D. J. Benney

Finite Amplitude Effects in an Unstable Laminar Boundary Layer

The mean flows induced by the interaction of a two‐ and a three‐dimensional wave are calculated for a profile consisting of two straight lines. Although this is a simplified model of an actual boundary layer, the results are consistent with the experimental work done at the National Bureau of Standards.

Statistical Properties of the Sea

The long‐time behavior of weakly interacting random waves on the ocean surface is shown to be a solvable theoretical problem. Asymptotic closures are obtained for both the free and forced cases.

Lump Interactions and Collapse in the Modified Zakharov–Kuznetsov Equation

Two-dimensional solitary wave (lump) interactions and the formation of singularities in the modified Zakharov-Kuznetsov (mZK) equation are considered. The mZK equation represents an anisotropic two-dimensional generalization of the Korteweg-deVries equation and can be derived in a magnetized plasma for small amplitude Alfven waves at a critical angle to the undisturbed magnetic field. The radially symmetric positive solutions (lumps) for the mZK equation are computed. It is shown that when two lumps interact, the initial energy exchange between them is followed by the emergence of a single collapsing lump and a radiation field behind it. Connections to the analytic theory of collapse for the mZK equation are discussed.