The waves excited topographically in the water surface, stratified fluids or roating fluids are reviewed with an emphasis on their nonlinear aspects. Those waves appear in different contexts but, as is well known, have many mathematical similarities. For example, the long water waves, as well as long internal waves, long inertial waves and the long Rossby waves are in general governed by the 'KdV-type' equations. An important exception occurs when the flow has uniform stratification, uniform rotation or no zonal shear. In these cases the long waves are governed by the strongly nonlinear equation derived by 'Grimshaw & Yi.' In this review, the comparisons are made between the numerical solutions of the Navier-Stokes or the quasi-geostrophic equations and the theoretical predictions, illustrating the applicabilities and the shortcomings of the existing theories.

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Sefl-excited sound caused by flow is discussed specifically categorizing it into four groups : (1) Self-excited sound due to interaction between shear layer (s) and solid surface (s), which includes edge tone, hole tone, pipe tone, cavity tone, etc., (2) self-excited sound due to Karman vortex shedding, (3) self-excited sound due to swirling flow such as vortex whistle, and (4) self-excited sound due to supersonic jets such as screech. The common features are the existence of shear layer (s) in the flow field and the occurrence of feed back pressure signals to sustain the self-excited oscillation of the system. The nonlinear features of the phenomena such as sound generation mechanism, mode selection scheme and alteration of time-averaged flow field due to sound generation are also illustrated.

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Time-dependent and independent wave equations are developed for waves propagating over a porous rippled layer, with rapid undulations about the mean water depth satisfying the mild slope assumption, on an impermeable slowly varying bottom also satisfying the mild slope assumption. The ripples are assumed to have wavelengths of the same order as those of surface gravity waves. The time-dependent equation developed here contains the existing theories of Berkhoff (1972) and Kirby (1986). A parabolic approximation is applied to the time-independent wave equation, and coupled parabolic equations are developed. Using these equations, the Bragg scattering is analyzed.

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Nonlinear waves excited in the axisymmetric swirling flow passing through a long cylindrical tube are considered. The waves are excited either by an obstacle on the tube axis or by the local expansion/contraction of the tube wall. The applicability of the weakly and strongly nonlinear theories is discussed by comparing their predictions with the solution of the fully nonlinear navier-Stokes equations. In the case of the solid-body rotation, the onset of the axial flow reversal when the resonantly excited wave amplitude becomes large is well predicted by the strongly nonlinear theory by Grimshaw & Yi. On the other hand, when the incoming flow does not have a solid-body rotation and has a swirl such as the Burgers vortex, the resonantly excited waves are well described by the weakly nonlinear theory, i.e., the forced KdV equation.

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The effective Hamiltonian method is reviewed with a special emphasis on its applicability to the relative diffusion in a turbulent flow. It gives an expression of the mean square value of the relative distance between a pair of fluid particles which holds in the entire range of the time difference, shows the reasonable time dependence and includes the mechanism in leading to Richardson's four-thirds law. In addition, it may be helpful to develop a new analytical method.

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The present paper deals with the numerical simulation of the growth of viscous fingers in a thin liquid layer. A new type of computational model for that problem is proposed. The govering flow equations are derived from the three-dimensional Navier-Stokes equations and the equation of continuity by averaging them in the direction of thickness of the layer. They are expressed in terms of velocity and pressure. To avoid the handling of a deformable solution domain with a moving free surface, we solve two-phase flows composed of liquid and its adjacent fluid (gas in the present paper) on the solution domain with only fixed boundaries. The liquid free surface is recognized as a line of density discontinuity. The flow equations are discritized by the finite element method in space and by the finite difference method in time. Three characteristic phenomena of spreading, splitting and shielding and their combined phenomena have been calculated. The present results agreed well with other numerical results.

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