A model for the viscous dissipation rate in stably stratified, sheared turbulence

Fossum, Hannibal E.; Wingstedt, Emma M. M.; Reif, Bjørn Anders Pettersson

doi:10.1002/grl.50663

Cited by 2 publications

(3 citation statements)

References 18 publications

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“…Fossum et al. (2013) instead suggest a model for in terms of , pointing out that itself may be replaced by vertical density derivatives via a suitable tuning coefficient. To our knowledge, the empirical models (2.12) and (2.13) constitute a first attempt to construct an explicit theoretical model for dissipation rates during the transition of such a flow from a near-isotropic to a buoyancy-dominated regime based on vertical derivatives of velocity and density only.…”

Section: Methodsmentioning

confidence: 99%

“…The majority of models for and are based on the fundamental assumption that turbulence is homogeneous and isotropic at small scales, although there have been efforts to model dissipation in stratified turbulence by use of a suitable proxy that captures the modifying influence of the stratification (Weinstock 1981; Fossum, Wingstedt & Reif 2013). We appeal to modern data-driven tools to supplement and extend existing theoretical models for and in the anisotropic stratified turbulent regime.…”

Section: Introductionmentioning

confidence: 99%

“…Weinstock (1981) proposes a modified model for ε in stratified turbulence that depends on r.m.s. vertical velocities w 2 and the buoyancy frequency N. Fossum et al (2013) instead suggest a model for ε in terms of χ , pointing out that χ itself may be replaced by vertical density derivatives via a suitable tuning coefficient. To our knowledge, the empirical models (2.12) and (2.13) constitute a first attempt to construct an explicit theoretical model for dissipation rates during the transition b, c and d also appear to be roughly consistent across studies, although a more detailed investigation would be required to quantitatively verify this.…”

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confidence: 99%

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

Lewin,

de Bruyn Kops,

Caulfield

et al. 2023

J. Fluid Mech.

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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.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Lewin,

de Bruyn Kops,

Caulfield

et al. 2023

J. Fluid Mech.

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Anisotropy and shear-layer edge dynamics of statistically unsteady, stratified turbulence

et al. 2015

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rotating frame of reference both have a tendency to suppress turbulence fluctuations and even cause relaminarization. In the latter case, both internal frictional losses and the mixing of momentum are substantially reduced. The implications are a significantly reduced rate of conversion of turbulence kinetic energy to internal energy (by the action of viscosity), reduced scale separation between small and large scale turbulence, and possibly increased large-scale anisotropy.Transport and dispersion of passive contaminants are governed by turbulence and mean flow advection, rather than by molecular diffusion; the contaminant simply follows the large-scale three-dimensional and time-dependent velocity field. Passive contaminant transport is therefore expected to respond significantly to changes in the componental structure of the flow field caused by the imposition of a stably stratified background. An analogous situation occurs for dense-gas releases in an isothermal environment. In this case, the density variation is caused by the density difference between the contaminant itself and the ambient air.Regardless of origin, spatial variation of fluid density generally affects all turbulence scales of the flow, changing the spatial and componental structure and in some cases even the rate of transfer of kinetic energy to internal energy. These particular features make stably stratified fluid flows challenging to model, both using statistically based turbulence closures and eddy-resolving simulations that rely on subgrid-scale models. The practical importance of stably stratified shear turbulence in general and its relevance to contaminant transport and dispersion constitute the primary motivations for the present study.The componental structure of the flow is most commonly characterized by considering the anisotropy of the turbulence, e.g., the departure from an equipartitioning of turbulence energy in the three spatial directions. Several quantities can be derived and examined in order to analyze the anisotropy of a turbulent flow. In the work of Smyth and Moum, 1 anisotropy tensors are derived from the Reynolds stress tensor and the viscous dissipation rate tensor, among others. Investigation of the anisotropy tensor components, the invariants, and the principal axes of these anisotropy tensors is conducted to shed light on the anisotropy of the flow. Smyth and Moum 1 also consider various spectral measures of the flow, but no examination of the vertical variations within the shear layer is carried out.A more straight-forward analysis of turbulence anisotropy is found in Thoroddsen and Van Atta, 2 where the ratios of various components of the Reynolds stress and viscous dissipation rate tensors are reported. Reynolds-stress correlation coefficients, cf., e.g., Kim, Moin, and Moser, 3 may also shed light on turbulence anisotropy. Lumley 4 demonstrates the use of the well-known "anisotropy invariant map" in order to characterize the anisotropy of a tensor, whereas Kassinos, Reynolds, and Rogers 5 show how the structu...

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A model for the viscous dissipation rate in stably stratified, sheared turbulence

Cited by 2 publications

References 18 publications

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

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

Anisotropy and shear-layer edge dynamics of statistically unsteady, stratified turbulence

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