Turbulence in forced stratified shear flows

Smith, Katherine M.; Caulfield, C. P.; Taylor, John R.

doi:10.1017/jfm.2020.994

Cited by 26 publications

(16 citation statements)

References 65 publications

(187 reference statements)

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“…(2017 b ) and Smith et al. (2021), suggesting that as goes to zero the diapycnal flux is not fully suppressed within this regime.…”

Section: Parameterization Of Mixing Efficiency Applicability and Comparisonmentioning

confidence: 85%

“…In past studies, Zhou et al. (2017 b ) and Smith, Caulfield & Taylor (2021) have shown that the framework may be also applied to inhomogeneous shear flows to evaluate irreversible mixing across a midplane shear interface through appropriate spatial and temporal integration over the shear layer. However, in stratified open-channel flow where we are interested in investigating the correlation between mixing efficiency and local flow parameters across a broad range of vertical locations, rather than a single central shear layer, the framework presents obvious limitations.…”

Section: Flow Overviewmentioning

confidence: 99%

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Parameterization of mixing in stratified open channel flow

et al. 2022

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The dynamics and parameterization of mixing in temporally evolving turbulent open-channel flow is investigated through direct numerical simulations as the flow transitions from an initially neutral state to stable stratification. We observe three distinctly different mixing regimes separated by transitional values of turbulent Froude number $Fr$ : a weakly stratified regime for $Fr >1$ ; an intermediate regime for $0.3< Fr<1$ ; and a saturated regime for $Fr<0.3$ . The mixing coefficient $\varGamma =B/\epsilon _K$ , (where $B$ is the buoyancy flux and $\epsilon _K$ is the dissipation rate of kinetic energy), is well predicted by the parameterization schemes of Maffioli et al. (J. Fluid Mech., vol. 794, 2016) and Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323–333) across all three regimes through instantaneous measurements of $Fr$ and the ratio $L_E/L_O$ , where $L_E$ and $L_O$ are the Ellison and Ozmidov length scales, respectively. The flux Richardson number $R_f = B/(B+\epsilon _K)$ shows linear dependence on the gradient Richardson number $Ri_g$ up to a transitional value of $Ri_g =0.25$ , past which it saturates again to a constant value independent of $Fr$ or $Ri_g$ . By examining the flow as a balance of inertial, shear and buoyancy forces, we derive physically based scaling relationships to demonstrate that $Ri_g \sim Fr^{-2}$ and $Ri_g \sim Fr^{-1}$ in the weakly and moderately stratified regimes and that $Ri_g$ becomes independent of $Fr$ in the saturated regime. Our results suggest that the $L_E/L_O \sim Fr^{-1}$ scaling of Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323–333) in the intermediate regime manifests due to the influence of mean shear. The differences in the relationships between $Fr$ and $L_E/L_O$ for non-sheared flows within this regime are discussed.

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“…(2017 b ) and Smith et al. (2021), suggesting that as goes to zero the diapycnal flux is not fully suppressed within this regime.…”

Section: Parameterization Of Mixing Efficiency Applicability and Comparisonmentioning

confidence: 85%

Section: Flow Overviewmentioning

confidence: 99%

Parameterization of mixing in stratified open channel flow

et al. 2022

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“…Context -Over the last decades, Holmboe waves (defined here as being the long-lived, finite-amplitude waves originating from the linear Holmboe instability) have been the focus of numerous numerical and experimental studies. Direct numerical simulations (DNSs) in two and three dimensions have shed light on some aspects of their rich nonlinear behaviors, such as interaction between the two traveling waves, mixing of the density interface [1][2][3][4][5][6][7]. Laboratory experiments in salt-stratified exchange flows have also observed, measured, and attempted to explain and classify Holmboe waves [6,[8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear Holmboe waves

Cudby

Lefauve

2021

Phys. Rev. Fluids

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Holmboe waves are long-lived traveling waves commonly found in environmental stratified shear flows in which a relatively sharp, stable density interface is embedded within a more diffuse shear layer. Although previous research has focused on their linear properties (the Holmboe instability), and on their turbulent properties (Holmboe wave turbulence), little is known about their finite-amplitude properties in the nonlinear but nonturbulent regime. In this paper we tackle this problem with a weakly-nonlinear temporal stability analysis of Holmboe waves. We employ the rigorous and versatile amplitude expansion method recently proposed by Pham & Suslov (R. Soc. Open Sci. 5: 180746, 2018), which remains well-posed a finite distance away from the critical point of linear instability. Starting with the most amplified linear Fourier mode (order 1 in amplitude), we systematically derive the hierarchy of nonlinear modes (order 2 and 3) required to obtain Landau coefficients that allow the instability to eventually saturate to a stable equilibrium amplitude. We introduce the algorithm step by step, first on a single-mode instability (suited to the weakly-stratified Kelvin-Helmholtz instability), before extending it to the more subtle case of a double-mode instability (suited to the more strongly-stratified Holmboe instability of interest). We present numerical solutions for the canonical stratified shear layer with hyperbolic-tangent symmetric profiles, shear-to-density thickness ratio R = 5, and Prandtl (or Schmidt) number P r = 700. We select four locations on the linear stability boundary: three qualitatively distinct Holmboe cases (having widely different Reynolds numbers Re, Richardson numbers J, steamwise wavenumbers k, and phase speeds), and one Kelvin-Helmholtz case to serve as a comparison. We produce supercritical bifurcation diagrams for each case, both in Re and J, and we find great differences in the scaling and magnitude of stable equilibrium branches, be it between Holmboe cases, between the Holmboe and Kelvin-Helmholtz cases, and between bifurcations in supercritical Re or J. We also study phase portraits to delve into the transient dynamics of the two counter-propagating Holmboe modes, and we find a special case in which specific initial conditions can lead to the non-monotonic growth or decay of individual modes. Next, we deconstruct the perturbation expansions to investigate in detail the spatial structures of all the component modes (linear and nonlinear), and highlight the underlying saturation mechanisms. We again find differences between Holmboe cases, and Re or J (such as the dominance of order 2 vs order 3 terms, and of various wavenumber harmonics 0, k, 2k, 3k). Finally, we discuss the potential relevance of our analysis to recent experimental measurements of supercritical Holmboe waves, and its possible extension to asymmetric Holmboe waves to tackle the question of mode selection. We believe these results provide a basis for a future fully-nonlinear analysis of the Holmboe dynamical system.

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“…Almost any turbulent flow of a fluid is of shear character, its layers moving past each other under a shear force. Therefore, turbulence in shear flows is the main problem considered in that context [2]. Of special interest is the case of free shear flow, i.e., the flow of a fluid confined within another fluid.…”

Section: Introductionmentioning

confidence: 99%

Turbulent shear flow of solids

Beygelzimer

Filippov

Kulagin

et al. 2021

Preprint

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The term ‘solid-state turbulence’ may sound like an oxymoron, but in fact it is not. In this article we demonstrate that solid-state turbulence may emerge owing to a defining property of the solid state: the ability of a solid to retain its shape. We consider shear flow of layers of solids with different stiffness and show that the stiffer ones may spontaneously decompose into a set of blocks. This breakdown of isometry is a key to plasticity of solids and is fundamental for the occurrence of solid-state turbulence. To visualise the piecewise isometric transformations of the blocky structure in a turbulent flow regime, we use a heuristic model based on discretisation of a continuum into interacting ‘particles’. The outcomes of the numerical experiments conducted support the occurrence of pulsations of velocity and pressure in plastically deforming solids and the emergence of vortices characteristic of classical turbulence. This phenomenon may have important practical implications for solid-state mixing as an ecologically beneficial alternative to conventional metallurgical processing routes.

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Turbulence in forced stratified shear flows

Abstract: Abstract

Cited by 26 publications

References 65 publications

Parameterization of mixing in stratified open channel flow

Parameterization of mixing in stratified open channel flow

Weakly nonlinear Holmboe waves

Turbulent shear flow of solids

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