Velocity perturbations and Reynolds stresses in Holmboe instabilities

Yang, Adam Jiankang; Tedford, Edmund W.; Olsthoorn, Jason; Lefauve, Adrien; Lawrence, Gregory A.

doi:10.1063/5.0097624

Cited by 6 publications

(2 citation statements)

References 66 publications

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“…The HWI and DVLWI have a pair of conjugate modes, represented by oscillating profiles, due to the synchronisation of complex-conjugate modes, as discussed in Yang et al. (2022). Interestingly, after the nonlinear bursting at , the nonlinear HWI still maintains the oscillating pattern (Lefauve et al.…”

Section: Nonlinear Evolution Of Unstable Modesmentioning

confidence: 97%

Long-wave instabilities of sloping stratified exchange flows

Zhu,

Atoufi,

Lefauve

et al. 2024

J. Fluid Mech.

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We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin–Helmholtz instability and Holmboe wave instability, in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$ , which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number, Prandtl number, base flow profile and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin–Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

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Section: Nonlinear Evolution Of Unstable Modesmentioning

confidence: 97%

Long-wave instabilities of sloping stratified exchange flows

Zhu,

Atoufi,

Lefauve

et al. 2024

J. Fluid Mech.

Self Cite

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show abstract

“…We emphasize that wavenumbers and are an illustration of the red crosses computed in figure 1. Subsequently, we expand the Reynolds stress term in (4.3), using the modal decomposition (4.4), and we find where denotes complex transposition, and and (a similar description with only one pair of modes can be found in Yang et al 2022). We distinguish in (4.5) the contributions from self- and cross-interactions between a fixed set of discretized modes.…”

Section: Weakly Nonlinear Saturation Near the Onsetmentioning

confidence: 99%

Localized layers of turbulence in stratified horizontally sheared Poiseuille flow

et al. 2023

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This paper presents a numerical analysis of the instability developing in horizontally sheared Poiseuille flow, when stratification extends along the vertical direction. Our study builds on the previous work that originally detected the linear instability of such a configuration, by means of experiments, theoretical analysis and numerical simulations (Le Gal et al., J. Fluid Mech., vol. 907, 2021, R1). We extend this investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We find that the flow loses its vertical homogeneity through a secondary bifurcation, due to harmonic resonances, and describe this symmetry-breaking mechanism in the vicinity of the instability threshold. When departing from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of horizontal localized layers of stratified turbulence surrounded by quiescent regions of meandering waves.

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Asymmetric Holmboe instabilities in arrested salt-wedge flows

et al. 2022

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The asymmetric Holmboe instabilities that form on an arrested salt wedge are investigated in the laboratory. The flow is characterized by three regions. Near the tip of the salt wedge, there is little wave activity; immediately downstream, mostly positive waves form; further downstream, both positive and negative waves are present. The appearance of these regions is determined by the spatial variation in the thickness of the saline layer, the shear layer thickness, and the offset between the density interface and velocity interface. We predict the growth of the instabilities by applying linear stability theory to the mean flow field. The predicted initial growth rate is consistent with the laboratory measurements until the Holmboe wave reaches a steepness ratio of [Formula: see text] %. Then, the growth of the Holmboe wave is nonlinear. We found that the Holmboe wavelength increases downstream along the salt wedge. This wave stretching is related to the increase in the shear layer thickness and is supported by the gradual acceleration of the upper layer fluid. Eventually, the growth of the wave amplitude and the wave stretching balance a maximum wave steepness ratio of 10%. Although the wave is nonlinear, the predicted wave speed and wavelength are consistent with the laboratory measurements.

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Velocity perturbations and Reynolds stresses in Holmboe instabilities

Cited by 6 publications

References 66 publications

Long-wave instabilities of sloping stratified exchange flows

Long-wave instabilities of sloping stratified exchange flows

Localized layers of turbulence in stratified horizontally sheared Poiseuille flow

Asymmetric Holmboe instabilities in arrested salt-wedge flows

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