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 as , where , energy (density) flux as . The proportional factor , known as the Kolmogorov constant, has a theoretical value of (we show that this value holds only after a formulation in the original derivation is corrected). The scaling has been extensively, but not conclusively, tested; the scaling has been investigated experimentally, but until recently remains controversial, while direct confirmation of the value of remains elusive. We conduct a direct numerical investigation implementing the primitive Euler equations. For sufficiently high nonlinearity, the theoretical and scalings as well as value of are well recovered by our numerical results. For a given number of numerical modes , as nonlinearity decreases, the long-time spectra deviate from theoretical predictions with respect to scaling with , with calculated values of and , all due to finite box effect.
- Received 28 August 2013
DOI:https://doi.org/10.1103/PhysRevLett.113.094501
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