# Regime transitions and energetics of sustained stratified shear flows

## TL;DR

This study investigates the long-term behavior of stratified shear flows in a laboratory setting, identifying flow regimes and deriving scaling laws for transitions based on experimental data and energy budget analysis.

## Contribution

It provides a physical basis and non-dimensional scaling laws for flow regime transitions in sustained stratified shear flows, validated by extensive experiments.

## Key findings

- Four distinct flow regimes identified: laminar, Holmboe waves, intermittent turbulence, vigorous turbulence.
- Scaling laws for regime transitions are consistent with experimental data.
- Energy budget analysis explains the physical mechanisms behind regime changes.

## Abstract

We describe the long-term dynamics of sustained stratified shear flows in the laboratory. The Stratified Inclined Duct (SID) experiment sets up a two-layer exchange flow in an inclined duct connecting two reservoirs containing salt solutions of different densities. This flow is primarily characterised by two non-dimensional parameters: the tilt angle of the duct with respect to the horizontal, $\theta$ (a few degrees at most), and the Reynolds number $Re$, an input parameter based on the density difference driving the flow. The flow can be sustained with constant forcing over arbitrarily long times and exhibits a wealth of dynamical behaviours representative of geophysically-relevant sustained stratified shear flows. Varying $\theta$ and $Re$ leads to four qualitatively different regimes: laminar flow; mostly laminar flow with finite-amplitude, travelling Holmboe waves; spatio-temporally intermittent turbulence with substantial interfacial mixing; and sustained, vigorous interfacial turbulence (Meyer & Linden, J. Fluid Mech., vol. 753, 2014, pp. 242-253). We seek to explain the scaling of the transitions between flow regimes in the two-dimensional plane of input parameters $(\theta, Re)$. We improve upon previous studies of this problem by providing a firm physical basis and non-dimensional scaling laws that are mutually consistent and in good agreement with the empirical transition curves we inferred from 360 experiments spanning $\theta \in [-1^\circ, 6^\circ]$ and $Re \in [300, 5000]$. To do so, we employ state-of-the-art simultaneous volumetric measurements of the density field and the three-component velocity field, and analyse these experimental data using time- and volume-averaged potential and kinetic energy budgets. We show that regime transitions are caused by ...

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Source: https://tomesphere.com/paper/1901.07585