FLOW OF A MULTILAYER IDEAL INCOMPRESSIBLE AND HEAVY FLUID PAST A BODY.

The two-dimensional steady flow of a layered fluid past a body with discontinuous stratification is discussed. The number of layers in finite, and the channel which has a horizontal floor is open. To study the flow behind the body, a hypothesis on the possibility of approximating the velocity profile at the body boundary by that which arises in weightless flow is postulated. It is shown that for any specified Froude number, the corresponding homogeneous integral equation has only a finite number of positive eigenvalues to which the oscillation modes correspond. It is also shown that if the flow velocity is close to one of a denumerable set of propagation velocities of long-wave modes, the corresponding harmonic becomes stronger because of the resonance.