Boundary-layer development beyond a critical value

Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problem...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Merkin, J. H. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Boundary-layer solutions Initial-value problems Large time behaviour Finite-time singularity

Übergeordnetes Werk:	Enthalten in: Meccanica - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966, 54(2018), 1-2 vom: 17. Dez., Seite 85-100
Übergeordnetes Werk:	volume:54 ; year:2018 ; number:1-2 ; day:17 ; month:12 ; pages:85-100

Links:	Volltext

DOI / URN:	10.1007/s11012-018-00926-9

Katalog-ID:	SPR015704432

Internformat


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520			\|a Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$.
650		4	\|a Boundary-layer solutions \|7 (dpeaa)DE-He213
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650		4	\|a Finite-time singularity \|7 (dpeaa)DE-He213
773	0	8	\|i Enthalten in \|t Meccanica \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 \|g 54(2018), 1-2 vom: 17. Dez., Seite 85-100 \|w (DE-627)311009638 \|w (DE-600)2004031-3 \|x 1572-9648 \|7 nnns
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912			\|a GBV_ILN_40
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912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
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912			\|a GBV_ILN_100
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912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
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Indexfelder

author_variant	j h m jh jhm
matchkey_str	article:15729648:2018----::onayaedvlpeteodc
hierarchy_sort_str	2018
bklnumber	33.11 50.30 50.31
publishDate	2018
allfields	10.1007/s11012-018-00926-9 doi (DE-627)SPR015704432 (SPR)s11012-018-00926-9-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Merkin, J. H. verfasserin aut Boundary-layer development beyond a critical value 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$. Boundary-layer solutions (dpeaa)DE-He213 Initial-value problems (dpeaa)DE-He213 Large time behaviour (dpeaa)DE-He213 Finite-time singularity (dpeaa)DE-He213 Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 54(2018), 1-2 vom: 17. Dez., Seite 85-100 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100 https://dx.doi.org/10.1007/s11012-018-00926-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 54 2018 1-2 17 12 85-100
spelling	10.1007/s11012-018-00926-9 doi (DE-627)SPR015704432 (SPR)s11012-018-00926-9-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Merkin, J. H. verfasserin aut Boundary-layer development beyond a critical value 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$. Boundary-layer solutions (dpeaa)DE-He213 Initial-value problems (dpeaa)DE-He213 Large time behaviour (dpeaa)DE-He213 Finite-time singularity (dpeaa)DE-He213 Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 54(2018), 1-2 vom: 17. Dez., Seite 85-100 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100 https://dx.doi.org/10.1007/s11012-018-00926-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 54 2018 1-2 17 12 85-100
allfields_unstemmed	10.1007/s11012-018-00926-9 doi (DE-627)SPR015704432 (SPR)s11012-018-00926-9-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Merkin, J. H. verfasserin aut Boundary-layer development beyond a critical value 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$. Boundary-layer solutions (dpeaa)DE-He213 Initial-value problems (dpeaa)DE-He213 Large time behaviour (dpeaa)DE-He213 Finite-time singularity (dpeaa)DE-He213 Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 54(2018), 1-2 vom: 17. Dez., Seite 85-100 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100 https://dx.doi.org/10.1007/s11012-018-00926-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 54 2018 1-2 17 12 85-100
allfieldsGer	10.1007/s11012-018-00926-9 doi (DE-627)SPR015704432 (SPR)s11012-018-00926-9-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Merkin, J. H. verfasserin aut Boundary-layer development beyond a critical value 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$. Boundary-layer solutions (dpeaa)DE-He213 Initial-value problems (dpeaa)DE-He213 Large time behaviour (dpeaa)DE-He213 Finite-time singularity (dpeaa)DE-He213 Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 54(2018), 1-2 vom: 17. Dez., Seite 85-100 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100 https://dx.doi.org/10.1007/s11012-018-00926-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 54 2018 1-2 17 12 85-100
allfieldsSound	10.1007/s11012-018-00926-9 doi (DE-627)SPR015704432 (SPR)s11012-018-00926-9-e DE-627 ger DE-627 rakwb eng 600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Merkin, J. H. verfasserin aut Boundary-layer development beyond a critical value 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$. Boundary-layer solutions (dpeaa)DE-He213 Initial-value problems (dpeaa)DE-He213 Large time behaviour (dpeaa)DE-He213 Finite-time singularity (dpeaa)DE-He213 Enthalten in Meccanica Dordrecht [u.a.] : Springer Science + Business Media B.V, 1966 54(2018), 1-2 vom: 17. Dez., Seite 85-100 (DE-627)311009638 (DE-600)2004031-3 1572-9648 nnns volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100 https://dx.doi.org/10.1007/s11012-018-00926-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 33.11 ASE 50.30 ASE 50.31 ASE AR 54 2018 1-2 17 12 85-100
language	English
source	Enthalten in Meccanica 54(2018), 1-2 vom: 17. Dez., Seite 85-100 volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100
sourceStr	Enthalten in Meccanica 54(2018), 1-2 vom: 17. Dez., Seite 85-100 volume:54 year:2018 number:1-2 day:17 month:12 pages:85-100
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Boundary-layer solutions Initial-value problems Large time behaviour Finite-time singularity
dewey-raw	600
isfreeaccess_bool	false
container_title	Meccanica
authorswithroles_txt_mv	Merkin, J. H. @@aut@@
publishDateDaySort_date	2018-12-17T00:00:00Z
hierarchy_top_id	311009638
dewey-sort	3600
id	SPR015704432
language_de	englisch
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H.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Boundary-layer development beyond a critical value</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. 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author	Merkin, J. H.
spellingShingle	Merkin, J. H. ddc 600 bkl 33.11 bkl 50.30 bkl 50.31 misc Boundary-layer solutions misc Initial-value problems misc Large time behaviour misc Finite-time singularity Boundary-layer development beyond a critical value
authorStr	Merkin, J. H.
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topic_title	600 ASE 33.11 bkl 50.30 bkl 50.31 bkl Boundary-layer development beyond a critical value Boundary-layer solutions (dpeaa)DE-He213 Initial-value problems (dpeaa)DE-He213 Large time behaviour (dpeaa)DE-He213 Finite-time singularity (dpeaa)DE-He213
topic	ddc 600 bkl 33.11 bkl 50.30 bkl 50.31 misc Boundary-layer solutions misc Initial-value problems misc Large time behaviour misc Finite-time singularity
topic_unstemmed	ddc 600 bkl 33.11 bkl 50.30 bkl 50.31 misc Boundary-layer solutions misc Initial-value problems misc Large time behaviour misc Finite-time singularity
topic_browse	ddc 600 bkl 33.11 bkl 50.30 bkl 50.31 misc Boundary-layer solutions misc Initial-value problems misc Large time behaviour misc Finite-time singularity
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title	Boundary-layer development beyond a critical value
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title_full	Boundary-layer development beyond a critical value
author_sort	Merkin, J. H.
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title_sort	boundary-layer development beyond a critical value
title_auth	Boundary-layer development beyond a critical value
abstract	Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$.
abstractGer	Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$.
abstract_unstemmed	Abstract Two initial-value problems are considered involving a parameter %$\alpha %$, the corresponding steady states have a critical value at %$\alpha =\alpha _c<0%$ with steady state solutions possible only if %$\alpha \ge \alpha _c%$. The aim is to compare how the solution to these two problems evolves in time. For the first problem we find that a solution exists for all time with a two-region structure having a self-similar relatively thin front region moving away from the wall and an inner inviscid region, increasing exponentially in thickness at a rate proportional to %$\hbox {e}^{\|\alpha \|\,t}%$. A finite-time singularity develops in the second problem, the nature of this singularity being derived in terms of the time difference %$\tau =t_s-t%$, where the singularity occurs at time %$t_s%$, showing that the velocity becomes singular at a rate proportional to %$\tau ^{-1}%$ and the thickness of the boundary-layer increasing at a rate proportional to %$\tau ^{-1/2}%$.
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container_issue	1-2
title_short	Boundary-layer development beyond a critical value
url	https://dx.doi.org/10.1007/s11012-018-00926-9
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doi_str	10.1007/s11012-018-00926-9
up_date	2024-07-03T18:04:29.613Z
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