# Marius Ungarish's An Introduction to Gravity Currents and Intrusions PDF

By Marius Ungarish

ISBN-10: 1584889039

ISBN-13: 9781584889038

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Extra resources for An Introduction to Gravity Currents and Intrusions

Example text

4 An introduction to gravity currents and intrusions The full behavior by numerical solution The knowledge accumulated to this point allows us to proceed to a global solution of the typical gravity current. This is achieved by a numerical finitedifference solution. , 0 ≤ x ≤ xN (t)). 2. To be specific, we solved here the dimensionless system for a current released from a rectangular lock. Initially h = 1 and u = 0 in the domain 0 ≤ x ≤ xN (0) = 1. The thickness ratio of the ambient to lock is H = 3.

For simplicity, we also drop the overbar which denotes the z-averaged velocity. We keep in mind that in the SW framework we solve for the averaged u(x, t). The results are given below. 35) = 0. 36) In characteristic form, this becomes ht uh + ut 1u hx ux = 0 . 37) The characteristic curves and relationships provide useful information for the solution of the system. 1. 1) we readily identify that in the present case H = h, U = u, A = 1, B = u, and S1 = S2 = 0. 1, and with an obvious change of notation, we obtain the characteristic balances h−1/2 dh ± du = 0 on dx = c± = u ± h1/2 .

In the classical hydraulic dam-break problem the nose height of the water (that propagates against the negligible resistance of the embedding air) decreases smoothly to zero at xN (t), and hence the velocity of the tip of the current follows straightforwardly from the internal solution. 1). For the Boussinesq gravity current the nose, that encounters the resistance of the quite dense embedding fluid, is a discontinuity. We can view it as a moving piston, or interface jump, of height hN and velocity uN .