Asymptotic Dynamics of High Dynamic Range Stratified Turbulence.

Direct numerical simulations of homogeneous sheared and stably stratified turbulence are considered to probe the asymptotic high dynamic range regime suggested by Gargett et al. J. Fluid Mech. 144, 231 (1984)10.1017/S0022112084001592 and Shih et al. J. Fluid Mech. 525, 193 (1999)10.1017/S0022112004002587. We consider statistically stationary configurations of the flow that span three decades in dynamic range defined by the separation between the Ozmidov length scale L_{O}=sqrt[ε/N^{3}] and the Kolmogorov length scale L_{K}=(ν^{3}/ε)^{1/4}, up to Re_{b}≡(L_{O}/L_{K})^{4/3}=ε/(νN^{2})∼O(1000), where ε is the mean turbulent kinetic energy dissipation rate, ν is the kinematic viscosity, and N is the buoyancy frequency. We isolate the effects of Re_{b}, particularly on irreversible mixing, from the effects of other flow parameters of stratified and sheared turbulence. Specifically, we evaluate the influence of dynamic range independent of initial conditions. We present evidence that the flow approaches an asymptotic state for Re_{b}⪆300, characterized both by an asymptotic partitioning between the potential and kinetic energies and by the approach of components of the dissipation rate to their expected values under the assumption of isotropy. As Re_{b} increases above 100, there is a slight decrease in the turbulent flux coefficient Γ=χ/ε, where χ is the dissipation rate of buoyancy variance, but, for this flow, there is no evidence of the commonly suggested Γ∝Re_{b}^{-1/2} dependence when 100≤Re_{b}≤1000.This work was funded by the U.S. Office of Naval Research via grant N00014-15-1-2248. High performance computing resources were provided through the U.S. Department of Defense High Performance Computing Modernization Program by the Army Engineer Research and Development Center, the Army Research Laboratory and the Navy DSRC under Frontier Project FP-CFD-FY14- 007. The research activity of C.P.C. is supported by EPSRC Programme Grant EP/K034529/1 entitled `Mathematical Underpinnings of Stratified Turbulence'

Testing the assumptions underlying ocean mixing methodologies using direct numerical simulations

AbstractDirect numerical simulations of stratified turbulence are used to test several fundamental assumptions involved in the Osborn, Osborn–Cox, and Thorpe methods commonly used to estimate the turbulent diffusivity from field measurements. The forced simulations in an idealized triply periodic computational domain exhibit characteristic features of stratified turbulence including intermittency and layer formation. When calculated using the volume-averaged dissipation rates from the simulations, the vertical diffusivities inferred from the Osborn and Osborn–Cox methods are within 40% of the value diagnosed using the volume-averaged buoyancy flux for all cases, while the Thorpe-scale method performs similarly well in the simulation with a relatively large buoyancy Reynolds number (Reb ≃ 240) but significantly overestimates the vertical diffusivity in simulations with Reb &lt; 60. The methods are also tested using a limited number of vertical profiles randomly selected from the computational volume. The Osborn, Osborn–Cox, and Thorpe-scale methods converge to their respective estimates based on volume-averaged statistics faster than the vertical diffusivity calculated directly from the buoyancy flux, which is contaminated with reversible contributions from internal waves. When applied to a small number of vertical profiles, several assumptions underlying the Osborn and Osborn–Cox methods are not well supported by the simulation data. However, the vertical diffusivity inferred from these methods compares reasonably well to the exact value from the simulations and outperforms the assumptions underlying these methods in terms of the relative error. Motivated by a recent theoretical development, it is speculated that the Osborn method might provide a reasonable approximation to the diffusivity associated with the irreversible buoyancy flux.</jats:p

Robust identification of dynamically distinct regions in stratified turbulence

We present a new robust method for identifying three dynamically distinct regions in a stratified turbulent flow, which we characterise as quiescent flow, intermittent layers and turbulent patches. The method uses the cumulative filtered distribution function of the local density gradient to identify each region. We apply it to data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to $8192\times 8192\times 4096$ grid points. In addition to classifying regions consistently with contour plots of potential enstrophy, our method identifies quiescent regions as regions where \unicode[STIX]{x1D716}/\unicode[STIX]{x1D708}N^{2}\sim O(1), layers as regions where \unicode[STIX]{x1D716}/\unicode[STIX]{x1D708}N^{2}\sim O(10) and patches as regions where \unicode[STIX]{x1D716}/\unicode[STIX]{x1D708}N^{2}\sim O(100). Here, \unicode[STIX]{x1D716} is the dissipation rate of turbulence kinetic energy, \unicode[STIX]{x1D708} is the kinematic viscosity and $N$ is the (overall) buoyancy frequency. By far the highest local dissipation and mixing rates, and the majority of dissipation and mixing, occur in patch regions, even when patch regions occupy only 5 % of the flow volume. We conjecture that treating stratified turbulence as an instantaneous assemblage of these different regions in varying proportions may explain some of the apparently highly scattered flow dynamics and statistics previously reported in the literature.The research activities of G.D.P. and S.dB.K. were funded by the US Office of Naval Research via grant N00014-15-1-2248. Additional support to G.D.P. and S.dB.K. was provided from the UK Engineering and Physical Sciences Research Council grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’, which also funds the research activity of J.R.T. and C.P.C. H.S. gratefully acknowledges the award of a Crighton Fellowship at the Department of Applied Mathematics & Theoretical Physics, University of Cambridge. High-performance computing resources were provided through the US Department of Defense High Performance Computing Modernization Program by the Army Engineer Research and Development Center and the Army Research Laboratory under Frontier Project FP-CFD-FY14-007.This is the author accepted manuscript. The final version is available from Cambridge University Press via https://doi.org/10.1017/jfm.2016.61

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically-stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyze spatial correlations between the vertical density gradient $\partial\rho/\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$, the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\Gamma\equiv\chi/\epsilon=0.2$, often assumed in ocean mixing parameterizations, extreme values of $\chi$ within the statically-stable interfaces, associated with elevated $\Gamma$, strongly skew the bulk statistics. Our findings suggest that current parameterizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.Comment: 17 pages, 7 figures. Version accepted for publication in the Journal of Fluid Mechanics. DOI link to final typeset version provide