Andres Posada-Bedoya, Jason Olsthoorn, Leon Boegman
{"title":"The boundary layer instability beneath internal solitary waves and its sensitivity to vortex wakes","authors":"Andres Posada-Bedoya, Jason Olsthoorn, Leon Boegman","doi":"10.1017/jfm.2024.506","DOIUrl":null,"url":null,"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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline1.png\"/> <jats:tex-math>$Re_{ISW}=90$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and convectively unstable at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline2.png\"/> <jats:tex-math>$Re_{ISW}=300$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. At laboratory-scale <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline3.png\"/> <jats:tex-math>$Re_{ISW}=300$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, 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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline4.png\"/> <jats:tex-math>$Re_{ISW}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> 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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline5.png\"/> <jats:tex-math>$Re_{ISW}=900$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, 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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline6.png\"/> <jats:tex-math>$Re_{ISW}=300$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline7.png\"/> <jats:tex-math>$Re_{ISW}=900$</jats:tex-math> </jats:alternatives> </jats:inline-formula> 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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline8.png\"/> <jats:tex-math>$Re_{ISW}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> 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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005068_inline9.png\"/> <jats:tex-math>$Re_{ISW}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fluid Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1017/jfm.2024.506","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
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 $Re_{ISW}$.
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.