Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability
Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defin...
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description | Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r0/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r0/λ is large enough (r0≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r0 can reduce the NSA of the second harmonic for arbitrary A at r0≲2λ while increase it for A ≲ 0.6 at r0≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design. |
doi_str_mv | 10.1063/1.4901088 |
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fullrecord | <record><control><sourceid>proquest_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_22403243</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2126503009</sourcerecordid><originalsourceid>FETCH-LOGICAL-c320t-b0f7bd7cadfcc62c97d122ff9d6c423438eaada0f7eba6619c529e9fe277091d3</originalsourceid><addsrcrecordid>eNpFkctKBDEQRYMo-Fz4BwFXLlrz6El3liLjAwYEUXAXqvNwMvQkY5JG5hf8aqMjuLrFrVOXogqhc0quKBH8ml61klDS93voqIpsOtG1-z91Rxoh2rdDdJzzihDSill_hL7mzlldMo4O--CLhxEnMH76dcrSVrfY5EBbDMHgm_IZo8FhWg824RhwiGH0wULCGcqUoPhqwnoz-jIZm-s41ttKmOR1zX6G7Wj9-7J5qUVMtZ0LDL7S21N04GDM9uxPT9Dr3fzl9qFZPN0_3t4sGs0ZKc1AXDeYToNxWgumZWcoY85JI3TLeMt7C2CgUnYAIajUMyatdJZ1HZHU8BN0scuNuXiVtS9WL3UMod5BMdYSzlr-T21S_JhsLmoVpxTqYopRJmaEEyIrdbmjdIo5J-vUJvk1pK2iRP08RFH19xD-Dd7wgCQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2126503009</pqid></control><display><type>article</type><title>Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability</title><source>AIP Journals Complete</source><source>Alma/SFX Local Collection</source><creator>Liu, Wanhai ; Yu, Changping ; Li, Xinliang</creator><creatorcontrib>Liu, Wanhai ; Yu, Changping ; Li, Xinliang</creatorcontrib><description>Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r0/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r0/λ is large enough (r0≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r0 can reduce the NSA of the second harmonic for arbitrary A at r0≲2λ while increase it for A ≲ 0.6 at r0≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.</description><identifier>ISSN: 1070-664X</identifier><identifier>EISSN: 1089-7674</identifier><identifier>DOI: 10.1063/1.4901088</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY ; AMPLITUDES ; CYLINDRICAL CONFIGURATION ; DISTURBANCES ; HARMONICS ; Inertial confinement fusion ; INTERFACES ; Nonlinear analysis ; NONLINEAR PROBLEMS ; PERTURBATION THEORY ; Plasma physics ; RAYLEIGH-TAYLOR INSTABILITY ; SATURATION ; Stability ; Stability analysis ; Taylor instability ; THERMONUCLEAR IGNITION</subject><ispartof>Physics of plasmas, 2014-11, Vol.21 (11)</ispartof><rights>2014 AIP Publishing LLC.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c320t-b0f7bd7cadfcc62c97d122ff9d6c423438eaada0f7eba6619c529e9fe277091d3</citedby><cites>FETCH-LOGICAL-c320t-b0f7bd7cadfcc62c97d122ff9d6c423438eaada0f7eba6619c529e9fe277091d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/22403243$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Wanhai</creatorcontrib><creatorcontrib>Yu, Changping</creatorcontrib><creatorcontrib>Li, Xinliang</creatorcontrib><title>Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability</title><title>Physics of plasmas</title><description>Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r0/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r0/λ is large enough (r0≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r0 can reduce the NSA of the second harmonic for arbitrary A at r0≲2λ while increase it for A ≲ 0.6 at r0≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.</description><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</subject><subject>AMPLITUDES</subject><subject>CYLINDRICAL CONFIGURATION</subject><subject>DISTURBANCES</subject><subject>HARMONICS</subject><subject>Inertial confinement fusion</subject><subject>INTERFACES</subject><subject>Nonlinear analysis</subject><subject>NONLINEAR PROBLEMS</subject><subject>PERTURBATION THEORY</subject><subject>Plasma physics</subject><subject>RAYLEIGH-TAYLOR INSTABILITY</subject><subject>SATURATION</subject><subject>Stability</subject><subject>Stability analysis</subject><subject>Taylor instability</subject><subject>THERMONUCLEAR IGNITION</subject><issn>1070-664X</issn><issn>1089-7674</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNpFkctKBDEQRYMo-Fz4BwFXLlrz6El3liLjAwYEUXAXqvNwMvQkY5JG5hf8aqMjuLrFrVOXogqhc0quKBH8ml61klDS93voqIpsOtG1-z91Rxoh2rdDdJzzihDSill_hL7mzlldMo4O--CLhxEnMH76dcrSVrfY5EBbDMHgm_IZo8FhWg824RhwiGH0wULCGcqUoPhqwnoz-jIZm-s41ttKmOR1zX6G7Wj9-7J5qUVMtZ0LDL7S21N04GDM9uxPT9Dr3fzl9qFZPN0_3t4sGs0ZKc1AXDeYToNxWgumZWcoY85JI3TLeMt7C2CgUnYAIajUMyatdJZ1HZHU8BN0scuNuXiVtS9WL3UMod5BMdYSzlr-T21S_JhsLmoVpxTqYopRJmaEEyIrdbmjdIo5J-vUJvk1pK2iRP08RFH19xD-Dd7wgCQ</recordid><startdate>20141101</startdate><enddate>20141101</enddate><creator>Liu, Wanhai</creator><creator>Yu, Changping</creator><creator>Li, Xinliang</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20141101</creationdate><title>Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability</title><author>Liu, Wanhai ; Yu, Changping ; Li, Xinliang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c320t-b0f7bd7cadfcc62c97d122ff9d6c423438eaada0f7eba6619c529e9fe277091d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</topic><topic>AMPLITUDES</topic><topic>CYLINDRICAL CONFIGURATION</topic><topic>DISTURBANCES</topic><topic>HARMONICS</topic><topic>Inertial confinement fusion</topic><topic>INTERFACES</topic><topic>Nonlinear analysis</topic><topic>NONLINEAR PROBLEMS</topic><topic>PERTURBATION THEORY</topic><topic>Plasma physics</topic><topic>RAYLEIGH-TAYLOR INSTABILITY</topic><topic>SATURATION</topic><topic>Stability</topic><topic>Stability analysis</topic><topic>Taylor instability</topic><topic>THERMONUCLEAR IGNITION</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Wanhai</creatorcontrib><creatorcontrib>Yu, Changping</creatorcontrib><creatorcontrib>Li, Xinliang</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Physics of plasmas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Wanhai</au><au>Yu, Changping</au><au>Li, Xinliang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability</atitle><jtitle>Physics of plasmas</jtitle><date>2014-11-01</date><risdate>2014</risdate><volume>21</volume><issue>11</issue><issn>1070-664X</issn><eissn>1089-7674</eissn><abstract>Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r0/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r0/λ is large enough (r0≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r0 can reduce the NSA of the second harmonic for arbitrary A at r0≲2λ while increase it for A ≲ 0.6 at r0≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4901088</doi><oa>free_for_read</oa></addata></record> |
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subjects | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY AMPLITUDES CYLINDRICAL CONFIGURATION DISTURBANCES HARMONICS Inertial confinement fusion INTERFACES Nonlinear analysis NONLINEAR PROBLEMS PERTURBATION THEORY Plasma physics RAYLEIGH-TAYLOR INSTABILITY SATURATION Stability Stability analysis Taylor instability THERMONUCLEAR IGNITION |
title | Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability |
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