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Energy balance and mixing between waves and eddies in stably stratified turbulence

Published online by Cambridge University Press:  30 July 2021

H. Lam Open the ORCID record for H. Lam [Opens in a new window] ,
A. Delache  and
F.S. Godeferd Open the ORCID record for F.S. Godeferd [Opens in a new window]
H. Lam*
Affiliation:
Université de Lyon, École Centrale de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, LMFA, UMR5509, 69130 Ecully, France
A. Delache
Affiliation:
Université de Lyon, École Centrale de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, LMFA, UMR5509, 69130 Ecully, France Université Jean Monnet, 42100 Saint-Étienne, France
F.S. Godeferd
Affiliation:
Université de Lyon, École Centrale de Lyon, CNRS, Université Claude Bernard Lyon 1, INSA Lyon, LMFA, UMR5509, 69130 Ecully, France
*
†Email address for correspondence: [email protected]
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Abstract

We explore the strong stratification regime of stably stratified turbulence and the intermediate regime towards the viscosity-affected stratified state. Three-dimensional velocity-density fields from direct numerical simulations are decomposed into internal gravity waves (IGWs) and eddy motion based on Riley's decomposition (Riley et al., AIP Conf. Proc., vol. 76, issue 1, 1981, pp. 79–112) extended to account for the space–time properties of waves, their modification by vertically sheared horizontal flow and the vertical mixing by eddies (Lam et al., Atmosphere, vol. 11, issue 4, 2020, p. 420). We establish the evolution equations for the IGW and eddy parts separately. Up to buoyancy Reynolds number ${Re}_b\sim 1$, we observe a large exchange of energy that pumps energy from the IGW to eddy. For ${Re}_b>1$, the IGW and eddy dynamics seem to be separate and no global exchange is observed. Our decomposition enables computation of the contributions to the mixing coefficient in terms of the IGW and eddy. At the largest ${Re}_b$ considered, the mixing due to eddies is four times that due to waves.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Wave-turbulence interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A31
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Lam Supplementary Movie

b, be, bw in the (x; z) vertical plane at mid y span for 200 successive timesteps 10Δt. Superimposed density lines are in black (density includes the background density gradient)

Download Lam Supplementary Movie(Video)
Video 7.4 MB