The two-dimensional problem of steady waves on water of finite depth: regimes without waves of small amplitude

The two-dimensional problem of steady waves on water of finite depth is considered without assumptions about periodicity and symmetry of waves. A new form of Bemoulli's equation is derived, and it involves a new bifurcation parameter which is the product of the Froude number mu and the rate of flow omega. The main result obtained from this equation is the absence of waves, having sufficiently small amplitude, provided vertical bar mu omega vertical bar > 1.