Predicting vortex merging and ensuing turbulence characteristics in shear layers from initial conditions

Guha, Anirban; Rahmani, Mona

doi:10.1017/jfm.2019.721

Cited by 8 publications

(10 citation statements)

References 36 publications

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“…Billow evolution can be categorized as laminar pairing, turbulent pairing or non-pairing (Dong et al. 2019; Guha & Rahmani 2019; Liu et al. 2022).…”

Section: Pairingmentioning

confidence: 99%

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The effects of boundary proximity on Kelvin–Helmholtz instability and turbulence

2023

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Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial flow as an isolated shear layer. In geophysical cases, however, the instability often occurs near boundaries and may therefore be influenced by boundary proximity effects. Ensembles of direct numerical simulations are conducted to understand the effect of boundary proximity on the evolution of the instability and the resulting turbulence. Ensemble averages are used to reduce sensitivity to small variations in initial conditions. Both the transition to turbulence and the resulting turbulent mixing are modified when the shear layer is near a boundary: the time scales for the onset of instability and turbulence are longer, and the height of the KH billow is reduced. Subharmonic instability is suppressed by the boundary because phase lock is prevented due to the diverging phase speeds of the KH and subharmonic modes. In addition, the disruptive influence of three-dimensional secondary instabilities on pairing is more profound as the two events coincide more closely. When the shear layer is far from the boundary, the shear-aligned convective instability is dominant; however, secondary central-core instability takes over when the shear layer is close to the boundary, providing an alternate route for the transition to turbulence. Both the efficiency of the resulting mixing and the turbulent diffusivity are dramatically reduced by boundary proximity effects.

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“…Billow evolution can be categorized as laminar pairing, turbulent pairing or non-pairing (Dong et al. 2019; Guha & Rahmani 2019; Liu et al. 2022).…”

Section: Pairingmentioning

confidence: 99%

“…Thereafter, the mean shear feeds energy to the pairing billows, and a single vortex is formed (Dong et al. 2019; Guha & Rahmani 2019). The opposite value of the optimal is (figure 7 b ).…”

Section: Pairingmentioning

confidence: 99%

The effects of boundary proximity on Kelvin–Helmholtz instability and turbulence

2023

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“…6 and may account for the more pronounced pause in subharmonic growth (cf. Dong et al 2019;Guha & Rahmani 2019). In contrast, in the laminar pairing cases no.…”

Section: Phase Evolutionmentioning

confidence: 92%

“…(2019) showed that different phase relationships between the primary and subharmonic Fourier components of the initial state can lead to a significant difference in the potential energy change due to mixing. Guha & Rahmani (2019) extended these results to include multiple levels of pairing in unstratified shear layers. Here, we extend Kaminski & Smyth (2019) by looking beyond the amplitude of the initial noise field to see how the details of its spatial form influence the flow evolution.…”

Section: Introductionmentioning

confidence: 92%

“…Here, we extend Kaminski & Smyth (2019) by looking beyond the amplitude of the initial noise field to see how the details of its spatial form influence the flow evolution. Moreover, we extend Guha & Rahmani (2019) by including stable stratification and Dong et al (2019) by increasing the Reynolds numbers to values where different secondary instabilities, specifically the subharmonic pairing mode (e.g. Klaassen & Peltier 1989) and the various three-dimensional secondary modes, compete strongly such that pairing may be suppressed altogether (Mashayek & Peltier 2011.…”

Section: Introductionmentioning

confidence: 99%

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The butterfly effect and the transition to turbulence in a stratified shear layer

2022

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In a stably stratified shear layer, multiple competing instabilities produce sensitivity to small changes in initial conditions, popularly called the butterfly effect (as a flapping wing may alter the weather). Three ensembles of 15 simulated mixing events, identical but for small perturbations to the initial state, are used to explore differences in the route to turbulence, the maximum turbulence level and the total amount and efficiency of mixing accomplished by each event. Comparisons show that a small change in the initial state alters the strength and timing of the primary Kelvin–Helmholtz instability, the subharmonic pairing instability and the various three-dimensional secondary instabilities that lead to turbulence. The effect is greatest in, but not limited to, the parameter regime where pairing and the three-dimensional secondary instabilities are in strong competition. Pairing may be accelerated or prevented; maximum turbulence kinetic energy may vary by up to a factor of 4.6, flux Richardson number by 12 %–15 % and net mixing by a factor of 2.

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Velocity perturbations and Reynolds stresses in Holmboe instabilities

et al. 2022

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The velocity perturbations and Reynolds stresses associated with finite-amplitude Holmboe instabilities are investigated using linear stability analysis, numerical simulations, and a laboratory experiment. The rightward and leftward propagating Holmboe instabilities are separated, allowing for a direct comparison of the perturbation fields between the numerical simulations and the linear stability analysis. The decomposition and superposition of the perturbation fields provide insights into the structure and origin of Reynolds stresses in Holmboe instabilities. Shear instabilities in stratified flows introduce a directional preference (anisotropy) in velocity perturbation fields, thereby generating Reynolds stresses. Here, we investigate this anisotropy by comparing pairs of horizontal and vertical velocity perturbations (u',w'), obtained from the simulations and the laboratory experiment, with predictions from linear stability analysis. For an individual Holmboe mode, both the simulations and linear theory yield elliptical (u',w')-pairs that are oriented towards the 2nd and 4th quadrants (u'w'<0), corresponding to the tilted elliptical trajectories of particle movement. Combining the leftward and rightward Holmboe modes yields (u',w') ellipses whose orientation and aspect ratio are phase-dependent. When averaged over a full cycle, the joint probability density functions of (u',w') in the linear theory and single wavelength simulations exhibit `steering wheel' structures. This `steering wheel' is smeared out in multiple wavelength simulations and the laboratory experiment due to varying wavelengths, resulting in an elliptical cloud. All of the approaches adopted in the present study yield Reynolds stresses that are comparable to those reported in previous laboratory and field investigations.

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Predicting vortex merging and ensuing turbulence characteristics in shear layers from initial conditions

Cited by 8 publications

References 36 publications

The effects of boundary proximity on Kelvin–Helmholtz instability and turbulence

The effects of boundary proximity on Kelvin–Helmholtz instability and turbulence

The butterfly effect and the transition to turbulence in a stratified shear layer

Velocity perturbations and Reynolds stresses in Holmboe instabilities

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