European Journal of Applied Mathematics


A note on the flow of a homogeneous intrusion into a two-layer fluid

G. C. HOCKINGa1 and L. K. FORBESa2

a1 Mathematics & Statistics, Murdoch University, Murdoch, WA, 6150, Australia email:

a2 School of Mathematics & Physics, University of Tasmania, Hobart, Australia


The intrusion of a constant density fluid at the interface of a two-layer fluid is considered. Numerical solutions are computed for a model of a steady intrusion resulting from flow down a bank and across a broad lake or reservoir. The incoming fluid is homogeneous and spreads across the lake at its level of neutral buoyancy. Solutions are obtained for a range of different inflow angles, flow rate and density differences. Except in extreme cases, the nature of the solution is predicted quite well by linear theory, with the wavelength at any Froude number given by a dispersion relation and wave steepness determined largely by entry angle. However, some extreme solutions with rounded meandering flows and non-unique solutions in the parameter space are also obtained.

(Received August 02 2007)

(Revised February 23 2007)