Adrian van Kan, Keith Julien, Benjamin Miquel, Edgar Knobloch
{"title":"Bridging the Rossby number gap in rapidly rotating thermal convection","authors":"Adrian van Kan, Keith Julien, Benjamin Miquel, Edgar Knobloch","doi":"arxiv-2409.08536","DOIUrl":null,"url":null,"abstract":"Geophysical and astrophysical fluid flows are typically buoyantly driven and\nare strongly constrained by planetary rotation at large scales. Rapidly\nrotating Rayleigh-B\\'enard convection (RRRBC) provides a paradigm for direct\nnumerical simulations (DNS) and laboratory studies of such flows, but the\naccessible parameter space remains restricted to moderately fast rotation\n(Ekman numbers $\\rm Ek \\gtrsim 10^{-8}$), while realistic $\\rm Ek$ for\nastro-/geophysical applications are significantly smaller. Reduced equations of\nmotion, the non-hydrostatic quasi-geostrophic equations describing the\nleading-order behavior in the limit of rapid rotation ($\\rm Ek \\to 0$) cannot\ncapture finite rotation effects, leaving the physically most relevant part of\nparameter space with small but finite $\\rm Ek$ currently inaccessible. Here, we\nintroduce the rescaled incompressible Navier-Stokes equations (RiNSE), a\nreformulation of the Navier-Stokes-Boussinesq equations informed by the\nscalings valid for $\\rm Ek\\to 0$. We provide the first full DNS of RRRBC at\nunprecedented rotation strengths down to $\\rm Ek=10^{-15}$ and below and show\nthat the RiNSE converge to the asymptotically reduced equations.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"35 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Geophysics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Geophysical and astrophysical fluid flows are typically buoyantly driven and
are strongly constrained by planetary rotation at large scales. Rapidly
rotating Rayleigh-B\'enard convection (RRRBC) provides a paradigm for direct
numerical simulations (DNS) and laboratory studies of such flows, but the
accessible parameter space remains restricted to moderately fast rotation
(Ekman numbers $\rm Ek \gtrsim 10^{-8}$), while realistic $\rm Ek$ for
astro-/geophysical applications are significantly smaller. Reduced equations of
motion, the non-hydrostatic quasi-geostrophic equations describing the
leading-order behavior in the limit of rapid rotation ($\rm Ek \to 0$) cannot
capture finite rotation effects, leaving the physically most relevant part of
parameter space with small but finite $\rm Ek$ currently inaccessible. Here, we
introduce the rescaled incompressible Navier-Stokes equations (RiNSE), a
reformulation of the Navier-Stokes-Boussinesq equations informed by the
scalings valid for $\rm Ek\to 0$. We provide the first full DNS of RRRBC at
unprecedented rotation strengths down to $\rm Ek=10^{-15}$ and below and show
that the RiNSE converge to the asymptotically reduced equations.