AN EXACTLY SOLVABLE MODEL OF INTRUSION
Abstract
The conformal-mapping approach (Bazant, Crowdy, 2005; Tanveer, 1993; Zakharov, Dyachenko, 1996; Yoshikawa, Balk, 1999, 2003) is used to formulate a minimal exactly solvable model for studying the lock-exchange gravity currents in an infinite horizontal channel (Simpson, 1999; Ungarish, 2009). The distinctive feature of such flows is a pressure jump which arises at the interface between two incompressible fluids of different densities at once after removing a lock gate. Because of this, the process of intrusion does not fit into Benjamin’s scenario (Benjamin, 1968) but rather is like propagation of two shock waves.
This work was supported by the RFBR (Project No. 18-05-00831) and by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».
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