The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water

A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravit...
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Autor*in:	Majumder D.P. [verfasserIn] Dhar A.K. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	capillary gravity waves randomness evolution equation instability 76b15 76e17

Übergeordnetes Werk:	In: International Journal of Applied Mechanics and Engineering - Sciendo, 2015, 20(2015), 4, Seite 835-855
Übergeordnetes Werk:	volume:20 ; year:2015 ; number:4 ; pages:835-855

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1515/ijame-2015-0054

Katalog-ID:	DOAJ049320890

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520			\|a A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
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spelling	10.1515/ijame-2015-0054 doi (DE-627)DOAJ049320890 (DE-599)DOAJ717e5bba14b643218340e78f2be7e406 DE-627 ger DE-627 rakwb eng TA349-359 Majumder D.P. verfasserin aut The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation. capillary gravity waves randomness evolution equation instability 76b15 76e17 Mechanics of engineering. Applied mechanics Dhar A.K. verfasserin aut In International Journal of Applied Mechanics and Engineering Sciendo, 2015 20(2015), 4, Seite 835-855 (DE-627)864734018 (DE-600)2864256-9 23539003 nnns volume:20 year:2015 number:4 pages:835-855 https://doi.org/10.1515/ijame-2015-0054 kostenfrei https://doaj.org/article/717e5bba14b643218340e78f2be7e406 kostenfrei https://doi.org/10.1515/ijame-2015-0054 kostenfrei https://doaj.org/toc/1734-4492 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4 835-855
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allfieldsGer	10.1515/ijame-2015-0054 doi (DE-627)DOAJ049320890 (DE-599)DOAJ717e5bba14b643218340e78f2be7e406 DE-627 ger DE-627 rakwb eng TA349-359 Majumder D.P. verfasserin aut The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation. capillary gravity waves randomness evolution equation instability 76b15 76e17 Mechanics of engineering. Applied mechanics Dhar A.K. verfasserin aut In International Journal of Applied Mechanics and Engineering Sciendo, 2015 20(2015), 4, Seite 835-855 (DE-627)864734018 (DE-600)2864256-9 23539003 nnns volume:20 year:2015 number:4 pages:835-855 https://doi.org/10.1515/ijame-2015-0054 kostenfrei https://doaj.org/article/717e5bba14b643218340e78f2be7e406 kostenfrei https://doi.org/10.1515/ijame-2015-0054 kostenfrei https://doaj.org/toc/1734-4492 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4 835-855
allfieldsSound	10.1515/ijame-2015-0054 doi (DE-627)DOAJ049320890 (DE-599)DOAJ717e5bba14b643218340e78f2be7e406 DE-627 ger DE-627 rakwb eng TA349-359 Majumder D.P. verfasserin aut The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation. capillary gravity waves randomness evolution equation instability 76b15 76e17 Mechanics of engineering. Applied mechanics Dhar A.K. verfasserin aut In International Journal of Applied Mechanics and Engineering Sciendo, 2015 20(2015), 4, Seite 835-855 (DE-627)864734018 (DE-600)2864256-9 23539003 nnns volume:20 year:2015 number:4 pages:835-855 https://doi.org/10.1515/ijame-2015-0054 kostenfrei https://doaj.org/article/717e5bba14b643218340e78f2be7e406 kostenfrei https://doi.org/10.1515/ijame-2015-0054 kostenfrei https://doaj.org/toc/1734-4492 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2015 4 835-855
language	English
source	In International Journal of Applied Mechanics and Engineering 20(2015), 4, Seite 835-855 volume:20 year:2015 number:4 pages:835-855
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spellingShingle	Majumder D.P. misc TA349-359 misc capillary gravity waves misc randomness misc evolution equation misc instability misc 76b15 misc 76e17 misc Mechanics of engineering. Applied mechanics The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water
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topic_title	TA349-359 The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water capillary gravity waves randomness evolution equation instability 76b15 76e17
topic	misc TA349-359 misc capillary gravity waves misc randomness misc evolution equation misc instability misc 76b15 misc 76e17 misc Mechanics of engineering. Applied mechanics
topic_unstemmed	misc TA349-359 misc capillary gravity waves misc randomness misc evolution equation misc instability misc 76b15 misc 76e17 misc Mechanics of engineering. Applied mechanics
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title	The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water
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title_full	The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water
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title_sort	effect of randomness on the stability of capillary gravity waves in the presence of air flowing over water
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title_auth	The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water
abstract	A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
abstractGer	A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
abstract_unstemmed	A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
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title_short	The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water
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