Author(s): J. Buhler; M. Princevac
Linked Author(s):
Keywords: Gravity currents; Turbidity currents; Top-hat scales; Jets; Plumes; Tracer distribution
Abstract: In the spirit of a well known approach by Ellison and Turner, the depth-average (top-hat) width and the velocity of gravity currents in deep water bodies are generally derived from the fluxes of volume and momentum, i. e. from the mean velocity distribution. Similarly, the excess density scale is derived from the excess mass flux. The resulting shallow water equations for gravity currents correspond to the Bresse equations for open channel flows, except for the definition of the flow scales. It is shown here that full consistency of the two sets of equations can be achieved by deriving the depth and density scale of the underflow from the distribution of the excess mass instead, and by relating the velocity scale to the excess mass flux. A consequence of this approach is that gravity currents have two depth scales, a depth h for the extent of the excess density distribution, and a larger depth γh denoting the total depth of flow. The use of different width scales for the excess mass and excess velocity distributions is similar to the added mass concept for thermals, and consistent with measurements of wind speeds in a katabatic layer, which suggest a larger flow depth than the corresponding distributions of potential temperature do. Analogous mass-based flow scales can also be derived for axisymmetric plumes, as well as for non-buoyant shear flows containing a passive tracer. They are computed from experimental data on gravity currents, katabatic winds in a co-flow, as well as for plane and axisymmetric jets and plumes.
Year: 2007