Gravity-current box model

A gravity-current box model replaces the current by a well-mixed region with uniform depth and density. Integral volume, scalar, and front-speed balances then reduce the spreading problem to ordinary differential equations.

If a finite-volume gravity current loses or dilutes the scalar that supplies its reduced gravity, its front can approach a finite runout length of a gravity current. A box model couples the scalar balance to a gravity-current front condition; eliminating time then gives the front position directly as a function of the remaining scalar concentration.

A particle-laden gravity current is driven by the excess density of suspended particles. Deposition decreases its reduced gravity, so a finite-volume current can approach a finite runout length.

The runout length is the limiting horizontal distance reached by a gravity current after its driving buoyancy has been exhausted or balanced by resistance.