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Prandtl number dependence of stratified turbulence

Published online by Cambridge University Press:  21 September 2020

Jesse D. Legaspi Open the ORCID record for Jesse D. Legaspi [Opens in a new window]  and
Michael L. Waite
Jesse D. Legaspi*
Affiliation:
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, OntarioN2L 3G1, Canada
Michael L. Waite
Affiliation:
Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, OntarioN2L 3G1, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Stratified turbulence has a horizontally layered structure with quasi-two-dimensional vortices due to buoyancy forces that suppress vertical motion. The Prandtl number $\textit {Pr}$ quantifies the relative strengths of viscosity and buoyancy diffusivity, which damp small-scale velocity and buoyancy fluctuations at different microscales. Direct numerical simulations (DNS) require high resolution to resolve the smallest flow features for large $\textit {Pr}$. To reduce computational demand, $\textit {Pr}$ is often set to 1. In this paper, we explore how varying $\textit {Pr}$ affects stratified turbulence. DNS of homogeneous forced stratified turbulence with $0.7 \le \textit {Pr} \le 8$ are performed for four stratification strengths and buoyancy Reynolds numbers $\textit {Re}_b$ between 0.5 and 60. Energy spectra, buoyancy flux spectra, spectral energy flux and physical space fields are compared for scale-specific $\textit {Pr}$-sensitivity. For $\textit {Re}_b \gtrsim 10$, $\textit {Pr}$-dependence in the kinetic energy is mainly found at scales around and below the Kolmogorov scale. The potential energy and flux exhibit more prominent $\textit {Pr}$-sensitivity. As $\textit {Re}_b$ decreases, this $\textit {Pr}$-dependence extends upscale. With increasing $\textit {Pr}$, the spectra suggest eventual convergence to a limiting spectrum shape at large, finite $\textit {Pr}$, at least at scales at and above the Ozmidov scale. The $\textit {Pr}$-sensitivity of the spectra in the most strongly stratified $\textit {Re}_b<1$ case differed from the rest, since large horizontal scales are affected by viscosity and diffusion. These findings suggest that $\textit {Pr}=1$ DNS reasonably approximate $\textit {Pr} > 1$ DNS with large $\textit {Re}_b$, as long as the focus is on kinetic energy at scales much larger than the Kolmogorov scale, but otherwise stray from $\textit {Pr} > 1$ spectra around and below the Kolmogorov scale, and even upscale when $\textit {Re}_b \lesssim 1$.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A12
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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