Fully 3D fluid outflow from a spherical source

Lawrence  Forbes; Stephen Walters

doi:10.21914/anziamj.v64.17015

Authors

Lawrence Forbes University of Tasmania https://orcid.org/0000-0002-9135-3594
Stephen Walters University of Tasmania https://orcid.org/0000-0002-4480-767X

DOI:

https://doi.org/10.21914/anziamj.v64.17015

Keywords:

distributed source, interfacial flows, spectral methods, stability

Abstract

We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories are also discussed and an approximate stability condition for early stages in the outflow is derived. Nonlinear solutions are presented and different outflow shapes adopted by the fluid interface are investigated.

doi: 10.1017/S1446181122000098

Author Biographies

Lawrence Forbes, University of Tasmania

Mathematics Department, University of Tasmania, Hobart TAS 7005, Australia.

Stephen Walters, University of Tasmania