Direct numerical simulations are performed to investigate a stratified shear layer at high Reynolds number ( $Re$ ) in a study where the Richardson number ( $Ri$ ) is varied among cases. Unlike previous work on a two-layer configuration in which the shear layer resides between two layers with constant density, an unbounded fluid with uniform stratification is considered here. The evolution of the shear layer includes a primary Kelvin–Helmholtz shear instability followed by a wide range of secondary shear and convective instabilities, similar to the two-layer configuration. During transition to turbulence, the shear layers at low $Ri$ exhibit a period of thickness contraction (not observed at lower $Re$ ) when the momentum and buoyancy fluxes are counter-gradient. The behaviour in the turbulent regime is significantly different from the case with a two-layer density profile. The transition layers, which are zones with elevated shear and stratification that form at the shear-layer edges, are stronger and also able to support a significant internal wave flux. After the shear layer becomes turbulent, mixing in the transition layers is shown to be more efficient than that which develops in the centre of the shear layer. Overall, the cumulative mixing efficiency ( $E^C$ ) is larger than the often assumed value of 1/6. Also, $E^C$ is found to be smaller than that in the two-layer configuration at moderate Ri . It is relatively less sensitive to background stratification, exhibiting little variation for $0.08 \leqslant Ri \leqslant 0.2$ . The dependence of mixing efficiency on buoyancy Reynolds number during the turbulence phase is qualitatively similar to homogeneous sheared turbulence.
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A comparative study of turbulent stratified shear layers: effect of density gradient distribution
Abstract Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number ( $$Ri_{b,0}$$ R i b , 0 ); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed $$Ri_{b,0}$$ R i b , 0 is found to be highest in the case with two-layer density profile and lowest in the case with uniform stratification. However, the parameterizations of the flux coefficient based on buoyancy Reynolds number and the ratio of Ozmidov and Ellison scales show similar scaling in all cases.
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- Award ID(s):
- 1851390
- NSF-PAR ID:
- 10356816
- Date Published:
- Journal Name:
- Environmental Fluid Mechanics
- ISSN:
- 1567-7419
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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High Reynolds number wall-bounded turbulent flows subject to buoyancy forces are fraught with complex dynamics originating from the interplay between shear generation of turbulence ( $S$ ) and its production or destruction by density gradients ( $B$ ). For horizontal walls, $S$ augments the energy budget of the streamwise fluctuations, while $B$ influences the energy contained in the vertical fluctuations. Yet, return to isotropy remains a tendency of such flows where pressure–strain interaction redistributes turbulent energy among all three velocity components and thus limits, but cannot fully eliminate, the anisotropy of the velocity fluctuations. A reduced model of this energy redistribution in the inertial (logarithmic) sublayer, with no tuneable constants, is introduced and tested against large eddy and direct numerical simulations under both stable ( $B<0$ ) and unstable ( $B>0$ ) conditions. The model links key transitions in turbulence statistics with flux Richardson number (at $Ri_{f}=-B/S\approx$ $-2$ , $-1$ and $-0.5$ ) to shifts in the direction of energy redistribution. Furthermore, when coupled to a linear Rotta-type closure, an extended version of the model can predict individual variance components, as well as the degree of turbulence anisotropy. The extended model indicates a regime transition under stable conditions when $Ri_{f}$ approaches $Ri_{f,max}\approx +0.21$ . Buoyant destruction $B$ increases with increasing stabilizing density gradients when $Ri_{f}more » « less
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null (Ed.)Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of high-resolution and fast-response cold-wire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate ε and temperature structure function parameter C T 2 from one-dimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating ε and C T 2 valid for Kolmogorov turbulence in steady state, the flux Richardson number R f and the mixing efficiency χ m are then estimated. The statistical analysis confirms the variability of R f and χ m around ~ 0.13 − 0.14 and ~ 0.16 − 0.17 , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, the Ozmidov length scale L O , the buoyancy Reynolds number R e b , and the gradient Richardson number Ri. Finally, a case study is presented showing altitude differences between the peaks of N 2 , C T 2 and ε , suggesting turbulent stirring at the margin of a stable temperature gradient sheet. The possible contribution of this sheet and layer structure on clear air radar backscattering mechanisms is examined.more » « lessmore » « lessAbstract The flux Richardson number
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10652-022-09873-2
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