Consistent energy-based framework of amplification mechanisms for the second mode in hypersonic boundary layers
The second mode is of general interest in hypersonic boundary layer flows due to its underlying responsibilities for transition to turbulence. However, a long-term debate exists on the detailed energy sources that sustain the modal exponential growth. Currently, three influential energy-based approa...
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Veröffentlicht in: | Physics of fluids (1994) 2023-12, Vol.35 (12) |
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description | The second mode is of general interest in hypersonic boundary layer flows due to its underlying responsibilities for transition to turbulence. However, a long-term debate exists on the detailed energy sources that sustain the modal exponential growth. Currently, three influential energy-based approaches appear to show different significant energy sources due to dissimilar mathematical formulations, including the momentum potential theory, the inviscid Lagrangian energy analysis, and the relative phase analysis. In this study, these three fundamental approaches are employed and examined in conjunction with direct numerical simulations. The purpose is to seek a possible unified explanation of the source terms that dominate the exponential evolution of the second mode. In the considered Mach 6 flow state, all three approaches consistently point to the same local energy amplification route driven by two pronounced source terms: the dilatation term in the near-wall region and the Reynolds thermal stress term or heat exchange term across the outer layer region, depending on the selection of the specific energy norm. The mathematical forms of the corresponding sources are derived or discussed explicitly. Theoretical and simulation results provide a unified understanding of the local energy amplification mechanisms of the second mode. |
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However, a long-term debate exists on the detailed energy sources that sustain the modal exponential growth. Currently, three influential energy-based approaches appear to show different significant energy sources due to dissimilar mathematical formulations, including the momentum potential theory, the inviscid Lagrangian energy analysis, and the relative phase analysis. In this study, these three fundamental approaches are employed and examined in conjunction with direct numerical simulations. The purpose is to seek a possible unified explanation of the source terms that dominate the exponential evolution of the second mode. In the considered Mach 6 flow state, all three approaches consistently point to the same local energy amplification route driven by two pronounced source terms: the dilatation term in the near-wall region and the Reynolds thermal stress term or heat exchange term across the outer layer region, depending on the selection of the specific energy norm. The mathematical forms of the corresponding sources are derived or discussed explicitly. Theoretical and simulation results provide a unified understanding of the local energy amplification mechanisms of the second mode.</description><identifier>ISSN: 1070-6631</identifier><identifier>EISSN: 1089-7666</identifier><identifier>DOI: 10.1063/5.0176245</identifier><identifier>CODEN: PHFLE6</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Amplification ; Boundary layer flow ; Boundary layer transition ; Direct numerical simulation ; Energy resources ; Energy sources ; Heat exchange ; Hypersonic boundary layer ; Mathematical analysis ; Potential theory ; Specific energy ; Thermal stress</subject><ispartof>Physics of fluids (1994), 2023-12, Vol.35 (12)</ispartof><rights>Author(s)</rights><rights>2023 Author(s). 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The mathematical forms of the corresponding sources are derived or discussed explicitly. Theoretical and simulation results provide a unified understanding of the local energy amplification mechanisms of the second mode.</description><subject>Amplification</subject><subject>Boundary layer flow</subject><subject>Boundary layer transition</subject><subject>Direct numerical simulation</subject><subject>Energy resources</subject><subject>Energy sources</subject><subject>Heat exchange</subject><subject>Hypersonic boundary layer</subject><subject>Mathematical analysis</subject><subject>Potential theory</subject><subject>Specific energy</subject><subject>Thermal stress</subject><issn>1070-6631</issn><issn>1089-7666</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsFYP_oMFTwqps0l2khyl-AUFL3oO-2m3NrtxN0Xy701tz55mGB7eeXkIuWawYIDFPV8AqzAv-QmZMaibrELE0_1eQYZYsHNykdIGAIomxxkJy-CTS4PxAzXexM8xkyIZTW0UnfkJ8YsGS0XXb511SgwueNoZtRbepS5RGyId1oYmo4LXtAvaUOfpeuxNTME7RWXYeS3iSLdinG6X5MyKbTJXxzknH0-P78uXbPX2_Lp8WGUqr6thaipBcM1AyzLnlnHNZYmyKZFLC7WoCyawsCUoIwQ2kmtV6gI1ggQrhC7m5OaQ28fwvTNpaDdhF_30ss3rpilrxCafqNsDpWJIKRrb9tF1U9uWQbv32fL26HNi7w5sUm74E_EP_AviVnda</recordid><startdate>202312</startdate><enddate>202312</enddate><creator>Chen, Yifeng</creator><creator>Guo, Peixu</creator><creator>Wen, Chihyung</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-6185-1058</orcidid><orcidid>https://orcid.org/0000-0002-1181-8786</orcidid><orcidid>https://orcid.org/0000-0001-6952-023X</orcidid></search><sort><creationdate>202312</creationdate><title>Consistent energy-based framework of amplification mechanisms for the second mode in hypersonic boundary layers</title><author>Chen, Yifeng ; Guo, Peixu ; Wen, Chihyung</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c287t-66b0a5d10db425f15d5b46b9465bf08a831a63f40ceaa69b5dc4d36d60b0faad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Amplification</topic><topic>Boundary layer flow</topic><topic>Boundary layer transition</topic><topic>Direct numerical simulation</topic><topic>Energy resources</topic><topic>Energy sources</topic><topic>Heat exchange</topic><topic>Hypersonic boundary layer</topic><topic>Mathematical analysis</topic><topic>Potential theory</topic><topic>Specific energy</topic><topic>Thermal stress</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Yifeng</creatorcontrib><creatorcontrib>Guo, Peixu</creatorcontrib><creatorcontrib>Wen, Chihyung</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics of fluids (1994)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Yifeng</au><au>Guo, Peixu</au><au>Wen, Chihyung</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Consistent energy-based framework of amplification mechanisms for the second mode in hypersonic boundary layers</atitle><jtitle>Physics of fluids (1994)</jtitle><date>2023-12</date><risdate>2023</risdate><volume>35</volume><issue>12</issue><issn>1070-6631</issn><eissn>1089-7666</eissn><coden>PHFLE6</coden><abstract>The second mode is of general interest in hypersonic boundary layer flows due to its underlying responsibilities for transition to turbulence. However, a long-term debate exists on the detailed energy sources that sustain the modal exponential growth. Currently, three influential energy-based approaches appear to show different significant energy sources due to dissimilar mathematical formulations, including the momentum potential theory, the inviscid Lagrangian energy analysis, and the relative phase analysis. In this study, these three fundamental approaches are employed and examined in conjunction with direct numerical simulations. The purpose is to seek a possible unified explanation of the source terms that dominate the exponential evolution of the second mode. In the considered Mach 6 flow state, all three approaches consistently point to the same local energy amplification route driven by two pronounced source terms: the dilatation term in the near-wall region and the Reynolds thermal stress term or heat exchange term across the outer layer region, depending on the selection of the specific energy norm. 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subjects | Amplification Boundary layer flow Boundary layer transition Direct numerical simulation Energy resources Energy sources Heat exchange Hypersonic boundary layer Mathematical analysis Potential theory Specific energy Thermal stress |
title | Consistent energy-based framework of amplification mechanisms for the second mode in hypersonic boundary layers |
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