Weakly nonlinear evolution of a cavity on a free-surface
Abstract
We formulate a second order asymptotic solution in two dimensional Cartesian coordinates to the initial value problem involving a finite-amplitude, localized perturbation resembling a cavity (Gaussian depression) on the free-surface of a horizontally unbounded, infinitely deep liquid. We employ the Hamiltonian theory for inviscid capillary-gravity waves and expand upto the three-wave interaction Hamiltonian. The Zakharov equation is numerically solved for the aforementioned Cauchy data on the canonical coordinates in our reduced Hamilton's equation. We compare the time evolution of our weakly nonlinear interfacial profile with the corresponding linear solution to the classical Cauchy-Poisson problem and results obtained from Direct Numerical Simulation (DNS) of the Euler's equation (including both gravity and surface tension) using Basilisk [basilisk.fr].
We thank Prime Minister's Research Fellowship (PMRF), Govt. of India and Department of Science and Technology, DST-SERB Grants EMR/2016/000830 and MTR/2019/001240 for funding support.- Publication:
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APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- 2020
- Bibcode:
- 2020APS..DFDQ12007B