Kelvin–Helmholtz instabilities and mixing in surface-propagating gravity currents

Gravity currents are stratified shear flows common in various geophysical settings. During propagation, mixing between the current and the ambient fluid can occur via Kelvin–Helmholtz instabilities, leading to the formation of billows (vortices) on the current surface. Although the Kelvin–Helmholtz instability has implications for the transport of heat, solutes and sediments, the properties of the billows remain poorly quantified, particularly for free-surface gravity currents. This study presents laboratory experiments on buoyant, full-depth, lock-release gravity currents propagating at a free surface during the slumping regime. By varying the density contrast, we show that current propagation speeds and mean shapes align with two-layer shallow water theory, with most of the fluid contained in a temporally thinning, spatially uniform thick head. Kelvin–Helmholtz billows consistently form at the current front, becoming more coherent with increasing current velocity. We find that billows are generated at intervals equal to the time required for the current to advance a distance equal to its thickness, and they propagate forward at 25% of the current speed. Billows also undergo merging, with spacing approaching the total flow depth. Volume-based entrainment coefficients increase with Reynolds number, mirroring trends in basal currents. These findings quantify key properties of finite-amplitude Kelvin–Helmholtz billows in free-surface gravity currents and provide a foundation for understanding mixing and transport in environmental stratified shear flows.