The boundary layer instability beneath internal solitary waves and its sensitivity to vortex wakes

IF 3.6 2区 工程技术 Q1 MECHANICS Journal of Fluid Mechanics Pub Date : 2024-08-14 DOI:10.1017/jfm.2024.506
Andres Posada-Bedoya, Jason Olsthoorn, Leon Boegman
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Abstract

We investigated the stability of the bottom boundary layer (BBL) beneath periodic internal solitary waves (ISWs) of depression over a flat bottom through two-dimensional direct numerical simulations. We explored the convective versus absolute/global nature of the BBL instability in response to changes in Reynolds number, and the sensitivity of the instability to seeding noise in the front of the ISW – spanning laboratory to geophysical scales. The BBL was laminar at $Re_{ISW}=90$ and convectively unstable at $Re_{ISW}=300$ . At laboratory-scale $Re_{ISW}=300$ , the convective wave packet was periodically amplified by each successive ISW, until vortex shedding occurred. The associated noise-amplification behaviour potentially explains the discrepancies of the critical $Re_{ISW}$ between the lock–release laboratory experiments and our Dubreil–Jacotin–Long-initialized numerical simulations as the result of the difference in background noise. Instability energy decreased under the front shoulder of the ISW, analogous to flow relaminarization under a favourable pressure gradient. At geophysical-scale $Re_{ISW}=900$ , the BBL was initially convectively unstable, and then the instability tracked with the ISW, appearing phenomenologically similar to a global instability. The simulated initial convective instability at both $Re_{ISW}=300$ and $Re_{ISW}=900$ is in agreement with local linear stability analysis which predicts that the instability group speed is always lower than the ISW celerity. Increased free stream perturbations in front of the ISW and larger $Re_{ISW}$ shift the location of vortex shedding (and enhanced bed shear stress) beneath the wave, closer to the ISW trough, thereby potentially changing the location of maximum sediment resuspension, in agreement with field observations at higher $Re_{ISW}$ .
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内孤波下的边界层不稳定性及其对涡旋湍流的敏感性
我们通过二维直接数值模拟,研究了平底上周期性凹陷内孤波(ISW)下底部边界层(BBL)的稳定性。我们探索了 BBL 不稳定性随雷诺数变化而产生的对流与绝对/全局性质,以及不稳定性对 ISW 前部播种噪声的敏感性 - 从实验室到地球物理尺度。当雷诺数为$Re_{ISW}=90时,BBL是层流的,而当雷诺数为$Re_{ISW}=300时,BBL是对流不稳定的。在实验室尺度 $Re_{ISW}=300$ 时,对流波包被每一个连续的 ISW 周期性放大,直到出现涡旋脱落。相关的噪声放大行为可能解释了锁定释放实验室实验与我们的 Dubreil-Jacotin-Long 初始化数值模拟之间临界值 $Re_{ISW}$ 的差异,这是背景噪声差异的结果。ISW前肩下的不稳定能量下降,类似于有利压力梯度下的流动再层流化。在地球物理尺度$Re_{ISW}=900$时,BBL最初是对流不稳定的,然后不稳定随着ISW的变化而变化,在现象上类似于全局不稳定。在$Re_{ISW}=300$和$Re_{ISW}=900$条件下模拟的初始对流不稳定性与局部线性稳定性分析一致,该分析预测不稳定群速度总是低于ISW速度。ISW 前方自由流扰动的增加和 $Re_{ISW}$ 的增大会使波浪下方的涡流脱落位置(和增强的床面剪应力)发生移动,从而更靠近 ISW 波谷,从而可能改变沉积物最大重悬浮位置,这与 $Re_{ISW}$ 较高时的现场观测结果一致。
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来源期刊
CiteScore
6.50
自引率
27.00%
发文量
945
审稿时长
5.1 months
期刊介绍: Journal of Fluid Mechanics is the leading international journal in the field and is essential reading for all those concerned with developments in fluid mechanics. It publishes authoritative articles covering theoretical, computational and experimental investigations of all aspects of the mechanics of fluids. Each issue contains papers on both the fundamental aspects of fluid mechanics, and their applications to other fields such as aeronautics, astrophysics, biology, chemical and mechanical engineering, hydraulics, meteorology, oceanography, geology, acoustics and combustion.
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