Jet from a very large, surface-gravity wave
We demonstrate that gravity acting alone at large length scales, can produce a jet from a large amplitude, axisymmetric surface deformation imposed on a quiescent, deep pool of liquid. Mechanistically, the jet owes it origin to the focussing of a concentric, surface wave towards the axis of symmetry...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
22.04.2023
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Subjects | |
Online Access | Get full text |
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Summary: | We demonstrate that gravity acting alone at large length scales, can produce
a jet from a large amplitude, axisymmetric surface deformation imposed on a
quiescent, deep pool of liquid. Mechanistically, the jet owes it origin to the
focussing of a concentric, surface wave towards the axis of symmetry, quite
analogous to such focussing of capillary waves and resultant jet formation,
observed during bubble collapse at small scales. A weakly non linear theory
based on the method of multiple scales and the potential flow limit, is
presented for a modal (single mode) initial condition representing the solution
to the primary Cauchy Poisson problem. A pair of novel, coupled, amplitude
equations are derived governing the modulation of the primary mode. For
moderate values of the perturbation parameter epsilon (a measure of the initial
perturbation amplitude), our second order theory captures the overshoot
(incipient jet) at the axis of symmetry quite well, demonstrating good
agreement with numerical simulation of the incompressible, Euler's equation
with gravity (Popinet 2014) and no surface tension. Expectedly, our theory
becomes inaccurate as epsilon approaches unity. In this strongly nonlinear
regime, slender jets form with surface accelerations exceeding gravity by three
orders of magnitude. In this inertial regime, the jets observed in our
simulations show excellent agreement with the inertial, self-similar,
analytical solution by Longuet-Higgins (1983). The physical mechanism of
axisymmetric jet formation is explained based on mass conservation arguments.
We demonstrate that the underlying wave focussing mechanism, may be understood
in terms of radially inward motion of nodal points of a linearised,
axisymmetric, standing wave. |
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DOI: | 10.48550/arxiv.2304.11365 |