Vertical shear instability with partially reflecting boundary conditions
ABSTRACT The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary discs (PPDs). Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disc surfaces. VSI depends critically on the boundary behaviours of waves at...
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Veröffentlicht in: | Monthly notices of the Royal Astronomical Society 2024-10, Vol.534 (1), p.948-956 |
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description | ABSTRACT
The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary discs (PPDs). Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disc surfaces. VSI depends critically on the boundary behaviours of waves at the disc surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disc surfaces naturally lead to non-symmetric modes relative to the disc mid-plane. The potential implications of our studies for further understanding planetary formation and evolution in PPDs are also briefly discussed. |
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The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary discs (PPDs). Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disc surfaces. VSI depends critically on the boundary behaviours of waves at the disc surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disc surfaces naturally lead to non-symmetric modes relative to the disc mid-plane. The potential implications of our studies for further understanding planetary formation and evolution in PPDs are also briefly discussed.</description><identifier>ISSN: 0035-8711</identifier><identifier>EISSN: 1365-2966</identifier><identifier>DOI: 10.1093/mnras/stae2141</identifier><language>eng</language><publisher>London: Oxford University Press</publisher><subject>Axisymmetric bodies ; Axisymmetric flow ; Boundary conditions ; Flow stability ; Kelvin-Helmholtz instability ; Numerical analysis ; Planet formation ; Planetary evolution ; Protoplanetary disks ; Wavelengths</subject><ispartof>Monthly notices of the Royal Astronomical Society, 2024-10, Vol.534 (1), p.948-956</ispartof><rights>2024 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. 2024</rights><rights>2024 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c226t-3bc19216ba8239fb6959545972bd39d7421dacf4d476206e5ddaedaadcc09b853</cites><orcidid>0000-0003-3180-0038 ; 0009-0003-7467-362X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,864,1604,27924,27925</link.rule.ids></links><search><creatorcontrib>Wu, Yuzi</creatorcontrib><creatorcontrib>Yu, Cong</creatorcontrib><creatorcontrib>Cui, Can</creatorcontrib><title>Vertical shear instability with partially reflecting boundary conditions</title><title>Monthly notices of the Royal Astronomical Society</title><description>ABSTRACT
The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary discs (PPDs). Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disc surfaces. VSI depends critically on the boundary behaviours of waves at the disc surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disc surfaces naturally lead to non-symmetric modes relative to the disc mid-plane. The potential implications of our studies for further understanding planetary formation and evolution in PPDs are also briefly discussed.</description><subject>Axisymmetric bodies</subject><subject>Axisymmetric flow</subject><subject>Boundary conditions</subject><subject>Flow stability</subject><subject>Kelvin-Helmholtz instability</subject><subject>Numerical analysis</subject><subject>Planet formation</subject><subject>Planetary evolution</subject><subject>Protoplanetary disks</subject><subject>Wavelengths</subject><issn>0035-8711</issn><issn>1365-2966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>TOX</sourceid><recordid>eNqFkD1PwzAYhC0EEqWwMkdiYkjr78QjqoAiVWIBVstfoa5SJ9iOUP89hsLM9A733L2nA-AawQWCgiz3Iaq0TFk5jCg6ATNEOKux4PwUzCAkrG4bhM7BRUo7CCElmM_A-s3F7I3qq7R1KlY-lADte58P1afP22pURVd9f6ii63pnsg_vlR6mYFU8VGYI1mc_hHQJzjrVJ3f1e-fg9eH-ZbWuN8-PT6u7TW0w5rkm2iCBEdeqxUR0mgsmGGWiwdoSYRuKkVWmo5Y2HEPumLXKWaWsMVDolpE5uDnmjnH4mFzKcjdMMZSXkiBEqBANF4VaHCkTh5RKczlGvy-NJYLyey35s5b8W6sYbo-GYRr_Y78A8F9vJA</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Wu, Yuzi</creator><creator>Yu, Cong</creator><creator>Cui, Can</creator><general>Oxford University Press</general><scope>TOX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-3180-0038</orcidid><orcidid>https://orcid.org/0009-0003-7467-362X</orcidid></search><sort><creationdate>20241001</creationdate><title>Vertical shear instability with partially reflecting boundary conditions</title><author>Wu, Yuzi ; Yu, Cong ; Cui, Can</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c226t-3bc19216ba8239fb6959545972bd39d7421dacf4d476206e5ddaedaadcc09b853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Axisymmetric bodies</topic><topic>Axisymmetric flow</topic><topic>Boundary conditions</topic><topic>Flow stability</topic><topic>Kelvin-Helmholtz instability</topic><topic>Numerical analysis</topic><topic>Planet formation</topic><topic>Planetary evolution</topic><topic>Protoplanetary disks</topic><topic>Wavelengths</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Yuzi</creatorcontrib><creatorcontrib>Yu, Cong</creatorcontrib><creatorcontrib>Cui, Can</creatorcontrib><collection>Oxford Journals Open Access Collection</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Monthly notices of the Royal Astronomical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Yuzi</au><au>Yu, Cong</au><au>Cui, Can</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Vertical shear instability with partially reflecting boundary conditions</atitle><jtitle>Monthly notices of the Royal Astronomical Society</jtitle><date>2024-10-01</date><risdate>2024</risdate><volume>534</volume><issue>1</issue><spage>948</spage><epage>956</epage><pages>948-956</pages><issn>0035-8711</issn><eissn>1365-2966</eissn><abstract>ABSTRACT
The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary discs (PPDs). Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disc surfaces. VSI depends critically on the boundary behaviours of waves at the disc surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disc surfaces naturally lead to non-symmetric modes relative to the disc mid-plane. The potential implications of our studies for further understanding planetary formation and evolution in PPDs are also briefly discussed.</abstract><cop>London</cop><pub>Oxford University Press</pub><doi>10.1093/mnras/stae2141</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0003-3180-0038</orcidid><orcidid>https://orcid.org/0009-0003-7467-362X</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Axisymmetric bodies Axisymmetric flow Boundary conditions Flow stability Kelvin-Helmholtz instability Numerical analysis Planet formation Planetary evolution Protoplanetary disks Wavelengths |
title | Vertical shear instability with partially reflecting boundary conditions |
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