 Award ID(s):
 1851390
 NSFPAR ID:
 10356816
 Date Published:
 Journal Name:
 Environmental Fluid Mechanics
 ISSN:
 15677419
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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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 twolayer 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 twolayer 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 countergradient. The behaviour in the turbulent regime is significantly different from the case with a twolayer density profile. The transition layers, which are zones with elevated shear and stratification that form at the shearlayer 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 twolayer 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.more » « less

High Reynolds number wallbounded 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 Rottatype 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}
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Abstract Flow over a surface can be stratified by imposing a fixed mean vertical temperature (density) gradient profile throughout or via cooling at the surface. These distinct mechanisms can act simultaneously to establish a stable stratification in a flow. Here, we perform a series of direct numerical simulations of openchannel flows to study adaptation of a neutrally stratified turbulent flow under the combined or independent action of the aforementioned mechanisms. We force the fully developed flow with a constant mass flow rate. This flow forcing technique enables us to keep the bulk Reynolds number constant throughout our investigation and avoid complications arising from the acceleration of the bulk flow if a constant pressure gradient approach were to be adopted to force the flow instead. When both stratification mechanisms are active, the dimensionless stratification perturbation number emerges as an external flow control parameter, in addition to the Reynolds, Froude, and Prandtl numbers. We demonstrate that significant deviations from the Monin–Obukhov similarity formulation are possible when both types of stratification mechanisms are active within an otherwise weakly stable flow, even when the flux Richardson number is well below 0.2. An extended version of the similarity theory due to Zilitinkevich and Calanca shows promise in predicting the dimensionless shear for cases where both types of stratification mechanisms are active, but the extended theory is less accurate for gradients of scalar. The degree of deviation from neutral dimensionless shear as a function of the vertical coordinate emerges as a qualitative measure of the strength of stable stratification for all the cases investigated in this study.

null (Ed.)Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of highresolution and fastresponse coldwire 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 onedimensional 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 » « less

Abstract The flux Richardson number
R _{f}, also called the mixing efficiency of stratified turbulence, is important in determining geophysical flow phenomena such as ocean circulation and air‐sea transports. MeasuringR _{f}in the field is usually difficult, thus parameterization ofR _{f}based on readily observed properties is essential. Here, estimates ofR _{f}in a strongly turbulent, sediment‐stratified estuarine flow are obtained from measurements of covariance‐derived turbulent buoyancy fluxes (B ) and spectrally fitted values of the dissipation rate of turbulent kinetic energy (ε ). We test scalings forR _{f}in terms of the buoyancy Reynolds number (Re _{b}), the gradient Richardson number (Ri ), and turbulent Froude number (Fr _{t}). Neither theRe _{b}‐based nor theRi ‐based scheme is able to describe the observed variations inR _{f}, but theFr _{t}‐based parameterization works well. These findings support further use of theFr _{t}‐ based parameterization in turbulent oceanic and estuarine environments.