A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.

The breaking of internal waves propagating in a stratified fluid of constant buoyancy frequency on a sloping boundary was investigated numerically. It was found that at the boundary, nonlinear non-resonant interactions between the incident and reflected waves produced higher-mode waves. These modes had frequencies greater than the local buoyancy frequency and so could not radiate from the interaction region. The energy level of trapped waves increased with time and subsequently led to overturning of the density field. At the critical frequency, when the reflected wave propagated in a direction parallel to the slope, wave overturning occurred near the wall, but the point of overturning moved off the bottom as the propagation angle changed away from that of the bottom slope as the waves became increasingly supercritical. The internal wave reflection coefficient generally increased as the effects of nonlinearity and viscosity decreased, but depended strongly on the forcing frequency and the angle of the sloping boundary.

The behaviour of internal waves at a caustic level, turning point and critical layer have been investigated numerically. At a caustic reflection, a triad interaction was formed within the reflection region and the internal wave energy was transferred to lower frequencies (subharmonics). This resulted in a local subharmonic instability. One of the excited internal waves penetrated the caustic level and propagated downwards. This downward propagating wave then produced a second caustic where further reflection could take place. At a turning point, nonlinear interaction between the incident and reflected waves transferred energy to higher frequencies (evanescent trapped waves) which resulted in a superharmonic instability. At the critical level, energy was transferred to the mean flow. As the degree of nonlinearity increased, more energy was found to be transferred and overturning resulted due to a shear instability.

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In this study we have investigated the behaviour of natural convection flow in open cavities, with both homogeneous and thermally stratified ambient, using direct numerical simulation. The cavity is insulated at the top and bottom boundaries, heated from the left-hand side boundary and open at the right-hand side. A wide range of Rayleigh numbers were considered (5 × 106 to 1 × 1010) with Pr = 0.7 for all cases. It was found that the homogeneous flow is steady for all Rayleigh numbers considered, whereas the stratified flow with a high enough Rayleigh number exhibits low- and high-frequency signals of the same type as are observed for closed cavity flow. The thermal boundary layer is examined in detail and it is shown that both low- and high-frequency signals are located predominantly in the upper region of the heated plate and are associated with a reverse-S-flow formed by the boundary layer exit jet interacting with the stratified interior. The low-frequency signal is associated with standing waves in the boundary layer, whereas the high-frequency signal is associated with travelling waves. The high-frequency signal occurs initially as a harmonic of the base low-frequency signal. A corner jet with the same inlet characteristics as the natural convection boundary layer exit jet is also examined and shown to exhibit a similar bifurcation, but with the low frequency always dominant. It is suggested that the generation mechanism for the bifurcation of the natural convection flow is the same as that for the corner jet.