PERMANENT WAVES IN SLOW FREE-SURFACE FLOW OF A HERSCHEL-BULKLEY FLUID

Unsteady flow of a viscoplastic fluid on an inclined plane is examined . The fluid is described by the three-parameter Herschel-Bulkley const itutive equation. The set of equations governing the flow is presented , recovering earlier results for a Bingham fluid and steady uniform mo tion. A permanent wave solution is then derived, and the relation betw een wave speed and flow depth is discussed. It is shown that more type s of gravity currents are possible than in a Newtonian fluid; these in clude some cases of flows propagating up a slope. The speed of permane nt waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index.