|M.Sc Student||Zemach Tamar|
|Subject||Gravity Currents: Two Layer and Asymptotic Extensions|
|Department||Department of Applied Mathematics||Supervisor||Professor Emeritus Marius Ungarish|
The behaviour of an inviscid, lock-released gravity current which propagates over a horizontal boundary in either a rectangular or an axisymmetric geometry is studied. The fluid motion is described theoretically by the inviscid shallow-water equations. We attempt to clarify the factors that regulate the propagation and structure of gravity currents that spread over a porous boundary or in a system rotating around a vertical axis. To evaluate the effects of a porous horizontal boundary on the gravity currents, the "one-layer'' model which assumes a purely hydrostatic balance in the ambient fluid domain, is used. We develop an asymptotic solution for currents spreading over a permeable boundary. An often used simplification of the governing equations leads to "box" models wherein horizontal and vertical variations within the flow are neglected. We show how to derive these models rigorously for the gravity currents spreading over a horizontal boundary for which the portion under the lock is impermeable and after the lock is permeable. A more sophisticated shallow-water approximation is the two-layer model, for which we consider the flow of a non-entraining gravity current of constant density as it propagates over a horizontal boundary under an ambient fluid which is sufficiently shallow so that its motion cannot be neglected. For the two-dimensional configuration we clarified that if the initial height of the current is less than one half of the total height of the ambient and the dense fluids, the upstream-propagating depression wave steepens into a hydraulic jump. We extended the two-layer investigation to the axisymmetric problem in a system rotating around a vertical axis in terms of upper- and lower- layers. We focus attention on situations in which the apparent importance of the Coriolis terms relative to the inertial terms, represented by parameter C (the inverse of a Rossby number) is not large, case in which a significant radius of propagation is obtained. We found that the major features predicted by the two-layer model differ only slightly from these obtained with an one-layer problem.