Motion of unstable two interfaces in a three-layer fluid with a non-zero uniform current
- 13 September 2021
- journal article
- research article
- Published by IOP Publishing in Fluid Dynamics Research
- Vol. 53 (5), 055502
- https://doi.org/10.1088/1873-7005/ac2620
Abstract
The nonlinear motion of two interfaces in a three-layer fluid with density stratification is investigated theoretically and numerically. We consider the situation such that a uniform current is present in one of the three layers. The linear dispersion relation is calculated by the Newton's method, from which the initial conditions for numerical computations are determined. When the uniform current is present in the upper (lower) layer, strong vorticity is induced on the upper (lower) interface, and it rolls up involving the other interface at the late stage of computations. When the current is present in the middle layer, a varicose wave appears at the initial stage, and it evolves into an asymmetric heart-shaped vortex sheet at the last computed stage. These phenomena are presented using the vortex sheet model (VSM) with and without regularizations.Keywords
Funding Information
- Japan Society for the Promotion of Science (17K05371)
- Osaka University (the joint research project of ILE)
- Osaka City University (Strategic Research Grant for top priority research)
This publication has 53 references indexed in Scilit:
- MAGNETIC FIELD AMPLIFICATION ASSOCIATED WITH THE RICHTMYER-MESHKOV INSTABILITYThe Astrophysical Journal, 2012
- A comparison of blob methods for vortex sheet roll-upJournal of Fluid Mechanics, 2006
- Linear instability of a corrugated vortex sheet – a model for streak instabilityJournal of Fluid Mechanics, 2003
- Varicose instabilities in turbulent boundary layersPhysics of Fluids, 2002
- Shock–planar curtain interactions in two dimensions: Emergence of vortex double layers, vortex projectiles, and decaying stratified turbulencePhysics of Fluids, 2002
- On the connection between thin vortex layers and vortex sheetsJournal of Fluid Mechanics, 1990
- On the Numerical Solution of the Regularized Birkhoff EquationsMathematics of Computation, 1989
- Quadrature methods for periodic singular and weakly singular Fredholm integral equationsJournal of Scientific Computing, 1988
- Rayleigh-Taylor instabilities in stratified fluidsPhysical Review A, 1982
- ‘Explosive’ resonant wave interactions in a three-layer fluid flowJournal of Fluid Mechanics, 1979