Abstract
We study the turbulent front of a current on a horizontal bed driven by a continuous buoyancy flux using a large-eddy simulation (LES) method that does not rely on the Boussinesq approximation, thereby enabling accurate simulation of flows with substantial density contrasts. The primary focus of the simulation is the frontal region, where entrained ambient fluid combines with the source fluid entering the neck of the current head to form a bulging, elevated head. The bulging current head, sustained by the flow through its neck, is significant for its role in sediment transport and its destructive force in the atmosphere and ocean. Despite numerous previous studies, the vortex model of current head proposed by Prandtl [1] remains poorly understood. Analysis of the LES results shows that the turbulence entrains ambient fluid primarily through the formation of a Kelvin-Helmholtz (K-H) vortex. The LES determine the maximum velocity and maximum flow through the neck of the current head from the formation of the frontal vortex to the attainment of the vortex's pinnacle. The vortex grows and then collapses, reaching a critical Richardson number of Ri [Formula: see text] 0.30 [Formula: see text] 0.42. More than eighty percent of the turbulent entrainment of ambient fluid into the current occurs within the current head. The pinnacle flow through the neck-a function of the source Froude number-is uniquely related to the frontal velocity and volume entrainment rate by an overall structure-similarity relationship for the coherent turbulence in the front. We evaluate the numerical accuracy and the LES model through a mesh-refinement study and a comparison with laboratory observations.