Direct Numerical Investigation of Turbulence of Capillary Waves
Name
PhysRevLett.113.094501.pdf
Size
1.24 MB
Format
Adobe PDF
Checksum (MD5)
3e7447104e71b05e1b2c3951a801317d
Author(s)
Pan, Yulin
Yue, Dick K. P.
Yue, Dick K. P.
Date Issued
August 2014
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
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
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevLett.113.094501
