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Shear instability in mode-2 internal Kelvin waves
Environmental Fluid Mechanics ( IF 1.7 ) Pub Date : 2022-09-23 , DOI: 10.1007/s10652-022-09895-w
Marek Stastna , David Deepwell , Andrew Grace

Shear instabilities of stratified fluids are a classical topic with a broad literature. The classic instability takes the form of Kelvin-Helmholtz billows that initially develop in two dimensions, one of which is the vertical. Spanwise instability develops later as part of the transition to a three-dimensionalized state. We simulate mode-2 internal waves on the laboratory scale in a rotating frame of reference that, in the absence of rotation, form spanwise aligned billows on the wave flanks. Rotation breaks the symmetry of the classical shear instability because the wave amplitude decays away from the focussing wall (i.e. the waves generated are internal Kelvin waves). We document the development of the wave and the shear instabilities as the Rossby number is varied, finding that (i) even weak rotation (high Rossby number) leads to a significant modification of the billow three-dimensionalization, (ii) strong rotation (low Rossby number) leads to a strong near wall focussing of turbulence transition that is clearly evident in the second invariant of the velocity gradient, Q, of turbulence theory. For low rotation rates, or intermediate to high Rossby numbers, we identify novel instabilities with billow cores aligned in the along-tank direction, rather than the typical spanwise direction.



中文翻译:

模式 2 内部开尔文波的剪切不稳定性

分层流体的剪切不稳定性是具有广泛文献的经典主题。经典的不稳定性采取开尔文-亥姆霍兹波浪的形式,最初在两个维度上发展,其中之一是垂直方向。作为向三维状态过渡的一部分,跨度不稳定性随后发展。我们在实验室尺度上模拟模式 2 内波,在旋转的参考系中,在没有旋转的情况下,在波侧形成展向对齐的波涛。旋转破坏了经典剪切不稳定性的对称性,因为波幅远离聚焦壁衰减(即产生的波是内部开尔文波)。随着罗斯比数的变化,我们记录了波的发展和剪切不稳定性,Q,湍流理论。对于低转速或中高罗斯比数,我们识别出新的不稳定性,其中波状核心沿储罐方向排列,而不是典型的展向方向。

更新日期:2022-09-24
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