In this paper the solitary-wave solutions of the Euler equations of motion are treated as a perturbation of the KdV equaton. We show analytically, that the amplitudes to two solitary waves are altered after interaction. This change in amplitude is calculated, showing that the smaller wave dereases in amplitude and the larger wave increases in amplitude.

A weakly nonlinear inviscid theory describing the interactions within a continuous spectrum of gravity-capillary waves is developed. The theory is based on the principle of least action and uses a Lagrangian in wavenumber-time space. Advantages of this approach compared to the method of Valenzuela & Laing (1972) are much simplified mathematics and final equations and validity on a longer timescale. It is shown that much of the development of the spectrum under the influence of nonlinear terms can be understood without actually having to integrate the equations. To this end multiwave space, a new concept comparable with phase space, is introduced. Using multiwave space the magnitude of the nonlinear transfer is estimated and it is shown how the energy goes through the spectrum. Also it is predicted that at fixed wavenumbers, the smallest being 520 m−1, finite peaks will arise in the spectrum. This is confirmed by numerical integrations. From the integrations it is also deduced that nonlinear interactions are at least as important to the development of the spectrum as wind growth. Finally it is shown numerically that the near-Gaussian statistics of the sea surface are unaffected by nonlinear interactions.

It is well known that heating a stable salinity gradient from below leads to the formation of a series of turbulently convecting layers separated by stable diffusive interfaces. It is argued theoretically and demonstrated experimentally that the first mixed layer grows to a critical height δc, which is determined by a balance between the vertical kinetic and potential energies of the turbulent eddies, before a growing second layer separated from the first layer by a quasi-stationary stable density interface can be formed. Although the thermal boundary layer that develops over the propagating turbulent front can become unstable and form a second mixed region before the first layer grows to δc, the density interface formed between these two layers is not sufficiently stable to resist quick entrainment of the second layer into the lower layer. Some aspects of the growth of the first turbulent layer and possible application of the results to oceanic situations are also discussed.

We present numerical solutions of natural convection in a shallow enclosure heated from a side. As a result of hydrodynamic instability transverse cells appear in the flow if the Prandtl number is sufficiently small. Both conducting and insulated top and bottom boundaries were considered. For fluids of small Prandtl number the differences in the flow patterns in these two cases are slight, the strength of the circulation in the cells being somewhat weaker when the boundaries are insulated. This is a result of a more stable flow in this case, caused by the kinetic energy being more vigorously expended in the work against the buoyant forces. Insulated boundaries allow the temperature field to adjust more freely in the end regions leading to crowding of the isotherms there and consequently to larger heat transfer than when the boundaries are conducting.