scholarly journals Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow

2014 ◽  
Vol 44 (10) ◽  
pp. 2661-2680 ◽  
Author(s):  
P. Ryan Jackson ◽  
Chris R. Rehmann
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Kinematic Viscosity ◽  
Laboratory Experiments ◽  
Density Ratio ◽  
Eddy Diffusivity ◽  
Buoyancy Frequency ◽  
Differential Diffusion ◽  
Rate Of Dissipation ◽  
Diffusivity Ratio

Abstract Laboratory experiments were performed to measure differential diffusion of temperature and salinity across a sheared density interface. The eddy diffusivity of temperature KT exceeded the eddy diffusivity of salinity KS by as much as 1.5 orders of magnitude at low ε/νN2, where ε is the rate of dissipation of turbulent kinetic energy, ν is the kinematic viscosity, and N is the buoyancy frequency in the pycnocline. The diffusivity ratio d = KS/KT increased from about 0.05 to 1 over the range 0.1 < ε/νN2 < 40. These differences made the eddy diffusivity of density depend on the density ratio. The trend of d with ε/νN2 was consistent with trends found in other experiments, simulations, and theory, and the collapse of several datasets allowed the diffusivity ratio to be expressed as a function of ε/νN2. However, shear decreased differential diffusion less in the experiments than predicted by theory for homogeneous turbulence subjected to constant shear and stratification. No strong effect of the density ratio on the diffusivity ratio was apparent. Because many flows in oceanography and limnology have values of ε/νN2 low enough to exhibit significant differential diffusion, accounting for differential diffusion in interpreting measurements and modeling stratified water bodies is recommended.

scholarly journals Layering in a Flow with Diffusively Stable Temperature and Salinity Stratification

2006 ◽  
Vol 36 (7) ◽  
pp. 1457-1470 ◽  
Author(s):  
Juan Ezequiel Martin ◽  
Chris R. Rehmann
Keyword(s):  
Laboratory Experiments ◽  
Density Ratio ◽  
Mixing Efficiency ◽  
Differential Diffusion ◽  
Salinity Stratification ◽  
Eddy Diffusivities ◽  
Stable Temperature ◽  
Work Input ◽  
The Difference ◽  
Rate Of Dissipation

Abstract Laboratory experiments were conducted to study the formation of layers and interfaces in a fluid stratified with two scalars. Fluid with initially linear, diffusively stable temperature and salinity profiles was stirred using an arrangement of horizontally oscillating, vertical rods. Layers occurred when the density ratio, or the ratio of the contributions of temperature and salinity to the density gradient, was small, but they did not form in similar conditions of turbulence intensity and stratification strength when the density ratio was large. The difference in behavior is ascribed to differential diffusion, or the preferential transport of temperature, which occurred in all of the experiments. Eddy diffusivities were linearly proportional to ɛa/νN 2, where ɛa is an averaged rate of dissipation of turbulent kinetic energy. The mixing efficiency, computed as the ratio of potential energy change to work input to the system, increased with the density ratio. As previous researchers have found, the Phillips–Posmentier mechanism describes the final layered state but not the initial, evolving states of the system.

On the inference of the state of turbulence and mixing efficiency in stably stratified flows

2019 ◽  
Vol 867 ◽  
pp. 323-333 ◽  
Author(s):  
Amrapalli Garanaik ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stratified Flows ◽  
Dynamic State ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Length Scale ◽  
Stratified Turbulence ◽  
Wide Range ◽  
Rate Of Dissipation

Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient $\unicode[STIX]{x1D6E4}=\unicode[STIX]{x1D716}_{PE}/\unicode[STIX]{x1D716}$ in stratified flows as a function of the turbulent Froude number $Fr=\unicode[STIX]{x1D716}/Nk$. Here, $N$ is the buoyancy frequency, $k$ is the turbulent kinetic energy, $\unicode[STIX]{x1D716}$ is the rate of dissipation of turbulent kinetic energy and $\unicode[STIX]{x1D716}_{PE}$ is the rate of dissipation of turbulent potential energy. We show that for $Fr\gg 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{-2}$, for $Fr\sim \mathit{O}(1)$, $\unicode[STIX]{x1D6E4}\propto Fr^{-1}$ and for $Fr\ll 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{0}$. These scaling results are tested using high-resolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of $Fr$ that encompasses weakly stratified to strongly stratified flow conditions. Given that the $Fr$ cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the $Fr$ from readily measurable quantities in the field. Scaling analyses show that $Fr\propto (L_{T}/L_{O})^{-2}$ for $L_{T}/L_{O}>O(1)$, $Fr\propto (L_{T}/L_{O})^{-1}$ for $L_{T}/L_{O}\sim O(1)$, and $Fr\propto (L_{T}/L_{O})^{-2/3}$ for $L_{T}/L_{O}<O(1)$, where $L_{T}$ is the Thorpe length scale and $L_{O}$ is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows.

scholarly journals Turbulence and hypoxia contribute to dense biological scattering layers in a Patagonian fjord system

Ocean Science ◽  
2018 ◽  
Vol 14 (5) ◽  
pp. 1185-1206 ◽  
Author(s):  
Iván Pérez-Santos ◽  
Leonardo Castro ◽  
Lauren Ross ◽  
Edwin Niklitschek ◽  
Nicolás Mayorga ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Water Column ◽  
Turbulent Kinetic Energy ◽  
Tidal Flow ◽  
Vertical Mixing ◽  
Acoustic Doppler Current Profiler ◽  
Marine Species ◽  
Eddy Diffusivity ◽  
Diel Vertical Migrations

Abstract. The aggregation of plankton species along fjords can be linked to physical properties and processes such as stratification, turbulence and oxygen concentration. The goal of this study is to determine how water column properties and turbulent mixing affect the horizontal and vertical distributions of macrozooplankton along the only northern Patagonian fjord known to date, where hypoxic conditions occur in the water column. Acoustic Doppler current profiler moorings, scientific echo-sounder transects and in situ plankton abundance measurements were used to study macrozooplankton assemblages and migration patterns along Puyuhuapi Fjord and Jacaf Channel in Chilean Patagonia. The dissipation of turbulent kinetic energy was quantified through vertical microstructure profiles collected throughout time in areas with high macrozooplankton concentrations. The acoustic records and in situ macrozooplankton data revealed diel vertical migrations (DVM) of siphonophores, chaetognaths and euphausiids. In particular, a dense biological backscattering layer was observed along Puyuhuapi Fjord between the surface and the top of the hypoxic boundary layer (∼100 m), which limited the vertical distribution of most macrozooplankton and their DVM, generating a significant reduction of habitat. Aggregations of macrozooplankton and fishes were most abundant around a submarine sill in Jacaf Channel. In this location macrozooplankton were distributed throughout the water column (0 to ∼200 m), with no evidence of a hypoxic boundary due to the intense mixing near the sill. In particular, turbulence measurements taken near the sill indicated high dissipation rates of turbulent kinetic energy (ε∼10-5 W kg−1) and vertical diapycnal eddy diffusivity (Kρ∼10-3 m2 s−1). The elevated vertical mixing ensures that the water column is well oxygenated (3–6 mL L−1, 60 %–80 % saturation), creating a suitable environment for macrozooplankton and fish aggregations. Turbulence induced by tidal flow over the sill apparently enhances the interchange of nutrients and oxygen concentrations with the surface layer, creating a productive environment for many marine species, where the prey–predator relationship might be favored.

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

2019 ◽  
Vol 866 ◽  
pp. 897-928 ◽  
Author(s):  
P. Orlandi
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Production ◽  
Compressive Strain ◽  
Turnover Time ◽  
Flow Structures ◽  
Wall Region ◽  
Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

Heat Transfer Predictions With Extended k–ε Turbulence Model in Radial Cooling Ducts Rotating in Orthogonal Mode

1994 ◽  
Vol 116 (2) ◽  
pp. 369-380 ◽  
Author(s):  
P. Tekriwal
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Rotation Number ◽  
Density Ratio ◽  
Rotating Systems ◽  
Model Predictions ◽  
Number Flow

Standard and extended k–ε turbulence closure models have been employed for three-dimensional heat transfer calculations for radially outward flow in rectangular and square cooling passages rotating in orthogonal mode. The objective of this modeling effort is to validate the numerical model in an attempt to fill the gap between model predictions and the experimental data for heat transfer in rotating systems. While the trend of heat transfer predictions by the standard k–ε turbulence model is satisfactory, the differences between the data and the predictions are approximately 30 percent or so in the case of high rotation number flow. The extended k–ε turbulence model takes an approach where an extra “source” term based on a second time scale of the turbulent kinetic energy production rate is added to the equation for the dissipation rate of turbulent kinetic energy. This yields a more effective calculation of turbulent kinetic energy as compared to the standard k–ε turbulence model in the case of high rotation number and high density ratio flow. As a result, comparison with the experimental data available in the literature shows that an improvement of up to a significant 15 percent (with respect to data) in the heat transfer coefficient predictions is achieved over the standard k–ε model in the case of high rotation number flow. Comparisons between the results of the standard k–ε model and the extended formulation are made at different rotation numbers, different Reynolds numbers, and varying temperature ratio. The results of the extended k–ε turbulence model are either as good or better than those of the standard k–ε model in all these cases of parametric study. Thus, the extended k–ε turbulence model proves to be more general and reduces the discrepancy between the model predictions and the experimental data for heat transfer in rotating systems.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

scholarly journals Experimental Analysis of Horizontal Turbulence of Flow over Flat and Deformed Beds

2015 ◽  
Vol 62 (3-4) ◽  
pp. 77-99 ◽  
Author(s):  
Donatella Termini
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Experimental Analysis ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Reynolds Shear Stress ◽  
Turbulent Structures ◽  
Quadrant Method ◽  
Initial Sequence

AbstractLaboratory experiments in a straight flume were carried out to examine the evolution of large-scale horizontal turbulent structures under flat-bed and deformed-bed conditions. In this paper, the horizontal turbulence of flow under these conditions is analyzed and compared. The conditioned quadrant method is applied to verify the occurrence of turbulent events. The distributions of horizontal Reynolds shear stress and turbulent kinetic energy are also presented and discussed. Results show the occurrence of an “initial” sequence of horizontal vortices whose average spatial length scales with the channel width. Under deformed-bed conditions, this spatial length does not change.

scholarly journals An Eddy Diffusivity–Mass Flux Approach to the Vertical Transport of Turbulent Kinetic Energy in Convective Boundary Layers

2011 ◽  
Vol 68 (10) ◽  
pp. 2385-2394 ◽  
Author(s):  
Marcin L. Witek ◽  
Joao Teixeira ◽  
Georgios Matheou
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Mass Flux ◽  
Eddy Diffusivity ◽  
Vertical Transport ◽  
Convective Boundary ◽  
Global Circulation Models ◽  
Convective Boundary Layers

Abstract In this study a new approach to the vertical transport of the turbulent kinetic energy (TKE) is proposed. The principal idea behind the new parameterization is that organized updrafts or convective plumes play an important role in transferring TKE vertically within convectively driven boundary layers. The parameterization is derived by applying an updraft environment decomposition to the vertical velocity triple correlation term in the TKE prognostic equation. The additional mass flux (MF) term that results from this decomposition closely resembles the features of the TKE transport diagnosed from the large-eddy simulation (LES) and accounts for 97% of the LES-diagnosed transport when the updraft fraction is set to 0.13. Another advantage of the MF term is that it is a function of the updraft vertical velocity and can be readily calculated using already existing parameterization. The new MF approach, combined with several eddy diffusivity (ED) formulations, is implemented into a simplified 1D TKE prognostic model. The 1D model results, compared against LES simulations of dry convective boundary layers, show substantial improvement in representing the vertical structure of TKE. The new combined ED–MF parameterization, as well as the MF term alone, surpasses in accuracy the ED parameterizations. The proposed TKE transport parameterization shows large potential of improving TKE simulations in mesoscale and global circulation models.

Eulerian and Lagrangian time microscales in isotropic turbulence

1975 ◽  
Vol 67 (3) ◽  
pp. 561-567 ◽  
Author(s):  
H. Tennekes
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Frequency Spectrum ◽  
Kinematic Viscosity ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Observation Point ◽  
Inertial Subrange ◽  
Mean Flow ◽  
Rate Of Dissipation

In isotropic ‘box’ turbulence without a mean flow, the Lagrangian frequency spectrum extends to frequencies of order $(\epsilon/\nu)^{\frac{1}{2}}$ (ε is the rate of dissipation of kinetic energy per unit mass and ν is the kinematic viscosity of the fluid). This leads to an estimate that makes the r.m.s. value of du/dt of order $(\epsilon^3/\nu)^{\frac{1}{4}}$. The Eulerian frequency spectrum, however, extends to higher frequencies than its Lagrangian counterpart; this is caused by spectral broadening associated with large-scale advection of dissipative eddies. As a consequence, the r.m.s. value of ∂u/∂t at a fixed observation point is (apart from a numerical factor) $R_{\lambda}^{\frac{1}{2}}$ times as large as the r.m.s. value of du/dt (RΛ is the turbulence Reynolds number based on the Taylor microscale). The results of a theoretical analysis based on these premises agree with data obtained by Comte-Bellot, Shlien and Corrsin. The analysis also suggests that the Eulerian frequency spectrum has a $\omega^{-\frac{5}{3}} $ behaviour in the inertial subrange, and that it is not governed by Kolmogorov similarity.

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