J. R. Fuentes, Bradley W. Hindman, Adrian E. Fraser, Evan H. Anders
{"title":"旋转流中半对流阶梯的演变:巨行星模糊内核的后果","authors":"J. R. Fuentes, Bradley W. Hindman, Adrian E. Fraser, Evan H. Anders","doi":"arxiv-2408.10833","DOIUrl":null,"url":null,"abstract":"Recent observational constraints on the internal structure of Jupiter and\nSaturn suggest that these planets have ``fuzzy\" cores, i.e., radial gradients\nof the concentration of heavy elements that might span $50\\%$ to $70\\%$ of each\nplanet's radius. These cores could be composed of a semi-convective staircase,\ni.e., multiple convective layers separated by diffusive interfaces arising from\ndouble-diffusive instabilities. However, to date, no study has demonstrated how\nsuch staircases can avoid layer mergers and persist over evolutionary time\nscales. In fact, previous work has found that these mergers occur rapidly,\nquickly leading to only a single convective layer. Using 3D simulations of\nconvective staircases in non-rotating and rotating flows, we demonstrate that\nrotation prolongs the lifetime of a convective staircase by increasing the\ntimescale for both layer merger and erosion of the interface between the final\ntwo layers. We present an analytic model for the erosion phase, predicting that\nrotation increases the erosion time by a factor of approximately\n$\\mathrm{Ro}^{-1/2}$, where $\\mathrm{Ro}$ is the Rossby number of the\nconvective flows (the ratio of the rotation period to the convective turnover\ntime). For Jovian conditions at early times after formation (when convection is\nvigorous enough to mix a large fraction of the planet), we find the erosion\ntime to be roughly $10^{9}~\\mathrm{yrs}$ in the non-rotating case and\n$10^{11}~\\mathrm{yrs}$ in the rotating case. Thus, the current existence of\nconvective staircases within the deep interiors of giant planets is a strong\npossibility, and rotation could be an important factor in the preservation of\ntheir fuzzy cores.","PeriodicalId":501270,"journal":{"name":"arXiv - PHYS - Geophysics","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evolution of Semi-convective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets\",\"authors\":\"J. R. Fuentes, Bradley W. Hindman, Adrian E. Fraser, Evan H. Anders\",\"doi\":\"arxiv-2408.10833\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent observational constraints on the internal structure of Jupiter and\\nSaturn suggest that these planets have ``fuzzy\\\" cores, i.e., radial gradients\\nof the concentration of heavy elements that might span $50\\\\%$ to $70\\\\%$ of each\\nplanet's radius. These cores could be composed of a semi-convective staircase,\\ni.e., multiple convective layers separated by diffusive interfaces arising from\\ndouble-diffusive instabilities. However, to date, no study has demonstrated how\\nsuch staircases can avoid layer mergers and persist over evolutionary time\\nscales. In fact, previous work has found that these mergers occur rapidly,\\nquickly leading to only a single convective layer. Using 3D simulations of\\nconvective staircases in non-rotating and rotating flows, we demonstrate that\\nrotation prolongs the lifetime of a convective staircase by increasing the\\ntimescale for both layer merger and erosion of the interface between the final\\ntwo layers. We present an analytic model for the erosion phase, predicting that\\nrotation increases the erosion time by a factor of approximately\\n$\\\\mathrm{Ro}^{-1/2}$, where $\\\\mathrm{Ro}$ is the Rossby number of the\\nconvective flows (the ratio of the rotation period to the convective turnover\\ntime). For Jovian conditions at early times after formation (when convection is\\nvigorous enough to mix a large fraction of the planet), we find the erosion\\ntime to be roughly $10^{9}~\\\\mathrm{yrs}$ in the non-rotating case and\\n$10^{11}~\\\\mathrm{yrs}$ in the rotating case. Thus, the current existence of\\nconvective staircases within the deep interiors of giant planets is a strong\\npossibility, and rotation could be an important factor in the preservation of\\ntheir fuzzy cores.\",\"PeriodicalId\":501270,\"journal\":{\"name\":\"arXiv - PHYS - Geophysics\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-20\",\"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-2408.10833\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Geophysics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.10833","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Evolution of Semi-convective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets
Recent observational constraints on the internal structure of Jupiter and
Saturn suggest that these planets have ``fuzzy" cores, i.e., radial gradients
of the concentration of heavy elements that might span $50\%$ to $70\%$ of each
planet's radius. These cores could be composed of a semi-convective staircase,
i.e., multiple convective layers separated by diffusive interfaces arising from
double-diffusive instabilities. However, to date, no study has demonstrated how
such staircases can avoid layer mergers and persist over evolutionary time
scales. In fact, previous work has found that these mergers occur rapidly,
quickly leading to only a single convective layer. Using 3D simulations of
convective staircases in non-rotating and rotating flows, we demonstrate that
rotation prolongs the lifetime of a convective staircase by increasing the
timescale for both layer merger and erosion of the interface between the final
two layers. We present an analytic model for the erosion phase, predicting that
rotation increases the erosion time by a factor of approximately
$\mathrm{Ro}^{-1/2}$, where $\mathrm{Ro}$ is the Rossby number of the
convective flows (the ratio of the rotation period to the convective turnover
time). For Jovian conditions at early times after formation (when convection is
vigorous enough to mix a large fraction of the planet), we find the erosion
time to be roughly $10^{9}~\mathrm{yrs}$ in the non-rotating case and
$10^{11}~\mathrm{yrs}$ in the rotating case. Thus, the current existence of
convective staircases within the deep interiors of giant planets is a strong
possibility, and rotation could be an important factor in the preservation of
their fuzzy cores.