Robust identification of dynamically distinct regions in stratified turbulence


Type
Article
Change log
Authors
De Bruyn Kops, SM 
Taylor, JR 
Salehipour, H 
Caulfield, CP 
Abstract

jats:pWe 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 jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline1" />jats:tex-math8192×8192×4096</jats:tex-math></jats:alternatives></jats:inline-formula> grid points. In addition to classifying regions consistently with contour plots of potential enstrophy, our method identifies quiescent regions as regions where jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline2" />jats:tex-math𝜖𝜈𝜖/𝜈N2O(1)</jats:tex-math></jats:alternatives></jats:inline-formula>, layers as regions where jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline3" />jats:tex-math𝜖𝜈𝜖/𝜈N2O(10)</jats:tex-math></jats:alternatives></jats:inline-formula> and patches as regions where jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline4" />jats:tex-math𝜖𝜈𝜖/𝜈N2O(100)</jats:tex-math></jats:alternatives></jats:inline-formula>. Here, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline5" />jats:tex-math𝜖𝜖</jats:tex-math></jats:alternatives></jats:inline-formula> is the dissipation rate of turbulence kinetic energy, jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline6" />jats:tex-math𝜈𝜈</jats:tex-math></jats:alternatives></jats:inline-formula> is the kinematic viscosity and jats:inline-formulajats:alternatives<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112016006170_inline7" />jats:tex-mathN</jats:tex-math></jats:alternatives></jats:inline-formula> 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.</jats:p>

Description
Keywords
stratified turbulence, turbulent flows
Journal Title
Journal of Fluid Mechanics
Conference Name
Journal ISSN
0022-1120
1469-7645
Volume Title
807
Publisher
Cambridge University Press (CUP)
Sponsorship
Engineering and Physical Sciences Research Council (EP/K034529/1)
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.
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