We assess the state of the art in numerical prediction of interfacial instabilities due to shear in layered flows of viscous fluids. Basic ingredients of this assessment include linear stability analysis results for both miscible (diffuse) and immiscible (sharp) interfaces, the physics and resolution requirements of the critical layer, and convergence properties of the relevant numerical schemes. Behaviors of physically and numerically diffuse interfaces are contrasted and the case for a sharp interface treatment for reliable predictions of this class of flows is made.

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