Gravity current flow over sinusoidal topography in a two-layer ambient

Abstract

We report upon a laboratory experimental study of dense full- and partial-depth locks released gravity currents propagating through a two-layer ambient and over sinusoidal topography of amplitude A and wavelength λ. Attention is restricted to a Boussinesq flow regime and the initial (or slumping) stage of motion. Because of the presence of the topography, the lower layer depth and channel depth vary in the downstream direction by as much as ±52% and ±40%, respectively. Despite such large variations, the instantaneous gravity current front speed typically changes by only a small amount from its average value, Ū. We conclude that the reason for this unexpected observation is a counterbalancing between the contraction/expansion of the channel on one hand and along-slope variations of the buoyancy force on the other hand. Compared to the case of gravity current flow over a horizontal surface, the topography has a retarding effect on Ū; we characterize the variation of Ū with the following parameters: A, A/λ, the interface height, the height of gravity current fluid inside the lock, and the layer densities as characterized by S ≡ (ρ1 − ρ2)/(ρ0 − ρ2) where ρ0 is the gravity current density, ρ1 is the lower ambient layer density, and ρ2 is the upper ambient layer density. The topography also alters the structure of the gravity current head by inducing large-scale Kelvin-Helmholtz (K-H) vortices directly downstream of regions of significant shear. These vortices are transient flow features; after formation and saturation, they relax at which point gravity current fluid sloshes back and forth in the topographic troughs. A simple geometric model is presented that prescribes the minimum number of topographic peaks a gravity current fluid will overcome. As in the horizontal bottom case, the forward advance of the gravity current can excite a downstream-propagating interfacial disturbance, which is more prominent for larger S. We identify when the gravity current front will travel faster (supercritical flow) or slower (subcritical flow) than the interfacial disturbance based on S and A/λ. Unlike in the horizontal-bottom case, however, we typically also observe interfacial oscillations far ahead of the gravity current front. These have wavelength approximately equal to λ and are due to spatial variations in the speed of the ambient return flow.