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

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

doi:10.1017/jfm.2023.412

Cited by 6 publications

(11 citation statements)

References 63 publications

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“…In addition, it is apparent that the magnitude of the power spectra increases with turbulence intensity. Figure 5b shows the time evolution of the kinetic energy, KE = KE + KE ′ , where KE = 1 2 U 2 and KE ′ = 1/2 u 2 + v 2 + w 2 where u, v, and w are components of velocity fluctuation in the x, y, and z directions, respectively At t ≈ 0.3 s, the kinetic energy values drop to a local minimum because the Kelvin-Helmholtz's billow structure is partly destroyed, as was also observed by Liu et al [25]. Then, KE increases, suggesting the emergence of turbulence.…”

Section: Effect Of Turbulencesupporting

confidence: 59%

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Influence of Cross Perturbations on Turbulent Kelvin–Helmholtz Instability

Sementilli,

Zangeneh,

Chen

2024

Fluids

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Kelvin–Helmholtz instability has been studied extensively in 2D. This study attempts to address the influence of turbulent flow and cross perturbation on the growth rate of the instability and the development of mixing layers in 3D by means of direct numerical simulation. Two perfect gases are considered to be working fluids moving as opposite streams, inducing shear instability at the interface between the fluids and resulting in Kelvin–Helmholtz instability. The results show that cross perturbation affects the instability by increasing the amplitude growth while adding turbulence has almost no effect on the amplitude growth. Furthermore, by increasing the turbulence intensity, a more distinct presence of the inner flow can be seen in the mixing layer of the two phases, and the presence of turbulence expands the range of high-frequency motion significantly due to turbulence structures. The results give a basis for which 3D Kelvin–Helmholtz phenomena should be further investigated using numerical simulation for predictive modeling, beyond the use of simplified 2D theoretical models.

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Section: Effect Of Turbulencesupporting

confidence: 59%

“…Rogers and Moser 1991 [21], Martinez 2006 [22], Soetrisno 1990 [23], and Wang 2016 [24] analyzed 3D KHI simulations. The study of turbulence in relation to KHI has only recently been explored [20,25].…”

Section: Introductionmentioning

confidence: 99%

Influence of Cross Perturbations on Turbulent Kelvin–Helmholtz Instability

Sementilli,

Zangeneh,

Chen

2024

Fluids

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“…The KHI arises due to the interaction of vorticity waves at two edges of finite shear layers, leading to a sequence of stationary vortex billows that roll up the denser fluids and cause significant mixing (Hazel 1972;Smyth & Peltier 1991;Carpenter et al 2011). However, unlike these previous studies (with the exception of the recent studies (Atoufi et al 2023;Liu, Kaminski & Smyth 2023)) the KHI observed here in the SIC geometry is bounded by no-slip solid boundaries at z = ±1.…”

Section: Kelvin-helmholtz Instabilitycontrasting

confidence: 47%

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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“…Previous theoretical research on shear instabilities has assumed a single, isolated stratified shear layer (e.g. Caulfield & Peltier 2000;Salehipour & Peltier 2015;Kaminski & Smyth 2019;Lewin & Caulfield 2021;Liu et al 2022Liu et al , 2023, neglecting the potential influence of nearby flow structures. Our goal here is to relax the assumption of a single, isolated shear layer.…”

Section: Introductionmentioning

confidence: 99%

Turbulence and mixing from neighbouring stratified shear layers

Liu,

Kaminski,

Smyth

2024

Preprint

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Studies of Kelvin-Helmholtz instability (KHI) have typically modeled 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 {\color{black} using both linear stability analysis and direct numerical simulation}. With sufficiently large layer separation, the characteristics of instability and mixing converge toward the familiar Kelvin-Helmholtz turbulence. 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 (SSI) 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 KHI and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

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

Cited by 6 publications

References 63 publications

Influence of Cross Perturbations on Turbulent Kelvin–Helmholtz Instability

Influence of Cross Perturbations on Turbulent Kelvin–Helmholtz Instability

Long-wave instabilities of sloping stratified exchange flows

Turbulence and mixing from neighbouring stratified shear layers

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