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

Liu, Chih-Lun; Kaminski, Alexis; Smyth, William D.

doi:10.1017/jfm.2022.985

Cited by 11 publications

(20 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ensembles of simulations are performed, each using a different seed to generate the random velocities (Liu et al. 2022). The choices of , grid sizes and repetition of runs for each set of simulations are presented in table 1.…”

Section: Methodsmentioning

confidence: 99%

“…Due to the sensitive dependence on initial conditions that may greatly alter the evolution of the instability and turbulent mixing (Liu et al. 2022), an adequate ensemble size is crucial for controlling sampling error. Therefore, we must compromise between , and ensemble size.…”

Section: Methodsmentioning

confidence: 99%

“…2019; Guha & Rahmani 2019; Liu et al. 2022). Laminar pairing involves the greatest amount of subharmonic kinetic energy (blue circles in figure 5), because at the time when is a maximum, turbulence has not yet grown strong enough to collapse the coherent billow structure.…”

Section: Pairingmentioning

confidence: 99%

“…Liu et al. (2022) showed that a small change in the initial random perturbation can lead to a substantial variation in the timing and strength of turbulence. This variation results from the interactions between mean flow, primary KH, subharmonic and various 3-D secondary instabilities.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

2023

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Pairingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…The instability mechanism is most easily understood as a constructive interference between vorticity waves that propagate horizontally above and below the inflection point and are therefore able to phase-lock (e.g., Carpenter et al 2013;Smyth and Carpenter 2019;Liu et al 2022).…”

Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

The Role of Ambient Turbulence in Canopy Wave Generation by Kelvin–Helmholtz Instability

Smyth

Mayor

Lian

2023

Boundary-Layer Meteorol

Self Cite

View full text Add to dashboard Cite

We test the hypothesis that internal waves observed in flow over forest canopies are generated by Kelvin–Helmholtz instability. The waves were observed at night, under stably stratified and weak wind conditions, with a horizontally scanning aerosol lidar and an instrumented tower. The lidar images are used to determine the salient wavelength and phase propagation velocity of each episode. Time series data measured at the tower are then used to form vertical profiles of background velocity and buoyancy just before each observed wave event. The profiles are input to the Taylor–Goldstein equation to predict the phase velocity, wavelength and period of the fastest-growing linear instability, and the results compared with the lidar observations. The observed wavelengths tend to be longer than predicted by the Taylor–Goldstein theory, typically by a factor of two. That discrepancy is removed when the theory is extended to account for the effects of ambient, small-scale turbulence.

show abstract

Turbulence and mixing from neighbouring stratified shear layers

Liu,

Kaminski,

Smyth

2024

J. Fluid Mech.

View full text Add to dashboard Cite

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$ , approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$ , billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$ , neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

show abstract

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

Cited by 11 publications

References 53 publications

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

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

The Role of Ambient Turbulence in Canopy Wave Generation by Kelvin–Helmholtz Instability

Turbulence and mixing from neighbouring stratified shear layers

Contact Info

Product

Resources

About