Richardson number

Cet article présente une étude de l'évaporation par convection mixte d'une plaque plane humide inclinée soumise à une densité de flux de chaleur constante. L'écoulement de l'air, les transferts de chaleur et de masse sont régis par les équations de continuité, de mouvement, d'énergie et de diffusion dont les approximations au niveau de la couche limite sont appliquées. La résolution des équations se procède comme suit : adimensionnalisation, application de la méthode implicite des différences finies et programmation sur Matlab. Notre travail se termine avec la présentation des résultats sur l'influence de du nombre de Richardson et de l'inclinaison pour la vitesse, la température, la concentration et les coefficients d'échanges associés à la convection mixte. Mots clés : convection mixte, nombre de Richardson, plaque plane inclinée, transfert de chaleur, transfert de masse, adimensionnalisation, différences finies Abstract This paper presents a study of the evaporation by mixed convection of an inclined wet flat plate subjected to a constant heat flux density. Air flow, heat and mass transfers are governed by the equations of continuity, motion, energy and diffusion to which boundary layer approximations are applied. Adimensionnalisation, implicit method for finite differences and programming on Matlab are used to solve the equations. Our work ends with the presentation of results about the influence of Richardson's number and flat's inclination for velocity, temperature, concentration and coefficients of exchange associated with mixed convection.

This study has focused on laminar mixed convection in an inclined square ventilated lid-driven
cavity fi lled with a copper–water nanofl uid. The governing equations in the two-dimensional
space are discretized by using the fi nite volume method with the SIMPLER algorithm. The effects
of independent parameters, including the Richardson number, Reynolds number, inclination angle,
and the solid volume fraction of nanoparticles, on the streamlines, isotherm lines, and the average
Nusselt number along the heat source have been studied. It is found that both the inclination angle
and solid volume fraction, especially the second one, have remarkable effects on the fl uid fl ow
and heat transfer characteristics in the cavity. Artifi cial neural networks (ANN) used to extract
a relation involve independent parameters for calculating the Nusselt number. The back propagation-
learning algorithm with the tangent sigmoid transfer function is used to train the ANN.
Finally, analytical relations for the nanofl uid mixed convection in a lid-driven cavity are derived
from the available ANN. It is found that the coeffi cient of multiple determinations (R2) between
the real values and ANN results is equal to 0.9999, the maximum error being less than 0.5829 and
the mean square error being equal to 5.37 × 10–5.

This paper suggests a simple way of including gravitational effects in the pres-sure-containing correlations that appear in the equations for the transport of Reynolds stress and heat flux. The predicted changes in structure due to the gravitational field are shown to agree closely with Webster's (1964) measurements in a stably stratified shear flow.

The light-wind, clear-sky, very stable boundary layer (vSBL) is characterized by large values of bulk Richardson number. The light winds produce weak shear, turbulence, and mixing, and resulting strong temperature gradients near the surface. Here five nights with weak-wind, very stable boundary layers during the Cooperative Atmosphere–Surface Exchange Study (CASES-99) are investigated. Although the winds were light and variable near the surface, Doppler lidar profiles of wind speed often indicated persistent profile shapes and magnitudes for periods of an hour or more, sometimes exhibiting jetlike maxima. The near-surface structure of the boundary layer (BL) on the five nights all showed characteristics typical of the vSBL. These characteristics included a shallow traditional BL only 10–30 m deep with weak intermittent turbulence within the strong surface-based radiation inversion. Above this shallow BL sat a layer of very weak turbulence and negligible turbulent mixing. The focus o...

: Propagation of energy (either acoustic or electromagnetic energy) through the region of the atmosphere close to the earth's surface depends on estimates of the vertical structure of wind, pressure, temperature, humidity, and refractive index near the earth's surface. To help predict these vertical structures, the TGRAD model has been developed. The model is based on flux- profile methods, requiring simple meteorological inputs as functions of time. The model's original purpose was to predict the vertical temperature gradient profile, hence the name TGRAD. The TGRAD model has been compared against a predecessor model (the Deardorff model) and has proven to characterize the near- surface atmosphere much better under foliated conditions. It characterizes the daytime atmosphere well under all conditions studied. It characterizes the nocturnal atmosphere well until the critical Richardson number is reached. For stronger nocturnal inversions an approach is discussed that may...

Meteorological model errors caused by imperfect parameterizations generally cannot be overcome simply by optimizing initial and boundary conditions. However, advanced data assimilation methods are capable of extracting significant information about parameterization behavior from the observations, and thus can be used to estimate model parameters while they adjust the model state. Such parameters should be identifiable, meaning that they must have a detectible impact on observable aspects of the model behavior, their individual impacts should be a monotonic function of the parameter values, and the various impacts should be clearly distinguishable from each other. A sensitivity analysis is conducted for the parameters within the Asymmetrical Convective Model, version 2 (ACM2) planetary boundary layer (PBL) scheme in the Weather Research and Forecasting model in order to determine the parameters most suited for estimation. A total of 10 candidate parameters are selected from what is, ...

A finite element method based computational study of steady laminar mixed convection flow inside a vented square cavity with a heat conducting horizontal solid circular cylinder placed at the center of the cavity is carried out in this paper. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy. The present work simulates practical systems such as cooling of electronic devices, ventilation of building etc. The effects of cylinder size and Richardson number on fluid flow and heat transfer performance are investigated. Richardson number is varied from 0.0 to 5.0 and the cylinder diameter is varied from 0.0 to 0.6. The results for the case of without cylinder are compared to those with cylinder to observe the effects cylinder on the flow and heat transfer inside the cavity. The phenomenon inside the cavity for the case of with and without cylinder is analyzed through streamline and isotherm patterns. It is found that the streamlines, ...

A transverse secondary circulation should result from vertical mixing of momentum in a stratified shear flow influenced by the earth's rotation. A rigidly mounted acoustic Doppler current profiler was deployed at the bottom of Juan de Fuca Strait, a stratified estuary on the west coast of ...

High-resolution observations from scanning Doppler and aerosol lidars, wind profiler radars, as well as surface and aircraft measurements during the Terrain-induced Rotor Experiment (T-REX) provide the first comprehensive documentation of small-scale intense vortices associated with atmospheric rotors that form in the lee of mountainous terrain. Although rotors are already recognized as potential hazards for aircraft, it is proposed that these small-scale vortices, or subrotors, are the most dangerous features because of strong wind shear and the transient nature of the vortices. A life cycle of a subrotor event is captured by scanning Doppler and aerosol lidars over a 5-min period. The lidars depict an amplifying vortex, with a characteristic length scale of ∼500–1000 m, that overturns and intensifies to a maximum spanwise vorticity greater than 0.2 s−1. Radar wind profiler observations document a series of vortices, characterized by updraft/downdraft couplets and regions of enhanc...

Widespread moderate turbulence was recorded on three specially equipped commercial airline flights over northern Kansas near the northern edge of the extensive cirrus anvil of a nocturnal mesoscale convective system (MCS) on 17 June 2005. A noteworthy aspect of the turbulence was its location several hundred kilometers from the active deep convection (i.e., large reflectivity) regions of the MCS. Herein, the MCS life cycle and the turbulence environment in its upper-level outflow are studied using Rapid Update Cycle (RUC) analyses and cloud-permitting simulations with the Weather Research and Forecast Model (WRF). It is demonstrated that strong vertical shear beneath the MCS outflow jet is critical to providing an environment that could support dynamic (e.g., shearing type) instabilities conducive to turbulence. Comparison of a control simulation to one in which the temperature tendency due to latent heating was eliminated indicates that strong vertical shear and corresponding reduc...

The presence of numerous haors (seasonal lakes), and the occurrence of flash floods and sedimentation are among the dominant physical and hydro-climatic features of North-East Bangladesh. These features for one of the haors (Hail Haor) in the region are studied using a conceptual hydrological model and a hydraulic routine. The hydrologic model used for daily runoff estimation from rainfall and evaporation information is the widely used tank model. Both soil-moisture movement and stream-flow routing are considered in the developed model. The tank runoff is used as an input to a hydraulic routine for estimation of stream water temperatures and suspended sediment load. Based on the stream sediment concentration, sedimentation in a downstream lake (Hail Haor) is estimated and it is found to be about 25 mm per annum. The relationship between monsoonal flooding and thermal response of the haor is investigated with one-year measured data of haor temperatures and water level. Different heat...

The presence of numerous haors (seasonal lakes), and the occurrence of flash floods and sedimentation are among the dominant physical and hydro-climatic features of North-East Bangladesh. These features for one of the haors (Hail Haor) in the region are studied using a conceptual hydrological model and a hydraulic routine. The hydrologic model used for daily runoff estimation from rainfall and evaporation information is the widely used tank model. Both soil-moisture movement and stream-flow routing are considered in the developed model. The tank runoff is used as an input to a hydraulic routine for estimation of stream water temperatures and suspended sediment load. Based on the stream sediment concentration, sedimentation in a downstream lake (Hail Haor) is estimated and it is found to be about 25 mm per annum. The relationship between monsoonal flooding and thermal response of the haor is investigated with one-year measured data of haor temperatures and water level. Different heat...