Direct Numerical Simulations (DNS) were conducted to study the shear instabilities in a one-layer model of coastal currents. The instabilities of the currents are affected by the wave-radiation damping, and depend on a convective Froude number, in a manner analogous to the known Mach-number effect in compressible flow. In addition to the energy loss due to the wave radiation, the shear instabilities are also affected by friction. In the limiting case of zero friction, the present DNS for the gravity-stratified flows of one layer are consistent with the LST (Linear Stability Theory) of Sandham and Reynolds (1991) for compressible flow. In the wave-less case, the DNS results agree with the LST of Chu, Wu and Khayat (1991) for open-channel flow. The general instabilities are correlated with two dimensionless parameters: convective Froude number and friction number. The convective Froude number, not the local Froude number, characterizes the wave radiation from the shear flows, while the friction number parameterizes the local energy dissipation. The wave-radiation damping and the frictional energy dissipation are mechanisms fundamental to the instabilities. Analogies are established from the DNS between open-channel flow and compressible flow, and between open-channel flow and gravity-stratified flow. The correlation of the instabilities with the Froude number and the friction number are valid for all currents admissible to waves.

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