a1 Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK [email protected]
We consider the behaviour of a gravity current in a porous medium when the horizontal surface along which it spreads is punctuated either by narrow fractures or by permeable regions of limited extent. We derive steady-state solutions for the current, and show that these form part of a long-time asymptotic description which may also include a self-similar ‘leakage current’ propagating beyond the fractured region with a length proportional to t1/2. We discuss the conditions under which a current can be completely trapped by a permeable region or a series of fractures.
(Received February 27 2006)
(Revised March 21 2007)