Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability

2017 ◽  
Vol 816 ◽  
pp. 619-660 ◽  
Author(s):  
Bhanesh Akula ◽  
Prasoon Suchandra ◽  
Mark Mikhaeil ◽  
Devesh Ranjan
Keyword(s):  
Richardson Number ◽  
Shear Flows ◽  
Mixing Layer ◽  
Layer Growth ◽  
Density Fluctuations ◽  
Inertial Subrange ◽  
Growth Equation ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Rt Instability

The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number$A_{t}$from 0.035 to 0.159, with varying amounts of shear and$\unicode[STIX]{x0394}U/U$ranging from 0 to 0.48, where$\unicode[STIX]{x0394}U$is the speed difference between the two flow streams being investigated and$U$is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.

An Ocean Refractometer: Resolving Millimeter-Scale Turbulent Density Fluctuations via the Refractive Index

2006 ◽  
Vol 23 (1) ◽  
pp. 121-137 ◽  
Author(s):  
Matthew H. Alford ◽  
David W. Gerdt ◽  
Charles M. Adkins
Keyword(s):  
Refractive Index ◽  
Density Fluctuations ◽  
Inertial Subrange ◽  
Conductivity Measurements ◽  
Velocity Fluctuations ◽  
Fiber Motion ◽  
Turbulent Spectrum ◽  
Ocean Measurements ◽  
Fiberoptic Sensor ◽  
Better Than

Abstract A fiberoptic sensor has been constructed to measure oceanic density fluctuations via their refractive index signature. The resolution (Δz = 1 mm, Δt = 0.2 ms) and precision (Δn < 10−8, Δρ = 3.4 × 10−5 kg m−3) of the device are far better than other methods and are sufficient to resolve the entire turbulent spectrum. Spectra show the salinity Batchelor rolloff at levels undetectable via conductivity measurements. However, the low-wavenumber portion of the spectrum occupied by the turbulent inertial subrange (≈1 m–1 cm scales) is marred by noise resulting from fiber motion in response to turbulent velocity fluctuations. The technique is described, and the first ocean measurements are reported.

Anisotropic pressure correlation spectra in turbulent shear flow

2012 ◽  
Vol 694 ◽  
pp. 50-77 ◽  
Author(s):  
Yoshiyuki Tsuji ◽  
Yukio Kaneda
Keyword(s):  
Mixing Layer ◽  
Inertial Subrange ◽  
Turbulent Shear ◽  
Pressure Probe ◽  
Anisotropic Pressure ◽  
Turbulent Shear Flow ◽  
Velocity Correlation ◽  
Mean Velocity ◽  
Correlation Spectrum ◽  
The Mean

AbstractWe measured the correlation spectrum ${\hat {Q} }_{p} (\mathbi{k})$ of pressure fluctuations in a driving mixing layer with a Taylor-scale Reynolds number ${R}_{\lambda } $ up to ${\simeq }700$ by a newly developed pressure probe with spatial and temporal resolutions that are sufficient to analyse inertial-subrange statistics. The influence of the mean velocity gradient tensor ${S}_{ij} $ in the mixing layer, which is almost constant near its centreline, is studied using an idea similar to that underlying the linear response theory developed in statistical mechanics for systems at or near thermal equilibrium. If we write the spectrum ${\hat {Q} }_{p} (\mathbi{k})$ as ${\hat {Q} }_{p} (\mathbi{k})= { \hat {Q} }_{p}^{(0)} (\mathbi{k})+ \mrm{\Delta} {\hat {Q} }_{p} (\mathbi{k})$, where ${ \hat {Q} }_{p}^{(0)} (\mathbi{k})$ is the isotropic Kolmogorov spectrum in the absence of mean shear, then for small ${S}_{ij} $ the deviation $ \mrm{\Delta} {\hat {Q} }_{p} (\mathbi{k})$ due to the shear is approximately linear and is determined by a few non-dimensional universal constants in addition to ${S}_{ij} $, $k$ and the mean energy dissipation rate. We also measured the pressure–velocity and velocity–velocity correlation spectra. Deviations from isotropy due to shear are shown to be approximately proportional to ${S}_{ij} $ at large ${R}_{\lambda } $.

scholarly journals Stratified Turbulence and Mixing Efficiency in a Salt Wedge Estuary

2016 ◽  
Vol 46 (6) ◽  
pp. 1769-1783 ◽  
Author(s):  
R. C. Holleman ◽  
W. R. Geyer ◽  
D. K. Ralston
Keyword(s):  
Boundary Layer ◽  
Richardson Number ◽  
Mixing Layer ◽  
High Energy ◽  
Inertial Subrange ◽  
Mixing Efficiency ◽  
Stratified Turbulence ◽  
Free Shear Layer ◽  
Lower Efficiency ◽  
Salt Wedge

AbstractHigh-resolution observations of velocity, salinity, and turbulence quantities were collected in a salt wedge estuary to quantify the efficiency of stratified mixing in a high-energy environment. During the ebb tide, a midwater column layer of strong shear and stratification developed, exhibiting near-critical gradient Richardson numbers and turbulent kinetic energy (TKE) dissipation rates greater than 10−4 m2 s−3, based on inertial subrange spectra. Collocated estimates of scalar variance dissipation from microconductivity sensors were used to estimate buoyancy flux and the flux Richardson number Rif. The majority of the samples were outside the boundary layer, based on the ratio of Ozmidov and boundary length scales, and had a mean Rif = 0.23 ± 0.01 (dissipation flux coefficient Γ = 0.30 ± 0.02) and a median gradient Richardson number Rig = 0.25. The boundary-influenced subset of the data had decreased efficiency, with Rif = 0.17 ± 0.02 (Γ = 0.20 ± 0.03) and median Rig = 0.16. The relationship between Rif and Rig was consistent with a turbulent Prandtl number of 1. Acoustic backscatter imagery revealed coherent braids in the mixing layer during the early ebb and a transition to more homogeneous turbulence in the midebb. A temporal trend in efficiency was also visible, with higher efficiency in the early ebb and lower efficiency in the late ebb when the bottom boundary layer had greater influence on the flow. These findings show that mixing efficiency of turbulence in a continuously forced, energetic, free shear layer can be significantly greater than the broadly cited upper bound from Osborn of 0.15–0.17.

The maintenance of Reynolds stress in turbulent shear flow

1967 ◽  
Vol 27 (1) ◽  
pp. 131-144 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Reynolds Stress ◽  
Mixing Layer ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
The Mean

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence\[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where${\cal A}$is a number, Θ the convected integral time scale of thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.

A unified approach for symmetries in plane parallel turbulent shear flows

2001 ◽  
Vol 427 ◽  
pp. 299-328 ◽  
Author(s):  
MARTIN OBERLACK
Keyword(s):  
Shear Flows ◽  
Stokes Equations ◽  
Turbulent Shear ◽  
Large Set ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Law Of The Wall ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
Logarithmic Law

A new theoretical approach for turbulent flows based on Lie-group analysis is presented. It unifies a large set of ‘solutions’ for the mean velocity of stationary parallel turbulent shear flows. These results are not solutions in the classical sense but instead are defined by the maximum number of possible symmetries, only restricted by the flow geometry and other external constraints. The approach is derived from the Reynolds-averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile not previously reported that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near-wall regions in both experimental and DNS data of turbulent channel flows. In the case of the logarithmic law of the wall, the scaling with the distance from the wall arises as a result of the analysis and has not been assumed in the derivation. All solutions are consistent with the similarity of the velocity product equations to arbitrary order. A method to derive the mean velocity profiles directly from the two-point correlation equations is shown.

scholarly journals Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer

1993 ◽  
Vol 251 ◽  
pp. 299-313 ◽  
Author(s):  
S. S. Hsiau ◽  
M. L. Hunt
Keyword(s):  
Diffusion Process ◽  
Granular Flow ◽  
Longitudinal Velocity ◽  
Mixing Layer ◽  
Particle Diameter ◽  
Vertical Channel ◽  
Square Root ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Self Diffusion

In flows of granular material, collisions between individual particles result in the movement of particles in directions transverse to the bulk motion. If the particles were distinguishable, a macroscopic overview of the transverse motions of the particles would resemble a self-diffusion of molecules as occurs in a gas. The present granular- flow study includes measurements of the self-diffusion process, and of the corresponding profiles of the average velocity and of the streamwise component of the fluctuating velocity. The experimental facility consists of a vertical channel fed by an entrance hopper that is divided by a splitter plate. Using differently-coloured but otherwise identical glass spheres to visualize the diffusion process, the flow resembles a classic mixing-layer experiment. Unlike molecular motions, the local particle movements result from shearing of the flow; hence, the diffusion experiments were performed for different shear rates by changing the sidewall conditions of the test section, and by varying the flow rate and the channel width. In addition, experiments were also conducted using different sizes of glass beads to examine the scaling of the diffusion process. A simple analysis based on the diffusion equation shows that the thickness of the mixing layer increases with the square-root of downstream distance and depends on the magnitude of the velocity fluctuations relative to the mean velocity. The results are also consistent with other studies that suggest that the diffusion coefficient is proportional to the particle diameter and the square-root of the granular temperature.

A theory of turbulence in stratified fluids

1970 ◽  
Vol 42 (2) ◽  
pp. 349-365 ◽  
Author(s):  
Robert R. Long
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Density Profile ◽  
Richardson Number ◽  
Mixed Volume ◽  
Volume Of Fluid ◽  
Velocity Shear ◽  
Mean Velocity ◽  
Large Wave ◽  
The Mean

An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with heightzabove a turbulent boundary layer and the mean density decreases asz3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.Thecurvatureof the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

scholarly journals The daytime mixing layer observed by radiosonde, profiler, and lidar during MILAGRO

2007 ◽  
Vol 7 (5) ◽  
pp. 15025-15065 ◽  
Author(s):  
W. J. Shaw ◽  
M. S. Pekour ◽  
R. L. Coulter ◽  
T. J. Martin ◽  
J. T. Walters
Keyword(s):  
Boundary Layer ◽  
Mexico City ◽  
Deep Convection ◽  
National Laboratory ◽  
Mixing Layer ◽  
Argonne National Laboratory ◽  
Pacific Northwest National Laboratory ◽  
Layer Growth ◽  
Hygroscopic Growth ◽  
Layer Depth

Abstract. During the MILAGRO campaign centered in the Mexico City area, Pacific Northwest National Laboratory (PNNL) and Argonne National Laboratory (ANL) operated atmospheric profiling systems at Veracruz and at two locations on the Central Mexican Plateau in the region around Mexico City. These systems included radiosondes, wind profilers, a sodar, and an aerosol backscatter lidar. An additional wind profiler was operated by the University of Alabama in Huntsville (UAH) at the Mexican Petroleum Institue (IMP) near the center of Mexico City. Because of the opportunity afforded by collocation of profilers, radiosondes, and a lidar, and because of the importance of boundary layer depth for aerosol properties, we have carried out a comparison of mixing layer depth as determined independently from these three types of measurement systems during the campaign. We have then used results of this comparison and additional measurements to develop a detailed description of the daily structure and evolution of the boundary layer on the Central Mexican Plateau during MILAGRO. Our analysis indicates that the profilers were more consistently successful in establishing the mixing layer depth during the daytime. The boundary layer growth was similar at the three locations, although the mixing layer tended to be slightly deeper in the afternoon in central Mexico City. The sodar showed that convection began about an hour after sunrise. Maximum daily mixing layer depths always reached 2000 m a.g.l. and frequently extended to 4000 m. The rate and variability of mixing layer growth was essentially the same as that observed during the IMADA-AVER campaign in the same season in 1997. This growth did not seem to be related to whether deep convection was reported on a given day. Wind speeds within the boundary layer exhibited a daily low-altitude maximum in the late afternoon with lighter winds aloft, consistent with previous reports of diurnal regional circulations. Norte events, which produced high winds at Veracruz, did not appreciably modulate the winds on the plateau. Finally, despite the typically dry conditions at the surface, radiosonde profiles showed that relative humidity often exceeded 50% in the early morning and in the upper part of the boundary layer. This suggests that aerosol particles would have experienced hygroscopic growth within the boundary layer on many days.

LES and Hybrid RANS/LES of a Fundamental Trailing Edge Slot

2014 ◽  
Author(s):  
Elizaveta Ivanova ◽  
Gregory M. Laskowski
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Numerical Study ◽  
Mixing Layer ◽  
Detached Eddy Simulation ◽  
Trailing Edge ◽  
Adiabatic Wall ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Delayed Detached Eddy Simulation

This paper presents the results of a numerical study on the predictive capabilities of Large Eddy Simulation (LES) and hybrid RANS/LES methods for heat transfer, mean velocity, and turbulence in a fundamental trailing edge slot. The geometry represents a landless slot (two-dimensional wall jet) with adjustable slot lip thickness. The reference experimental data taken from the publications of Kacker and Whitelaw [1] [2] [3] [4] contains the adiabatic wall effectiveness together with the velocity and the Reynolds-stress profiles for various blowing ratios and slot lip thicknesses. The simulations were conducted at three different lip thickness and several blowing ratio values. The comparison with the experimental data shows a general advantage of LES and hybrid RANS/LES methods against unsteady RANS. The predictive capability of the tested LES models (dynamic ksgs-equation [5] and WALE [6]) was comparable. The Improved Delayed Detached Eddy Simulation (IDDES) hybrid method [7] also shows satisfactory agreement with the experimental data. In addition to the described baseline investigations, the influence of the inlet turbulence boundary conditions and their implication for the initial mixing layer and heat transfer development were studied for both LES and IDDES.

Velocity fluctuations in a low-Reynolds-number fluidized bed

2008 ◽  
Vol 596 ◽  
pp. 467-475 ◽  
Author(s):  
SHANG-YOU TEE ◽  
P. J. MUCHA ◽  
M. P. BRENNER ◽  
D. A. WEITZ
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Fluidized Bed ◽  
Correlation Length ◽  
Volume Fraction ◽  
Low Reynolds Number ◽  
Density Fluctuations ◽  
Velocity Fluctuations ◽  
Similarities And Differences ◽  
Low Reynolds

The velocity fluctuations of particles in a low-Reynolds-number fluidized bed have important similarities and differences with the velocity fluctuations in a low-Reynolds-number sedimenting suspension. We show that, like sedimentation, the velocity fluctuations in a fluidized bed are described well by the balance between density fluctuations due to Poisson statistics and Stokes drag. However, unlike sedimentation, the correlation length of the fluctuations in a fluidized bed increases with volume fraction. We argue that this difference arises because the relaxation time of density fluctuations is completely different in the two systems.

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