Journal of Fluids Engineering-transactions of The Asme, Oct 25, 2005
Characteristics of Small Vortices in a Turbulent Axisymmetric Jet Characteristics of small vortic... more Characteristics of Small Vortices in a Turbulent Axisymmetric Jet Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale was approached by progressively decreasing the Reynolds number while still maintaining turbulent flow. A periodic forcing introduced far upstream of the jet nozzle ensured that the jet was turbulent. A vortex eduction tool was developed and applied to the high-pass filtered 2D velocity field in the axial plane of a turbulent jet while varying Re between 140 and 2600. Vortex population, energy, vorticity, and rms (root-meansquare velocity fluctuations) of the high-pass filtered field were measured to elucidate vortex characteristics. The observed population of vortices decreases dramatically at the Kolmogorov scale. The observed increase in vortex population with decreasing vortex size appears to be in accord with the space-filling argument, in that the vortex population in a two-dimensional domain should grow as R −2. The energy density curve obtained from vortex statistics reproduces the −5/3 slope for the inertial subrange, and the highpass filtered field accounts for approximately two-thirds of the total rms.
Bulletin of the American Physical Society, Mar 17, 2016
Navier-Stokes theory significantly underestimates energy-dissipation in time-dependent flows thro... more Navier-Stokes theory significantly underestimates energy-dissipation in time-dependent flows through flow guides such ones with helical geometry. We show the geometrodynamical theory of fluids (GTF) accounts for this anomalous energy-dissipation by predicting the excitation of transverse modes of flow leading to such dissipation. According to the GTF, the transverse modes are composed of vorticity and swirl fields which together constitute a vortex field F which is a function of the swirl and vorticity fields. Analysis shows the energy-dissipation depends on the wave energy, the dot product of the swirl and the vorticity, as well as their cross product. These lead to heating of the fluid at a rate proportional to the work the current does against the swirl field. For the constitutive parameters of the theory we find the values for water to be lamda = 0.01/(cm/s), and kappa = 1 [unitless]. A lower bound for the effective value of the speed of the first transverse modes is found to be 90 cm/sec. We determine that a dimensionless vortex number, Rv, usefully delineates the excitation of the transverse mode flow regime.
Bulletin of the American Physical Society, Nov 24, 2014
Submitted for the DFD14 Meeting of The American Physical Society Optimizing the determination of ... more Submitted for the DFD14 Meeting of The American Physical Society Optimizing the determination of roughness parameters of urban canopies AUVI RAHMAN, PABLO HUQ, University of Delaware-We present an optimization procedure to determine the roughness parameters for an urban canopy. The mean velocity profile above an urban canopy is described by the log law via the roughness parameters: zero-plane displacement height d, roughness length z 0 , and friction velocity u *. Traditionally these parameters are obtained from a single mean velocity profile. We have devised a new procedure which is akin to the bootstrap or jackknife resampling method where multiple mean velocity profiles are generated from a single mean velocity profile. Each of the generated profiles are then best fit to the log law and sets of d, z 0 , and u * are estimated. These sets of values show distinct clusters when plotted against the relative sensitivity of the log law to the zero-plane displacement height d. A single representative or optimal value of the roughness parameters are then obtained automatically by utilizing a standard clustering procedure. Application of this method is also presented for field and laboratory data.
Bulletin of the American Physical Society, Nov 24, 2013
UD-GMU COLLABORATION-We present the results of roughness length and displacement height based on ... more UD-GMU COLLABORATION-We present the results of roughness length and displacement height based on PIV velocity measurements in a water tunnel experiment of flow over idealized models of urban canopies. Experiments were conducted with large roughness elements of regular arrays of buildings of uniform height with aspect ratios of 1 and 3. Mean velocity profile above the canopy is described by the log law and a simple optimization procedure to compute the roughness length and displacement height has been developed. Laterally averaged values of displacement height d/H increase from 0 to 1 with plan area density λ p of the urban canopy. In contrast, laterally averaged roughness height z 0 /H increases to a maximum value (as λ f approaches a value of 0.2) and then decreases to zero. We present data for effective roughness heights (z 0 +d)/H as a function of aspect ratio H/w b of buildings. This also reveals three categories of values: street canyon, building wake, and laterally averaged values. Measurements taken at the centerline of canyons form a lower bound on the effective roughness height whereas measurements behind building wakes form an upper bound. Laterally averaged values of friction velocity u * /U H varied inversely with the aspect ratio (U H is the mean velocity at the building height).
The use of newtonian viscous dissipation theory in covariant fluid flow theories is known to lead... more The use of newtonian viscous dissipation theory in covariant fluid flow theories is known to lead to predictions that are inconsistent with the second law of thermodynamics and to predictions that are acausal. For instance, these problems effectively limit the covariant form of the Navier-Stokes theory (NST) to time-independent flow regimes. Thus the NST, the work horse of fluid dynamical theory, is limited in its ability to model time-dependent turbulent, stellar or thermonuclear flows. We show how such problems are avoided by a new geometrodynamical theory of fluids (GTF, Fluid Dynamics Research, 46, 055513,14 (2014)). This theory is based on a recent result of geometrodynamics showing current conservation implies gauge field creation, called the vortex field lemma (VFL, Phys. Lett., A 374, 3476-82 (2010)) and classification of flows by their Pfaff dimension. Experimental confirmation of the theory is reviewed.
... CE Database Search | Descriptions | Search Tips | Subject Heading List. Turbulence Measuremen... more ... CE Database Search | Descriptions | Search Tips | Subject Heading List. Turbulence Measurements in Low Froude Number Hydraulic Jumps. by James T. Kirby , John Bakunin , and Pablo Huq pp. 1239-1242 Purchase Information Permissions for Reuse ...
Experimental Confirmation of a Causal, Covariant, Relativistic Theory of Dissipative Fluid Flow D... more Experimental Confirmation of a Causal, Covariant, Relativistic Theory of Dissipative Fluid Flow DILLON SCOFIELD, Dept. Physics, Oklahoma State University, PABLO HUQ, College of Earth, Ocean & Environment, University of Delaware -Using newtonian viscous dissipation stress in covariant, relativistic fluid flow theories leads to a violation of the second law of thermodynamics and to acausality of their predictions. E.g., the Landau & Lifshitz theory, a Lorentz covariant formulation, suffers from these defects. These problems effectively limit such theories to time-independent flow régimes. Thus, these theories are of little fundamental interest to astrophysical, geophysical, or thermonuclear flow modeling. We discuss experimental confirmation of the new geometrodynamical theory of fluids solving these problems (GTF, Fluid Dynamics, Research, 46, 055513,055514 (2014), Submitted 2015). This theory is derived from recent results of geometrodynamics showing current conservation implies gauge field creation; the vortex field lemma (Phys. Lett. A 374 3476-82 (2010)).
Abstract: A Gaussian plume urban dispersion model is presented, where the horizontal and vertical... more Abstract: A Gaussian plume urban dispersion model is presented, where the horizontal and vertical diffusion coefficients are determined according to the theories of GI Taylor (1921) and Hunt, JCR and AH Weber (1979) respectively. The model is validated with dispersion ...
We present an objective optimization procedure to determine the roughness parameters for very rou... more We present an objective optimization procedure to determine the roughness parameters for very rough boundary-layer flow over model urban canopies. For neutral stratification the mean velocity profile above a model urban canopy is described by the logarithmic law together with the set of roughness parameters of displacement height d, roughness length z 0 , and friction velocity u *. Traditionally, values of these roughness parameters are obtained by fitting the logarithmic law through (all) the data points comprising the velocity profile. The new procedure generates unique velocity profiles from subsets or combinations of the data points of the original velocity profile, after which all possible profiles are examined. Each of the generated profiles is fitted to the logarithmic law for a sequence of values of d, with the representative value of d obtained from the minima of the summed least-squares errors for all the generated profiles. The representative values of z 0 and u * are identified by the peak in the bivariate histogram of z 0 and u *. The methodology has been verified against laboratory datasets of flow above model urban canopies.
Typically ammonia and chlorine are stored or transported as pressurized liquefied gas. There have... more Typically ammonia and chlorine are stored or transported as pressurized liquefied gas. There have been many accidents involving storage tanks and also accidents during transport. There is a need for accurate evaluation of the hazards associated with accidental releases of ammonia and chlorine which typically result in denser than air clouds which are toxic. The dense gas cloud slumps under the action of gravity into a thin layer with stable density gradients which suppress ambient atmospheric turbulence, and so complicating the physics of mixing. We present similarity analyses of one and two ton experimental releases of ammonia and chlorine at Jack Rabbit. Similarity analysis discriminates inertia-buoyancy and viscous-buoyancy regimes. Sequences of visualizations are used to determine propagation speeds of dense clouds. There is good agreement between observed speeds and the predictions of similarity analysis of the propagation of radial, dense gas clouds. Finally, comparison of one ton with two ton releases for both ammonia and chlorine lead to insights on scaling which are likely to be useful in the design of even larger scale experiments on dense gas clouds arising from similar configurations.
An experimental study of an incompressible circular jet in a crossflow and theoretical analysis b... more An experimental study of an incompressible circular jet in a crossflow and theoretical analysis based on inviscid flow models are described. The jet exits from a rigidly mounted pipe projecting distant from the floor of a tunnel carrying a steady stream of water; density of the jet and the stream are the same. The results of scalar and velocity measurements and visualizations showed that the jet bifurcated into two separated, counterrotating arms for values of ⑀ϭU ϱ /U JET , the ratio of the mean crossflow velocity U ϱ to the mean jet discharge velocity U JET , less than or equal to 0.25. The angle of separation between the two arms of the bifurcated jet was found to vary inversely with ⑀. For higher values of ⑀ the jet does not bifurcate but is dominated by a different mode of instability. The structure of the flow field, which is different for bifurcated and nonbifurcated jets, comprised a variety of vortical structures which survived for very long distances x beyond x/2aϾ400, where a is the radius of the jet exit and x is distance downstream from the jet axis. The location of the point of bifurcation is predicted from consideration of potential flow models and the characteristics of bifurcating elliptical jets. The location of the point of bifurcation is more distant from the jet exit for smaller values of ⑀, and experimental results were in good agreement with the theoretical predictions. The initial jet trajectory is shown to be associated with the presence in the wake of vorticity shed from the pipe. The near-field geometry and centerline trajectory of the jet are also found to be in accord with predictions in that it is observed that zϳx 1/2 and zϳ⑀ Ϫ1. Dilutions of bifurcated jets are found to be greater than for nonbifurcated jets.
An invariant helicity integral and a differential helicity evolution equation are found for visco... more An invariant helicity integral and a differential helicity evolution equation are found for viscous fluid flows. A geometrodynamical approach is used, which includes a vortex field. The vortex field is derivable from a vector potential A. The vector potential is then used to characterize the evolution of flow topology. The source of the helicity is found to be the topological parity k =2 • and the moving boundary surfaces of the fluid. Here, and are the vorticity and swirl components of the vortex field ͕ , ͖ and is a constitutive or material parameter of the fluid. Our first result using the vector calculus identifies the scalar helicity as h t = A. This result is then generalized using the calculus of differential forms, yielding other results including the existence of a helicity current vector proportional to ͑ -A ϫ ͒.
Results are reported of measurements of the turbulent Schmidt number Sc t in a stably stratified ... more Results are reported of measurements of the turbulent Schmidt number Sc t in a stably stratified water tunnel experiment. Sc t values varied with two parameters: Richardson number, Ri, and ratio of time scales, T*, of eddy turnover and eddy advection from the source of turbulence generation. For large values (T* $ 10) values of Sc t approach those of neutral stratification (Sc t % 1). In contrast for small values (T* $ 1) values of Sc t increase with Ri. The variation of Sc t with T* explains the large scatter of Sc t values observed in atmospheric and oceanic data sets as a range of values of T* occur at any given Ri. The dependence of Sc t values on advective processes upstream of the measurement location complicates the development of an algebraic formulation of Sc t = f (Ri, T*) from single point dynamical balances for use in turbulence closure models. Observations of values of T* $ O(1) for strong stratification argues against the existence of a critical Richardson number at which turbulence collapses to laminar flow.
Journal of Applied Meteorology and Climatology, 2007
The nature and role of the shear layer, which occurs at the level of the average building height ... more The nature and role of the shear layer, which occurs at the level of the average building height in urban canopies, are poorly understood. Velocity data are analyzed to determine the characteristics of the shear layer of the urban canopy, defined as the broad, linear segment of the mean velocity profile in a region of high shear. Particle image velocimetry measurements in a water tunnel were undertaken to resolve velocity profiles for urban canopies of two geometries typical of Los Angeles, California, and New York City, New York, for which the aspect ratios (average building height-to-width ratio) H/wb are 1 and 3, respectively. The shear layers evolve with distance differently: For H/wb = 1 the urban canopy shear layer extends quickly from above the building height to ground level, whereas for H/wb = 3 the urban canopy shear layer remains elevated at the vicinity of the building height, only reaching to a depth of z/H ∼ 0.5 far downstream. Profiles of the mean velocity gradient al...
Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale ... more Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale was approached by progressively decreasing the Reynolds number while still maintaining turbulent flow. A periodic forcing introduced far upstream of the jet nozzle ensured that the jet was turbulent. A vortex eduction tool was developed and applied to the high-pass filtered 2D velocity field in the axial plane of a turbulent jet while varying Re between 140 and 2600. Vortex population, energy, vorticity, and rms (root-meansquare velocity fluctuations) of the high-pass filtered field were measured to elucidate vortex characteristics. The observed population of vortices decreases dramatically at the Kolmogorov scale. The observed increase in vortex population with decreasing vortex size appears to be in accord with the space-filling argument, in that the vortex population in a two-dimensional domain should grow as R−2. The energy density curve obtained from vortex statistics reproduces the...
The statement and solution of a new problem are presented for fluid wave motions at the injection... more The statement and solution of a new problem are presented for fluid wave motions at the injection of vertical axisymmetric jet into a stable stratified fluid, which density linearly increases with the depth. Flow in the jet is assumed to be potential, the motion of stratified fluid is described by Boussincsq's approximation. The dispersion equation is derived and analysed. The conditions of wave e:istence arc found and the analysis of phase and group velocities and wave modes is presented. It is shown that in outer medium the wave disturbances propagate along the jet as it was observed in experiments.
A laboratory experiment investigates the influence of salinity on the characteristics of bubble c... more A laboratory experiment investigates the influence of salinity on the characteristics of bubble clouds in varying saline solutions. Bubble clouds were generated with a water jet. Salinity, surface tension, and water temperature were monitored. Measured bubble cloud parameters include the number of bubbles, the void fraction, the penetration depth, and the cloud shape. The number of large (above 0.5 mm diameter) bubbles within a cloud increases by a factor of three from fresh to saline water of 20 psu (practical salinity units), and attains a maximum value for salinity of 12-25 psu. The void fraction also has maximum value in the range 12-25 psu. The results thus show that both the number of bubbles and the void fraction vary nonmonotonically with increasing salinity. The lateral shape of the bubble cloud does not change with increasing salinity; however, the lowest point of the cloud penetrates deeper as smaller bubbles are generated.
Journal of Fluids Engineering-transactions of The Asme, Oct 25, 2005
Characteristics of Small Vortices in a Turbulent Axisymmetric Jet Characteristics of small vortic... more Characteristics of Small Vortices in a Turbulent Axisymmetric Jet Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale was approached by progressively decreasing the Reynolds number while still maintaining turbulent flow. A periodic forcing introduced far upstream of the jet nozzle ensured that the jet was turbulent. A vortex eduction tool was developed and applied to the high-pass filtered 2D velocity field in the axial plane of a turbulent jet while varying Re between 140 and 2600. Vortex population, energy, vorticity, and rms (root-meansquare velocity fluctuations) of the high-pass filtered field were measured to elucidate vortex characteristics. The observed population of vortices decreases dramatically at the Kolmogorov scale. The observed increase in vortex population with decreasing vortex size appears to be in accord with the space-filling argument, in that the vortex population in a two-dimensional domain should grow as R −2. The energy density curve obtained from vortex statistics reproduces the −5/3 slope for the inertial subrange, and the highpass filtered field accounts for approximately two-thirds of the total rms.
Bulletin of the American Physical Society, Mar 17, 2016
Navier-Stokes theory significantly underestimates energy-dissipation in time-dependent flows thro... more Navier-Stokes theory significantly underestimates energy-dissipation in time-dependent flows through flow guides such ones with helical geometry. We show the geometrodynamical theory of fluids (GTF) accounts for this anomalous energy-dissipation by predicting the excitation of transverse modes of flow leading to such dissipation. According to the GTF, the transverse modes are composed of vorticity and swirl fields which together constitute a vortex field F which is a function of the swirl and vorticity fields. Analysis shows the energy-dissipation depends on the wave energy, the dot product of the swirl and the vorticity, as well as their cross product. These lead to heating of the fluid at a rate proportional to the work the current does against the swirl field. For the constitutive parameters of the theory we find the values for water to be lamda = 0.01/(cm/s), and kappa = 1 [unitless]. A lower bound for the effective value of the speed of the first transverse modes is found to be 90 cm/sec. We determine that a dimensionless vortex number, Rv, usefully delineates the excitation of the transverse mode flow regime.
Bulletin of the American Physical Society, Nov 24, 2014
Submitted for the DFD14 Meeting of The American Physical Society Optimizing the determination of ... more Submitted for the DFD14 Meeting of The American Physical Society Optimizing the determination of roughness parameters of urban canopies AUVI RAHMAN, PABLO HUQ, University of Delaware-We present an optimization procedure to determine the roughness parameters for an urban canopy. The mean velocity profile above an urban canopy is described by the log law via the roughness parameters: zero-plane displacement height d, roughness length z 0 , and friction velocity u *. Traditionally these parameters are obtained from a single mean velocity profile. We have devised a new procedure which is akin to the bootstrap or jackknife resampling method where multiple mean velocity profiles are generated from a single mean velocity profile. Each of the generated profiles are then best fit to the log law and sets of d, z 0 , and u * are estimated. These sets of values show distinct clusters when plotted against the relative sensitivity of the log law to the zero-plane displacement height d. A single representative or optimal value of the roughness parameters are then obtained automatically by utilizing a standard clustering procedure. Application of this method is also presented for field and laboratory data.
Bulletin of the American Physical Society, Nov 24, 2013
UD-GMU COLLABORATION-We present the results of roughness length and displacement height based on ... more UD-GMU COLLABORATION-We present the results of roughness length and displacement height based on PIV velocity measurements in a water tunnel experiment of flow over idealized models of urban canopies. Experiments were conducted with large roughness elements of regular arrays of buildings of uniform height with aspect ratios of 1 and 3. Mean velocity profile above the canopy is described by the log law and a simple optimization procedure to compute the roughness length and displacement height has been developed. Laterally averaged values of displacement height d/H increase from 0 to 1 with plan area density λ p of the urban canopy. In contrast, laterally averaged roughness height z 0 /H increases to a maximum value (as λ f approaches a value of 0.2) and then decreases to zero. We present data for effective roughness heights (z 0 +d)/H as a function of aspect ratio H/w b of buildings. This also reveals three categories of values: street canyon, building wake, and laterally averaged values. Measurements taken at the centerline of canyons form a lower bound on the effective roughness height whereas measurements behind building wakes form an upper bound. Laterally averaged values of friction velocity u * /U H varied inversely with the aspect ratio (U H is the mean velocity at the building height).
The use of newtonian viscous dissipation theory in covariant fluid flow theories is known to lead... more The use of newtonian viscous dissipation theory in covariant fluid flow theories is known to lead to predictions that are inconsistent with the second law of thermodynamics and to predictions that are acausal. For instance, these problems effectively limit the covariant form of the Navier-Stokes theory (NST) to time-independent flow regimes. Thus the NST, the work horse of fluid dynamical theory, is limited in its ability to model time-dependent turbulent, stellar or thermonuclear flows. We show how such problems are avoided by a new geometrodynamical theory of fluids (GTF, Fluid Dynamics Research, 46, 055513,14 (2014)). This theory is based on a recent result of geometrodynamics showing current conservation implies gauge field creation, called the vortex field lemma (VFL, Phys. Lett., A 374, 3476-82 (2010)) and classification of flows by their Pfaff dimension. Experimental confirmation of the theory is reviewed.
... CE Database Search | Descriptions | Search Tips | Subject Heading List. Turbulence Measuremen... more ... CE Database Search | Descriptions | Search Tips | Subject Heading List. Turbulence Measurements in Low Froude Number Hydraulic Jumps. by James T. Kirby , John Bakunin , and Pablo Huq pp. 1239-1242 Purchase Information Permissions for Reuse ...
Experimental Confirmation of a Causal, Covariant, Relativistic Theory of Dissipative Fluid Flow D... more Experimental Confirmation of a Causal, Covariant, Relativistic Theory of Dissipative Fluid Flow DILLON SCOFIELD, Dept. Physics, Oklahoma State University, PABLO HUQ, College of Earth, Ocean & Environment, University of Delaware -Using newtonian viscous dissipation stress in covariant, relativistic fluid flow theories leads to a violation of the second law of thermodynamics and to acausality of their predictions. E.g., the Landau & Lifshitz theory, a Lorentz covariant formulation, suffers from these defects. These problems effectively limit such theories to time-independent flow régimes. Thus, these theories are of little fundamental interest to astrophysical, geophysical, or thermonuclear flow modeling. We discuss experimental confirmation of the new geometrodynamical theory of fluids solving these problems (GTF, Fluid Dynamics, Research, 46, 055513,055514 (2014), Submitted 2015). This theory is derived from recent results of geometrodynamics showing current conservation implies gauge field creation; the vortex field lemma (Phys. Lett. A 374 3476-82 (2010)).
Abstract: A Gaussian plume urban dispersion model is presented, where the horizontal and vertical... more Abstract: A Gaussian plume urban dispersion model is presented, where the horizontal and vertical diffusion coefficients are determined according to the theories of GI Taylor (1921) and Hunt, JCR and AH Weber (1979) respectively. The model is validated with dispersion ...
We present an objective optimization procedure to determine the roughness parameters for very rou... more We present an objective optimization procedure to determine the roughness parameters for very rough boundary-layer flow over model urban canopies. For neutral stratification the mean velocity profile above a model urban canopy is described by the logarithmic law together with the set of roughness parameters of displacement height d, roughness length z 0 , and friction velocity u *. Traditionally, values of these roughness parameters are obtained by fitting the logarithmic law through (all) the data points comprising the velocity profile. The new procedure generates unique velocity profiles from subsets or combinations of the data points of the original velocity profile, after which all possible profiles are examined. Each of the generated profiles is fitted to the logarithmic law for a sequence of values of d, with the representative value of d obtained from the minima of the summed least-squares errors for all the generated profiles. The representative values of z 0 and u * are identified by the peak in the bivariate histogram of z 0 and u *. The methodology has been verified against laboratory datasets of flow above model urban canopies.
Typically ammonia and chlorine are stored or transported as pressurized liquefied gas. There have... more Typically ammonia and chlorine are stored or transported as pressurized liquefied gas. There have been many accidents involving storage tanks and also accidents during transport. There is a need for accurate evaluation of the hazards associated with accidental releases of ammonia and chlorine which typically result in denser than air clouds which are toxic. The dense gas cloud slumps under the action of gravity into a thin layer with stable density gradients which suppress ambient atmospheric turbulence, and so complicating the physics of mixing. We present similarity analyses of one and two ton experimental releases of ammonia and chlorine at Jack Rabbit. Similarity analysis discriminates inertia-buoyancy and viscous-buoyancy regimes. Sequences of visualizations are used to determine propagation speeds of dense clouds. There is good agreement between observed speeds and the predictions of similarity analysis of the propagation of radial, dense gas clouds. Finally, comparison of one ton with two ton releases for both ammonia and chlorine lead to insights on scaling which are likely to be useful in the design of even larger scale experiments on dense gas clouds arising from similar configurations.
An experimental study of an incompressible circular jet in a crossflow and theoretical analysis b... more An experimental study of an incompressible circular jet in a crossflow and theoretical analysis based on inviscid flow models are described. The jet exits from a rigidly mounted pipe projecting distant from the floor of a tunnel carrying a steady stream of water; density of the jet and the stream are the same. The results of scalar and velocity measurements and visualizations showed that the jet bifurcated into two separated, counterrotating arms for values of ⑀ϭU ϱ /U JET , the ratio of the mean crossflow velocity U ϱ to the mean jet discharge velocity U JET , less than or equal to 0.25. The angle of separation between the two arms of the bifurcated jet was found to vary inversely with ⑀. For higher values of ⑀ the jet does not bifurcate but is dominated by a different mode of instability. The structure of the flow field, which is different for bifurcated and nonbifurcated jets, comprised a variety of vortical structures which survived for very long distances x beyond x/2aϾ400, where a is the radius of the jet exit and x is distance downstream from the jet axis. The location of the point of bifurcation is predicted from consideration of potential flow models and the characteristics of bifurcating elliptical jets. The location of the point of bifurcation is more distant from the jet exit for smaller values of ⑀, and experimental results were in good agreement with the theoretical predictions. The initial jet trajectory is shown to be associated with the presence in the wake of vorticity shed from the pipe. The near-field geometry and centerline trajectory of the jet are also found to be in accord with predictions in that it is observed that zϳx 1/2 and zϳ⑀ Ϫ1. Dilutions of bifurcated jets are found to be greater than for nonbifurcated jets.
An invariant helicity integral and a differential helicity evolution equation are found for visco... more An invariant helicity integral and a differential helicity evolution equation are found for viscous fluid flows. A geometrodynamical approach is used, which includes a vortex field. The vortex field is derivable from a vector potential A. The vector potential is then used to characterize the evolution of flow topology. The source of the helicity is found to be the topological parity k =2 • and the moving boundary surfaces of the fluid. Here, and are the vorticity and swirl components of the vortex field ͕ , ͖ and is a constitutive or material parameter of the fluid. Our first result using the vector calculus identifies the scalar helicity as h t = A. This result is then generalized using the calculus of differential forms, yielding other results including the existence of a helicity current vector proportional to ͑ -A ϫ ͒.
Results are reported of measurements of the turbulent Schmidt number Sc t in a stably stratified ... more Results are reported of measurements of the turbulent Schmidt number Sc t in a stably stratified water tunnel experiment. Sc t values varied with two parameters: Richardson number, Ri, and ratio of time scales, T*, of eddy turnover and eddy advection from the source of turbulence generation. For large values (T* $ 10) values of Sc t approach those of neutral stratification (Sc t % 1). In contrast for small values (T* $ 1) values of Sc t increase with Ri. The variation of Sc t with T* explains the large scatter of Sc t values observed in atmospheric and oceanic data sets as a range of values of T* occur at any given Ri. The dependence of Sc t values on advective processes upstream of the measurement location complicates the development of an algebraic formulation of Sc t = f (Ri, T*) from single point dynamical balances for use in turbulence closure models. Observations of values of T* $ O(1) for strong stratification argues against the existence of a critical Richardson number at which turbulence collapses to laminar flow.
Journal of Applied Meteorology and Climatology, 2007
The nature and role of the shear layer, which occurs at the level of the average building height ... more The nature and role of the shear layer, which occurs at the level of the average building height in urban canopies, are poorly understood. Velocity data are analyzed to determine the characteristics of the shear layer of the urban canopy, defined as the broad, linear segment of the mean velocity profile in a region of high shear. Particle image velocimetry measurements in a water tunnel were undertaken to resolve velocity profiles for urban canopies of two geometries typical of Los Angeles, California, and New York City, New York, for which the aspect ratios (average building height-to-width ratio) H/wb are 1 and 3, respectively. The shear layers evolve with distance differently: For H/wb = 1 the urban canopy shear layer extends quickly from above the building height to ground level, whereas for H/wb = 3 the urban canopy shear layer remains elevated at the vicinity of the building height, only reaching to a depth of z/H ∼ 0.5 far downstream. Profiles of the mean velocity gradient al...
Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale ... more Characteristics of small vortices were studied in axisymmetric jets wherein the Kolmogorov scale was approached by progressively decreasing the Reynolds number while still maintaining turbulent flow. A periodic forcing introduced far upstream of the jet nozzle ensured that the jet was turbulent. A vortex eduction tool was developed and applied to the high-pass filtered 2D velocity field in the axial plane of a turbulent jet while varying Re between 140 and 2600. Vortex population, energy, vorticity, and rms (root-meansquare velocity fluctuations) of the high-pass filtered field were measured to elucidate vortex characteristics. The observed population of vortices decreases dramatically at the Kolmogorov scale. The observed increase in vortex population with decreasing vortex size appears to be in accord with the space-filling argument, in that the vortex population in a two-dimensional domain should grow as R−2. The energy density curve obtained from vortex statistics reproduces the...
The statement and solution of a new problem are presented for fluid wave motions at the injection... more The statement and solution of a new problem are presented for fluid wave motions at the injection of vertical axisymmetric jet into a stable stratified fluid, which density linearly increases with the depth. Flow in the jet is assumed to be potential, the motion of stratified fluid is described by Boussincsq's approximation. The dispersion equation is derived and analysed. The conditions of wave e:istence arc found and the analysis of phase and group velocities and wave modes is presented. It is shown that in outer medium the wave disturbances propagate along the jet as it was observed in experiments.
A laboratory experiment investigates the influence of salinity on the characteristics of bubble c... more A laboratory experiment investigates the influence of salinity on the characteristics of bubble clouds in varying saline solutions. Bubble clouds were generated with a water jet. Salinity, surface tension, and water temperature were monitored. Measured bubble cloud parameters include the number of bubbles, the void fraction, the penetration depth, and the cloud shape. The number of large (above 0.5 mm diameter) bubbles within a cloud increases by a factor of three from fresh to saline water of 20 psu (practical salinity units), and attains a maximum value for salinity of 12-25 psu. The void fraction also has maximum value in the range 12-25 psu. The results thus show that both the number of bubbles and the void fraction vary nonmonotonically with increasing salinity. The lateral shape of the bubble cloud does not change with increasing salinity; however, the lowest point of the cloud penetrates deeper as smaller bubbles are generated.
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