Optimal energy growth in stably stratified turbulent Couette flow

2021 ◽  
Author(s):  
Grigory Zasko ◽  
Andrey Glazunov ◽  
Evgeny Mortikov ◽  
Yuri Nechepurenko ◽  
Pavel Perezhogin
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Couette Flow ◽  
Large Scale ◽  
Thin Layers ◽  
Plane Couette Flow ◽  
Turbulent Layer ◽  
Wide Range ◽  
The Mean ◽  
Optimal Disturbances

<p>In this report, we will try to explain the emergence of large-scale organized structures in stably stratified turbulent flows using optimal disturbances of the mean turbulent flow. These structures have been recently obtained in numerical simulations of turbulent stably stratified flows [1] (Ekman layer, LES) and [2] (plane Couette flow, DNS and LES) and indirectly confirmed by field measurements in the stable boundary layer of the atmosphere [1, 2]. In instantaneous temperature fields they manifest themselves as irregular inclined thin layers with large gradients (fronts), spaced from each other by distances comparable to the height of the entire turbulent layer, and separated by regions with weak stratification.</p><p>Optimal disturbances of a stably stratified turbulent plane Couette flow are investigated in a wide range of Reynolds and Richardson numbers. These disturbances were computed based on a simplified linearized system of equations in which turbulent Reynolds stresses and heat fluxes were approximated by isotropic viscosity and diffusion with coefficients obtained from DNS results. It was shown [3] that the spatial scales and configurations of the inclined structures extracted from DNS data coincide with the ones obtained from optimal disturbances of the mean turbulent flow.</p><p>Critical value of the stability parameter is found starting from which the optimal disturbances resemble inclined structures. The physical mechanisms that determine the evolution, energetics and spatial configuration of these optimal disturbances are discussed. The effects due to the presence of stable stratification are highlighted.</p><p>Numerical experiments with optimal disturbances were supported by the RSF (grant No. 17-71-20149). Direct numerical simulation of stratified turbulent Couette flow was supported by the RFBR (grant No. 20-05-00776).</p><p>References:</p><p>[1] P.P. Sullivan, J.C. Weil, E.G. Patton, H.J. Jonker, D.V. Mironov. Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer // J. Atmos. Sci., 2016, V. 73, P. 1815-1840.</p><p>[2] A.V. Glazunov, E.V. Mortikov, K.V. Barskov, E.V. Kadantsev, S.S. Zilitinkevich. Layered structure of stably stratified turbulent shear flows // Izv. Atmos. Ocean. Phys., 2019, V. 55, P. 312–323.</p><p>[3] G.V. Zasko, A.V. Glazunov, E.V. Mortikov, Yu.M. Nechepurenko. Large-scale structures in stratified turbulent Couette flow and optimal disturbances // Russ. J. Num. Anal. Math. Model., 2010, V. 35, P. 35–53.</p>

Relaminarization of spanwise-rotating viscoelastic plane Couette flow via a transition sequence from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow

2021 ◽  
Vol 931 ◽  
Author(s):  
Yabiao Zhu ◽  
Jiaxing Song ◽  
Fenghui Lin ◽  
Nansheng Liu ◽  
Xiyun Lu ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Couette Flow ◽  
Large Scale ◽  
Turbulent Regime ◽  
Flow State ◽  
Plane Couette Flow ◽  
Convective Momentum Transport ◽  
Flow Transitions ◽  
Spanwise Rotation ◽  
First Time

Direct numerical simulation of spanwise-rotation-driven flow transitions in viscoelastic plane Couette flow from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow state followed by full relaminarization is reported for the first time. Specifically, this novel flow transition begins with a drag-reduced inertial turbulent flow state at a low rotation number $0\leqslant Ro \leqslant 0.1$ , and then transitions to a rotation/polymer-additive-driven drag-enhanced inertial turbulent regime, $0.1\leqslant Ro \leqslant 0.3$ . In turn, the flow transitions to a drag-enhanced elasto-inertial turbulent state, $0.3\leqslant Ro \leqslant 0.9$ , and eventually relaminarizes at $Ro=1$ . In addition, two novel rotation-dependent drag enhancement mechanisms are proposed and substantiated. (1) The formation of large-scale roll cells results in enhanced convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow between adjacent roll cells at $Ro\leqslant 0.2$ . (2) Coriolis-force-generated turbulent vortices cause strong incoherent transport and homogenization of significant polymer stress in the bulk via their vortical circulations at $Ro=0.5 - 0.9$ .

An Upper Bound on the Stress in Plane Couette Flow

1973 ◽  
Vol 95 (4) ◽  
pp. 528-532 ◽  
Author(s):  
E. C. Nickerson
Keyword(s):  
Boundary Layer ◽  
Couette Flow ◽  
Upper Bound ◽  
Energy Integral ◽  
Plane Couette Flow ◽  
Mean Velocity ◽  
Boundary Layer Approximation ◽  
The Mean ◽  
Turbulent Plane ◽  
Consistent Constraint

An absolute upper bound on the momentum number in turbulent plane Couette flow is obtained proportional to the two-thirds power of the Reynolds number. The derivation is based upon the energy integral and the specification of an internally consistent constraint on the fluctuating velocity field. A boundary layer approximation for the mean velocity profile is also obtained and the results are found to be consistent with the two-thirds power law.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

scholarly journals Large-scale structures in stratified turbulent Couette flow and optimal disturbances

2019 ◽  
pp. 1-31
Author(s):  
Grigory Vladimirovich Zasko ◽  
Andrey Vasilyevich Glazunov ◽  
Evgeny Valeryevich Mortikov ◽  
Yuri Mikhailovich Nechepurenko
Keyword(s):  
Couette Flow ◽  
Large Scale ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Optimal Disturbances

scholarly journals Study of Mean- and Turbulent-Velocity Fields in a Large-Scale Turbine-Vane Passage

1980 ◽  
Vol 102 (1) ◽  
pp. 88-95 ◽  
Author(s):  
D. A. Bailey
Keyword(s):  
Boundary Layer ◽  
Laser Doppler Velocimetry ◽  
Large Scale ◽  
Guide Vane ◽  
Velocity Fields ◽  
Inlet Guide Vane ◽  
Test Conditions ◽  
Passage Vortex ◽  
Turbine Vane ◽  
The Mean

Laser-Doppler velocimetry was used to investigate the secondary flow in the endwall region of a large-scale turbine inlet-guide-vane passage. The mean and turbulent velocities were measured for three different test conditions. The different test conditions consisted of variations in the blade aspect ratio and the inlet boundary-layer thickness or all three cases, a passage vortex was identified and its development documented. The turbulent stresses within the vortex were found to be quite low in comparison with the turbulence in the inlet boundary layer.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

scholarly journals Transitional Flow Dynamics Behind a Micro-Ramp

2019 ◽  
Vol 104 (2-3) ◽  
pp. 533-552
Author(s):  
J. Casacuberta ◽  
K. J. Groot ◽  
Q. Ye ◽  
S. Hickel
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Large Scale ◽  
Vortex Pair ◽  
Base Flow ◽  
Transitional Flow ◽  
Mean Flow ◽  
Primary Vortex ◽  
The Mean ◽  
Near Wall

AbstractMicro-ramps are popular passive flow control devices which can delay flow separation by re-energising the lower portion of the boundary layer. We compute the laminar base flow, the instantaneous transitional flow, and the mean flow around a micro-ramp immersed in a quasi-incompressible boundary layer at supercritical roughness Reynolds number. Results of our Direct Numerical Simulations (DNS) are compared with results of BiLocal stability analysis on the DNS base flow and independent tomographic Particle Image Velocimetry (tomo-PIV) experiments. We analyse relevant flow structures developing in the micro-ramp wake and assess their role in the micro-ramp functionality, i.e., in increasing the near-wall momentum. The main flow feature of the base flow is a pair of streamwise counter-rotating vortices induced by the micro-ramp, the so-called primary vortex pair. In the instantaneous transitional flow, the primary vortex pair breaks up into large-scale hairpin vortices, which arise due to linear varicose instability of the base flow, and unsteady secondary vortices develop. Instantaneous vortical structures obtained by DNS and experiments are in good agreement. Matching linear disturbance growth rates from DNS and linear stability analysis are obtained until eight micro-ramp heights downstream of the micro-ramp. For the setup considered in this article, we show that the working principle of the micro-ramp is different from that of classical vortex generators; we find that transitional perturbations are more efficient in increasing the near-wall momentum in the mean flow than the laminar primary vortices in the base flow.

Wavelet Analysis on Eddy Structure in Micro Bubble Two Phase Flow Using PIV

2004 ◽  
Author(s):  
Ling Zhen ◽  
Claudia del Carmen Gutierrez-Torres
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Large Scale ◽  
Operating Conditions ◽  
Small Scale ◽  
Turbulent Structures ◽  
Two Phase ◽  
Multi Scale ◽  
Eddy Structures

The question of “where and how the turbulent drag arises” is one of the most fundamental problems unsolved in fluid mechanics. However, the physical mechanism responsible for the friction drag reduction is still not well understood. Over decades, it is found that the turbulence production and self-containment in a boundary layer are organized phenomena and not random processes as the turbulence looks like. The further study in the boundary layer should be able to help us know more about the mechanisms of drag reduction. The wavelet-based vector multi-resolution technique was proposed and applied to the two dimensional PIV velocities for identifying the multi-scale turbulent structures. The intermediate and small scale vortices embedded within the large-scale vortices were separated and visualized. By analyzing the fluctuating velocities at different scales, coherent eddy structures were obtained and this help us obtain the important information on the multi-scale flow structures in the turbulent flow. By comparing the eddy structures in different operating conditions, the mechanism to explain the drag reduction caused by micro bubbles in turbulent flow was proposed.

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