Direct Numerical Investigation of Turbulence of Capillary Waves
We consider the inertial range spectrum of capillary wave turbulence. Under the assumptions of weak turbulence, the theoretical surface elevation spectrum scales with wave number k as I[subscript η] ∼ k[superscript α], where α = α[subscript 0] = -19/4, energy (density) flux P as P[superscript 1/2]....
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| Format: | Article |
| Language: | English |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/89142 https://orcid.org/0000-0003-1273-9964 https://orcid.org/0000-0001-9740-4404 |
| _version_ | 1826191371750342656 |
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| author | Pan, Yulin Yue, Dick K. P. Yue, Dick K. P. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Pan, Yulin Yue, Dick K. P. Yue, Dick K. P. |
| author_sort | Pan, Yulin |
| collection | MIT |
| description | We consider the inertial range spectrum of capillary wave turbulence. Under the assumptions of weak turbulence, the theoretical surface elevation spectrum scales with wave number k as I[subscript η] ∼ k[superscript α], where α = α[subscript 0] = -19/4, energy (density) flux P as P[superscript 1/2]. The proportional factor C, known as the Kolmogorov constant, has a theoretical value of C = C[subscript 0] = 9.85 (we show that this value holds only after a formulation in the original derivation is corrected). The k[superscript -19/4] scaling has been extensively, but not conclusively, tested; the P[superscript 1/2] scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of C[subscript 0] remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical k[superscript -19/4] and P[superscript 1/2] scalings as well as value of C[subscript 0] are well recovered by our numerical results. For a given number of numerical modes N, as nonlinearity decreases, the long-time spectra deviate from theoretical predictions with respect to scaling with P, with calculated values of α < α[subscript 0] and C > C[subscript 0], all due to finite box effect. |
| first_indexed | 2024-09-23T08:54:53Z |
| format | Article |
| id | mit-1721.1/89142 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:54:53Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/891422022-09-30T12:07:18Z Direct Numerical Investigation of Turbulence of Capillary Waves Pan, Yulin Yue, Dick K. P. Yue, Dick K. P. Massachusetts Institute of Technology. Department of Mechanical Engineering Pan, Yulin Yue, Dick K. P. We consider the inertial range spectrum of capillary wave turbulence. Under the assumptions of weak turbulence, the theoretical surface elevation spectrum scales with wave number k as I[subscript η] ∼ k[superscript α], where α = α[subscript 0] = -19/4, energy (density) flux P as P[superscript 1/2]. The proportional factor C, known as the Kolmogorov constant, has a theoretical value of C = C[subscript 0] = 9.85 (we show that this value holds only after a formulation in the original derivation is corrected). The k[superscript -19/4] scaling has been extensively, but not conclusively, tested; the P[superscript 1/2] scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of C[subscript 0] remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical k[superscript -19/4] and P[superscript 1/2] scalings as well as value of C[subscript 0] are well recovered by our numerical results. For a given number of numerical modes N, as nonlinearity decreases, the long-time spectra deviate from theoretical predictions with respect to scaling with P, with calculated values of α < α[subscript 0] and C > C[subscript 0], all due to finite box effect. 2014-09-02T19:14:49Z 2014-09-02T19:14:49Z 2014-08 2013-08 2014-08-28T18:48:53Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/89142 Pan, Yulin, and Dick K. P. Yue. "Direct Numerical Investigation of Turbulence of Capillary Waves." Phys. Rev. Lett. 113, 094501 (August 2014). © 2014 American Physical Society https://orcid.org/0000-0003-1273-9964 https://orcid.org/0000-0001-9740-4404 en http://dx.doi.org/10.1103/PhysRevLett.113.094501 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Pan, Yulin Yue, Dick K. P. Yue, Dick K. P. Direct Numerical Investigation of Turbulence of Capillary Waves |
| title | Direct Numerical Investigation of Turbulence of Capillary Waves |
| title_full | Direct Numerical Investigation of Turbulence of Capillary Waves |
| title_fullStr | Direct Numerical Investigation of Turbulence of Capillary Waves |
| title_full_unstemmed | Direct Numerical Investigation of Turbulence of Capillary Waves |
| title_short | Direct Numerical Investigation of Turbulence of Capillary Waves |
| title_sort | direct numerical investigation of turbulence of capillary waves |
| url | http://hdl.handle.net/1721.1/89142 https://orcid.org/0000-0003-1273-9964 https://orcid.org/0000-0001-9740-4404 |
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