring Polycyclic Aromatic Hydrocarbons (PAH). The initial surrogate was found to form 40% more soot than the tested Diesel. Consequently, a second surrogate containing a lower a-methylnaphthalene concentration (20%) has been formulated. That composition which presents a Threshold Soot Index (TSI) very close to Diesel one is also consistent with our Diesel composition that indicates a relatively low PAH content. The spatially resolved measurements of soot and fluorescent soot precursors are quite identical (in shape and intensity) in the Diesel and in the second surrogate flames. Furthermore the concordance of the LII temporal decays suggests that a similar growth of the primary soot particles has occurred for Diesel and surrogates. In addition, the comparison of the LII fluence curves indicates that physical/optical properties of soot contained in the different flames might be similar. The chemical composition present at the surface of soot particles collected in Diesel and surrogate flames has been obtained by laser-desorption ionisation time-offlight mass spectrometry. An important difference is found between Diesel and surrogate samples indicating the influence of the fuel composition on soot content.

Buoyant surface discharges into ambient water bodies can exhibit multiple complex flow processes, which cover the spatial range from the near field with initial jet mixing to the far field with passive ambient diffusion. Multiple flow phenomena can occur, such as buoyant collapse motions, bottom attachment, deflection by the ambient current, and dynamic shoreline interaction, in the near field, and

The Danshui River estuarine system is the largest estuarine system in northern Taiwan and is formed by the confluence of Tahan Stream, Hsintien Stream, and Keelung River. A comprehensive one-dimensional (1-D) model was used to model the hydrodynamics and cohesive sediment transport in this branched river estuarine system. The applied unsteady model uses advection/dispersion equation to model the cohesive sediment transport. The erosion and deposition processes are modeled as source/sink terms. The equations are solved numerically using an implicit finite difference scheme. Water surface elevation and longitudinal velocity time series were used to calibrate and verify the hydrodynamics of the system. To calibrate and verify the mixing process, the salinity time series was used and the dispersion coefficient of the advection/dispersion equation was determined. The cohesive sediment module was calibrated by comparing the simulated and field measured sediment concentration data and the erosion coefficient of the system was determined. A minimum mean absolute error of 4.22 mg/L was obtained and the snapshots of model results and field measurements showed a reasonable agreement. Our modeling showed that a 1-D model is capable of simulating the hydrodynamics and sediment processes in this estuary and the sediment concentration has a local maximum at the limit of salinity intrusion. Furthermore, it was indicated that for Q 50 (the flow which is equaled or exceeded 50% times), the turbidity maximum location during neap tide is about 1 km closer to the mouth compared to that during spring tide. It was found that deposition is the dominant sediment transport process in the river during spring–neap periods. It was shown that, while sediment concentration at the upstream depends on the river discharge, the concentration in the downstream is not a function of river discharge.

The northern Gulf of California, Mexico, is one of the most productive and diverse marine ecosystems in the world. It currently harbors three marine protected areas, including two biosphere reserves. Despite its significance as a conservation site and its importance for Mexico's fisheries, proper knowledge of population connectivity and larvae dispersal from spawning sites is largely lacking. Our study focuses on connectivity in the northern gulf resulting from advection by currents and turbulent diffusion during summer, the main spawning period of various key commercial species. We calculated connectivity matrices in the northern Gulf from currents produced by the output of a three-dimensional baroclinic numerical model and a random walk process to simulate turbulent motions. We released 2000 hypothetical passive particles in each of 21 areas along the coast (between 0-60 m deep) during the summer and followed their trajectories for periods of 2, 4, 6, and 8 weeks. For the case of full time transport, the effects of tidal currents are minimal in the overall dispersal of passive particles on the time scales studied. However, this can be substantially altered if the particles are allowed to avoid being transported for periods of time; this is illustrated by striking differences between the connectivity matrices obtained by modeling also night-only and day-only advection. This "order zero" connectivity study (i.e., not including realistic larvae behavior, which is species-specific) reveals that during the summer spawning season of key commercial species, regional hydrodynamics produce a cyclonic downstream connectivity along the coast, from the mainland to the Baja California coast. Our results provide the basis for a full connectivity study where larvae behavior and settlement habitat will be included.

The paper describes the implementation and applicability of the Large eddy simulation (LES) technique for simulating turbulent flows. The LES approach is implemented in the in-house RANS research code Spider-3D. The Spider-LES code is validated by studying the unsteady flow over a backward-facing step (BFS). The LES simulation over the BFS is carried out at a Reynolds number of 5100 based on the inlet free-stream velocity. Finite-volume discretization schemes for the non-linear convective terms and sub-grid stress (SGS) models used for LES approach are discussed in the present study. To investigate mesh dependency, two types of grid resolution are studied. The results computed from Spider-LES are validated against DNS reference data by Le et al. The mean longitudinal, vertical velocity profile and the turbulence intensities compare satisfactory with the DNS data at the normalized coordinates X * = (x − X r ) /X r . The reattachment length X r in the longitudinal direction, varies from 7.2h to 7.4h with different SGS models used as compared to the DNS value of 6.28h.

The ability of optimum multiparameter (OMP) analysis to identify regions where diapycnal mixing is prominent is examined. OMP analysis and isopycnal analysis are applied to synthetic data sets constructed with predetermined mixing regimes and ratios. Oceanic conditions are modeled by including random noise representative of environmental variability found in the eastern Indian and Atlantic Oceans. Comparison of results from OMP and isopycnal analysis verifies that in the absence of environmental variability, OMP analysis can isolate regions with moderate diapycnal mixing. When environmental variability is included, the effects of diapycnal mixing have to be su'ong enough to be detected without ambiguity. It is shown that this is the case in the eastem Indian Ocean and, most probably, also in the eastern Atlantic Ocean. I I ß ß e© ßee -I.I ß ß ß el-Ira ß e ß eel ß ß ß .l-ß ß eel ee ß • ß ß ß ß eeee ß ß • ß ee ß ee eel ß ee ße ß ee ß -m-e ee eeee ß ee m eeleel ee ee m ßeelßeßß ee I I ß I ! ! 0.06 0-0.06 a2 lO I i I ß ß ß ß ß .e-e ii ße ß ß ß ß ßee ß me ß ß ß ß ß ß ß• ß ß eel ß ee ß ,m ß• ß eel ß ße ß m. ee ß ßß• ß ß ßel ßße ß ßeeee ! I 0.06 0-0.06 a• i i i mm ß ß ß ß

Two commercial CFD codes were used to simulate the strongly swirling single-phase flow with core recirculation within an axial hydrocyclone. Both packages used a Differential Reynolds Stress Model with default constants for the turbulence closure. The effect of omitting wall reflection terms was also investigated and it was generally found that this lead to better agreement with experiment. Interestingly, the predicted velocity profiles from the two CFD codes did not agree with each other. Possible reasons for this are different turbulence modelling approaches with different terms for the turbulent diffusion and rapid pressure-strain terms. ᭧

Mathematical modelling provides an essential tool for understanding aeolian transport of dust and sand, its spatial and temporal dynamics, and its role in the earth system. As much of the crucial action takes place at or just above land surfaces, adequate representation of land-surface processes is essential. In this paper, we review progress in aeolian transport modelling during last two decades, with emphasis on the representation of several key land-surface processes: (1) saltation; (2) dust uplift; (3) the threshold for particle motion, including the effects of surface sheltering and cohesion; (4) turbulent diffusion near the ground; and (5) deposition of particles to the surface. These process models are then placed in the context of integrated models of aeolian transport, in which the conservation equation for atmospheric dust is solved over a large region or the globe. We identify and assess four challenges in large-scale aeolian transport modelling: (1) the fidelity of process representations, (2) upscaling point-scale process models in the presence of unresolved heterogeneity in space and time (where a new approach is suggested), (3) availability of spatial data on model inputs and boundary conditions, and (4) large-scale parameter estimation. Crown

Particle deposition on the wall in a dilute turbulent vertical pipe flow is modeled. The different mechanisms of particle transport to the wall are considered, i.e., Brownian motion, turbulent diffusion and turbophoresis. The Saffman lift force, the electrostatic force, the virtual mass effect and wall surface roughness are taken into account in the model developed. A boundary condition that accounts for the probability of particle sticking to the wall is suggested. An analytical solution for deposition of small Brownian particles is obtained. A particle relaxation time range, where the model developed is reliably applicable, is evaluated. Computational results obtained at different particle-wall sticking probabilities in the wide particle relaxation time range are presented and discussed.

1] Improved turbulent closures for use in fully nonlinear Boussinesq-type models are described here. The approach extends previous works in order to give a more flexible and accurate description of the turbulence due to a breaking wave. Turbulent stresses are handled by means of the Boussinesq hypothesis, and the eddy viscosity is assumed to vary over the water depth according to different laws. The model is described in detail, and its performances are evaluated both against available analytical solutions and against experimental data of regular waves breaking over a slope. The influence of the vertical structure of turbulence under a breaking wave is analyzed by means of four different vertical profiles of eddy viscosity; the differences in terms of hydrodynamic features are also discussed. Among the four selected profiles, two of them (the uniform one and that with uniform eddy viscosity over the top half of the water column which linearly decreases to zero over the lower half ) give better overall performances when compared with experimental data concerning velocity profiles.

Obstructed shear flows (i.e. those over permeable media) are common in the environment. An archetypal example, flow over a submerged vegetation canopy, is investigated here. Like any flow through complex geometry, canopy flows are characterised by strong spatial gradients. The focus of this experimental study is the three-dimensionality of aquatic canopy flow, in particular that of the coherent interfacial vortices that govern mixing into and out of the canopy. It is shown here that the vortices have a finite lateral scale that is comparable to their vertical scale; both are of the order of the drag length scale of the canopy, (C D a) −1 , where a is the frontal area density and C D is a bulk drag coefficient. The finite lateral extent of the vortices generates strong lateral hydrodynamic gradients, both instantaneously and in the long-term. The instantaneous gradients, which can contribute greatly to the dispersion of dissolved and particulate species, are far more pronounced. Finally, the potential for canopies to generate differential roughness secondary circulation is examined. In the consideration of vertical scalar transport, this circulation can be of the same order as turbulent diffusion.

A multifractal method of analysis, initially developed in the framework of turbulence and having had developments and applications in various geophysical domains (meteorology, hydrology, climate, remote sensing, environmental monitoring, seismicity, volcanology), has previously been demonstrated to be an efficient tool to analyse the intermittent fluctuations of physical or biological oceanographic data (Seuront et al., Geophys. Res. Lett., 23, 3591-3594, 1996 and Nonlin. Processes Geophys., 3, 236-246, 1996). Thus, the aim of this paper is, first, to present the conceptual bases of multifractals and more precisely a stochastic multifractal framework which among different advantages lead in a rather straightforward manner to universal multifractals. We emphasize that contrary to basic analysis techniques such as power spectral analysis, universal multifractals allow the description of the whole statistics of a given field with only three basic parameters. Second, we provide a comprehensive detailed description of the analysis techniques applied in such a framework to marine ecologists and oceanographers; and third, we illustrate their applicability to an original time series of biological and related physical parameters. Our illustrative analyses were based on a 48 h high-frequency time series of in vivo fluorescence (i.e. estimate of phytoplankton biomass), simultaneously recorded with temperature and salinity in the tidally mixed coastal waters of the Eastern English Channel. Phytoplankton biomass, which surprisingly exhibits three distinct scaling regimes (i.e. a physical-biological-physical transition), was demonstrated to exhibit a very specific heterogeneous distribution, in the framework of universal multifractals, over smaller (<10 m) and larger (>500 m) scales dominated by different turbulent processes as over intermediate scales (10-500 m) obviously dominated by biological processes.

Properties of the North Atlantic Deep Water (NADW) depend on mixing that occurs in the Denmark Strait (DS) and the Faroe Bank Channel (FBC) overflow regions. How the sill's topography in those regions may affect mixing processes and downstream variability is thus investigated using a high-resolution terrain-following ocean model. Model results agree with observations that show enhanced mixing and entrainment downstream from the sill; however, mixing seems to occur over a longer distance downstream from the FBC sill and more abruptly downstream from the DS sill. Sensitivity experiments with various FBC sill widths demonstrate that the narrow sill is responsible for the enhanced mixing. The downstream flow variability, eddy propagation, and deep water properties are affected by sill width and background stratification. Similar to the laboratory overflow experiments of Cenedese et al. (2004), three distinct mixing regimes (characterized by the Froude number) are identified in the FBC simulations: a steady subcritical flow regime upstream from the sill, a supercritical wave-like flow regime downstream from the sill, and an irregular eddy-dominated regime farther away from the sill. Satellite altimeter data near the FBC show cyclonic anomalies propagating along the northern slope of the channel, resembling the surface eddies associated with the overflow variability in the model. A cross-channel circulation over the FBC sill, driven by frictional bottom boundary layers, resulted in convergence/divergence zones near the southern/northern slopes and pinching/spreading of isotherms across the channel, similar to the observation-based mechanism proposed by Johnson and Sanford (1992).

A perturbation analysis of the Lagrangian equations of motion is used to examine the diffusion induced by a random field of internal waves. At second order there is a random field of shearing motion in the horizontal plane. We calculate the single-particle, two-particle, and patch diffusivities that result from this motion. Patch and two-particle diffusivity both increase as scale raised to the power of 4/3 for an internal wave field in which the spectrum of horizontal velocity varies as o•-2

1] An array of instruments air-deployed ahead of Hurricane Frances measured the three-dimensional, time dependent response of the ocean to this strong (60 ms À1 ) storm. Sea surface temperature cooled by up to 2.2°C with the greatest cooling occurring in a 50-km-wide band centered 60 -85 km to the right of the track. The cooling was almost entirely due to vertical mixing, not air-sea heat fluxes. Currents of up to 1.6 ms À1 and thermocline displacements of up to 50 m dispersed as near-inertial internal waves. The heat in excess of 26°C, decreased behind the storm due primarily to horizontal advection of heat away from the storm track, with a small contribution from mixing across the 26°C isotherm. SST cooling under the storm core (0.4°C) produced a 16% decrease in air-sea heat flux implying an approximately 5 ms À1 reduction in peak winds.

The forces on the seabed in shallow water under waves influence near-shore transport processes. However, the actual nature of these forces is not yet fully understood. Sleath [1987] simultaneously measured horizontal shear force per unit area and Reynolds stress in oscillating turbulent flow over granular beds with the striking result that maximum Reynolds stress was significantly less than total shear force per unit area of bed. Trying to explain these measurements, we use a formulation which considers two kinds of flow perturbations, namely turbulent fluctuations and some disturbances due to boundary irregularities. The resulting spatially averaged Reynolds equations contain in particular two terms which do not appear in the smooth bed case: the force due to the mean momentum flux for boundary disturbances, here called "form-induced stress," which owes its existence to the vorticity of the disturbed motion, and the force exerted by the roughness elements on the fluid. The "jet regime" as introduced by Gim•nez-Curto and Comiero [1993] for steady flow is extended to oscillatory flow. In this regime, pressure drag on roughness elements is the fundamental force acting on the boundary, and forminduced stress due to vorticity generated by flow separation from bed irregularities becomes the leading stress, thus providing an explanation for Sleath's measurements by means of a physical mechanism which was already envisaged by Longuet-Higgins [1981] for two-dimensional rippled beds. A simple expression is derived for the friction coefficient which is subsequently compared with extensive series of measurements in the laboratory for granular beds as well as for rippled surfaces, showing an excellent agreement.

Buoyant surface discharges into ambient water bodies can exhibit multiple complex flow processes, which cover the spatial range from the near field with initial jet mixing to the far field with passive ambient diffusion. Multiple flow phenomena can occur, such as buoyant collapse motions, bottom attachment, deflection by the ambient current, and dynamic shoreline interaction, in the near field, and lateral and/or upstream spreading motions and turbulent diffusion processes, in the far field. Efficient and reliable predictive techniques covering the whole range of these processes are needed for the design and prediction of wastewater effluents that are subject to water quality regulations that can apply in either near and/or far field. A new comprehensive classification framework distinguishes among ten hydrodynamically distinct flow classes within four major flow categories: free jets, shoreline-attached jets, wall jets, and upstream intruding plumes. A prediction methodology for these discharges has been presented that covers the entire spatial domain from the near to the far field. It is based on the linkage of separate predictive modules in form of the expert system CORMIX3. These hydrodynamic modules are implemented by specific flow protocols and transition criteria determine their spatial extent. The methodology, corroborated by numerous detailed laboratory and some field data sources, constitutes a simple and efficient, yet accurate and robust, tool with few data requirements for surface discharge design and mixing analysis.

The growth rate of Langmuir cells is calculated from a linear stability analysis for different orientations of wind, waves, and cells as well as for various values of the dimensionless parameters describing wave-current interaction. These parameters could be the Stokes drift/friction velocity ratio and the shear ratio Sr which describes the relative strength of the Stokes drift shear and mean Eulerian shear. The growth rate is maximal overall when wind and waves are aligned. For a given angle between the Stokes drift and the wind (the misalignment angle), the direction of the cell axis for maximal growth lies between wind and waves and is mainly determined by (1) the misalignment angle and (2) the shear ratio. For a fixed value of the latter, the orientation of the fastest growing cells (the preferential cell direction) is nearly independent of the one other dimensionless parameter which could be the Stokes drift/friction velocity ratio or the Langmuir number. The direction of the fastest growing cells shifts closer toward the wave direction as the Stokes drift shear increases relative to the mean shear and vice versa. However, while the preferential cell direction lies close to the wind for small Sr, it does not align with the waves for reasonably large Sr. When wind and waves are not aligned and the Stokes drift shear and the mean shear are of the same order, the cells drift sideways at an angle to the cell axes, with a speed which is comparable with the magnitude of the mean Eulerian current at a depth of approximately 0.7 times the cell depth. The drift amplitude increases as the misalignment angle increases and is larger for larger values of the shear ratio. When wind and waves are oriented in the opposite directions, there is no source of instability, and the cells are damped. placed an earlier theory [Craik and Leibovich, 1976], suggests that the circulation originates as a result of an instability arising from the interaction between the Stokes drift, produced by irrotational surface waves, and wind-driven shear flow. This theory, as well as most of the previous and subsequent studies, assumes that the Stokes drift and wind are parallel and predicts the formation of Langmuir cells aligned with both wind and waves [Leibovich, 1983]. Analysis of the observed surface structure of Langmuir circulation (V. Polonichko and D. Farmer, Observations of Langmuir circulation when wind and waves are misaligned, manuscript in preparation, 1997) under changing wind conditions indicates that the orientation of windrows is affected by the relative orientation of the surface Stokes drift and wind vectors. These observations motivate us to ask the following theoretical question: How does the relative Copyright 1997 by the American Geophysical Union. Paper number 97JC00466. 0148-0227/97/97 JC-00466509.00 orientation of the wind and the Stokes drift affect the orientation of Langmuir cells? Leibovich [1983] pointed out that such wind-wave misalignment might affect generation and structure of Langmuir cells, but Gnanadesikan and Weller [1995, p. 3161] (hereinafter referred to as GW) were the first to address this problem. They analyzed wave-current interaction within an Ekman layer of constant depth and concluded that one should expect cells to be generated in a direction, between the wind and the Stokes drift, "closer to the strongest shear." GW suggested that the growth rate of the instabilities for a constant Eulerian mean shear decreases with the increase of the misalignment angle, that is, the angle between the wind and the Stokes drift, and when 15,773 15,774 POLONICHKO: GENERATION OF LANGMUIR CIRCULATION

Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of Large-Eddy Simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turns out to be compatible with the Richardson t 3 law for the average of square particle separation. This emerges from the application of nonstandard methods of analysis through which a precise measure of the Richardson constant was also possible. Its values is estimated as C 2 ∼ 0.5 in close agreement with recent experiments and three-dimensional direct numerical simulations.

A semi-empirical model based on a Gaussian vorticity distribution has been developed for determining eddy diffusivity and wind transport distributions in the polar stratosphere. The model uses as input data pressure surface heights measured at periods of the year when the stratospheric polar vortex exhibits .nearly circular patterns around the pole. The components of the polar wind velocities that result from a Prandtl eddy viscosity distribution are found to be in general agreement with those obtained by other investigators.^

A new phenomenon of turbulent thermal diusion is discussed. This eect is related to the dynamics of small inertial particles in low-Mach-number compressible turbulent¯uid¯ows. Turbulent thermal diusion is caused by the correlation between temperature and velocity¯uctuations of the surroundinḡ uid and leads to relatively strong nondiusive mean¯ux of inertial particles in regions with mean temperature gradients. It is shown that turbulent thermal diusion under certain conditions can cause a large-scale instability of spatial distribution of particles. Particles are concentrated in the vicinity of the minimum (or maximum) of the mean temperature of the surrounding¯uid depending on the ratio of material particle density to that of the surrounding¯uid. At large Reynolds and Peclet numbers the turbulent thermal diusion is much stronger than the molecular thermal diusion. Turbulent thermal diusion can be important in various naturally occurring and industrial multiphase¯ows. In particular, this eect may cause formation of inhomogeneities in spatial distribution of fuel droplets in internal combustion engines. It is conceivable to suggest that the eect of turbulent thermal diusion can play an important role in a process of soot formation in¯ames and in atmospheric dynamics of pollutants, e.g. smog and aerosol clouds formation. #

The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence of stirring. These variances can be weighted at various spatial scales, leading to a family of multi-scale mixing measures and efficiencies. We derive a priori estimates on these efficiencies from the advection-diffusion partial differential equation, focusing on a broad class of statistically homogeneous and isotropic incompressible flows. The analysis produces bounds on the mixing efficiencies in terms of the Péclet number, a measure the strength of the stirring relative to molecular diffusion. We show by example that the estimates are sharp for particular source, sink and flow combinations. In general the high-Péclet number behavior of the bounds (scaling exponents as well as prefactors) depends on the structure and smoothness properties of, and length scales in, the scalar source and sink distribution. The fundamental model of the stirring of a monochromatic source/sink combination by the random sine flow is investigated in detail via direct numerical simulation and analysis. The large-scale mixing efficiency follows the upper bound scaling (within a logarithm) at high Péclet number but the intermediate and small-scale efficiencies are qualitatively less than optimal. The Péclet number scaling exponents of the efficiencies observed in the simulations are deduced theoretically from the asymptotic solution of an internal layer problem arising in a quasi-static model.