Spreading of three-dimensional inclined gravity plumes

Geometric and kinematic behavior of three-dimensional (3-D) negatively buoyant gravity plume spreading on a steep sloping surface has been investigated in a laboratory tank. Simple analytical expressions are presented based on the balance of driving and resisting forces, i.e., gravity, buoyancy, inertia, and friction, in both the longitudinal and lateral flow directions. These analytical expressions for spreading depend on the bottom slope, the initial buoyancy flux, the Richardson number, and the geometry of the plume at the source. Similar relations for a two-dimensional (2-D) gravity plume are also presented for comparison. Mathematical solutions show satisfactory agreement with measured experimental data.