Surface waves in flowing water

摘要: Surface waves in flowing water and their stability are studied. With U(y) denoting the mean velocity d depth of water, following results obtained: (i) plane complex wave velocity, c = cr + ici, all eigenvalues with a positive ci lie within semicircle which has as its diameter range primary flow, y being vertical co-ordinate. (ii) If U″(y) does not change sign U is monotonic field singular neutral modes (for somewhere flow) impossible flow stable. (iii) analytic U″ vanishes at point or points where equal to same constant Uc U′ zero then least one mode exists Uc, provided U(d) ≠ Uc. (iv) U″/(U—c) finite non-zero critical (c real), vanishes, mentioned above contiguous unstable modes, (v) U(d). The eigenvalue for any k bounded.