Direct Numerical Investigation of Turbulence of Capillary Waves

Yulin Pan and Dick K. P. Yue
Phys. Rev. Lett. 113, 094501 – Published 27 August 2014

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 Iηkα, where α=α0=19/4, energy (density) flux P as P1/2. The proportional factor C, known as the Kolmogorov constant, has a theoretical value of C=C0=9.85 (we show that this value holds only after a formulation in the original derivation is corrected). The k19/4 scaling has been extensively, but not conclusively, tested; the P1/2 scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of C0 remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical k19/4 and P1/2 scalings as well as value of C0 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<α0 and C>C0, all due to finite box effect.

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  • Received 28 August 2013

DOI:https://doi.org/10.1103/PhysRevLett.113.094501

© 2014 American Physical Society

Authors & Affiliations

Yulin Pan and Dick K. P. Yue

  • Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

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Vol. 113, Iss. 9 — 29 August 2014

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