A data-driven method for modelling dissipation rates in stratified turbulence

Journal Article · 18 December 2023 · Journal of Fluid Mechanics

DOI: https://doi.org/10.1017/jfm.2023.679 · OSTI ID:2246688

Lewin, Samuel F. ; de Bruyn Kops, Stephen M. ; Caulfield, Colm-cille P. ; Portwood, Gavin D.

We present a deep probabilistic convolutional neural network (PCNN) model for predicting local values of small-scale mixing properties in stratified turbulent flows, namely the dissipation rates of turbulent kinetic energy and density variance, $$\varepsilon$$ and $$\chi$$ . Inputs to the PCNN are vertical columns of velocity and density gradients, motivated by data typically available from microstructure profilers in the ocean. The architecture is designed to enable the model to capture several characteristic features of stratified turbulence, in particular the dependence of small-scale isotropy on the buoyancy Reynolds number $$Re_b:=\varepsilon /(\nu N^2)$$ , where $$\nu$$ is the kinematic viscosity and $$N$$ is the background buoyancy frequency, the correlation between suitably locally averaged density gradients and turbulence intensity and the importance of capturing the tails of the probability distribution functions of values of dissipation. Empirically modified versions of commonly used isotropic models for $$\varepsilon$$ and $$\chi$$ that depend only on vertical derivatives of density and velocity are proposed based on the asymptotic regimes $$Re_b\ll 1$$ and $$Re_b\gg 1$$ , and serve as an instructive benchmark for comparison with the data-driven approach. When trained and tested on a simulation of stratified decaying turbulence which accesses a range of turbulent regimes (associated with differing values of $$Re_b$$ ), the PCNN outperforms assumptions of isotropy significantly as $$Re_b$ decreases, and additionally demonstrates improvements over the fitted empirical models. A differential sensitivity analysis of the PCNN facilitates a comparison with the theoretical models and provides a physical interpretation of the features enabling it to make improved predictions.

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344; AC05-00OR22725
• OSTI ID: 2246688
• Alternate ID(s): OSTI ID: 2301831
• Journal Information: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 977; ISSN 0022-1120
• Publisher: Cambridge University Press (CUP)Copyright Statement
• Country of Publication: United Kingdom
• Language: English