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In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of hydrodynamic instabilities, so called roll-waves, when steady flows are unstable.
Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel
In nature turbulent flows exist that are neither simply 2D nor 3D but boundary conditions, such as varying stratification, force them towards the one or the other. Here, we report the first evidence of the co-existence of 2D and 3D turbulence in an e
Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blas
This paper is concerned with the detailed behaviour of roll-waves undergoing a low-frequency perturbation. We rst derive the so-called Whithams averaged modulation equations and relate the well-posedness of this set of equations to the spectral stabi
Experimental and numerical study of the steady-state cyclonic vortex from isolated heat source in a rotating fluid layer is described. The structure of laboratory cyclonic vortex is similar to the typical structure of tropical cyclones from observati