Interaction of two-dimensional separated flows with a free surface at low Froude numbers

It is shown that the low Froude number wake of floating two-dimensional objects is convectively unstable. This is shown to be true for bluff objects, like a circular cylinder, and for streamlined objects, like a thin airfoil. As a result, the wake behind a floating object remains steady, even at high Reynolds numbers, characterized by a long region of recirculating flow. It is concluded that the presence of the free surface has a stabilizing effect at low Froude numbers, suppressing the unsteadiness of the wake. The structure of the dispersion relation, shows that, at low Froude numbers, a short wavelength interaction between the wake instability and ambient waves is possible in the form of a spatially growing response.