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We consider the steady flow of a stratified fluid over topography in a fluid of finite vertical extent, as typified by experimental flumes with a rigid lid or the ocean under the rigid lid approximation. We do not specify a functional form of the upstream stratification or background current and derive a general version of the Dubreil–Jacotin–Long equation appropriate for the problem. This elliptic equation is strongly nonlinear and we develop an efficient, pseudospectral, iterative method for its numerical solution. The method allows us to compute laminar, trapped waves with amplitudes more than 50% of the depth of the fluid. We find that when either a background shear current is present or the topography is narrow enough, multiple steady states are possible and we confirm this finding by using integrations of the full time-dependent Euler equations. We discuss instances of waves with closed streamlines, finding that the presence of shear allows for waves with vortex cores that persist for long times in time-dependent simulations and match well with solutions of the steady theory. In contrast, streamline overturning in the absence of upstream shear only occurs for flows that are stratified near the surface and in this instance, time-dependent simulations yield unsteady cores that do not match steady results very well.

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The water following characteristics of six different drifter types are investigated using two different operational marine environmental prediction systems: one produced by Environment and Climate Change Canada (ECCC) and the other produced by the Norwegian Meteorological Institute (METNO). These marine prediction systems include ocean circulation models, atmospheric models, and surface wave models. Two leeway models are tested for use in drift object prediction: an implicit leeway model where the Stokes drift is implicit in the leeway coefficient, and an explicit leeway model where the Stokes drift is provided by the wave model. Both leeway coefficients are allowed to vary in direction and time in order to perfectly reproduce the observed drifter trajectory. This creates a time series of the leeway coefficients which exactly reproduce the observed drifter trajectories. Mean values for the leeway coefficients are consistent with previous studies which utilized direct observations of the leeway. For all drifters and models, the largest source of variance in the leeway coefficient occurs at the inertial frequency and the evidence suggests it is related to uncertainties in the ocean inertial currents.

It has been known for some time that internal wave-induced currents can drive near bed instabilities in the bottom boundary layer over a flat bottom. When the bottom is not flat, the situation can become quite complicated, with a diverse set of mechanisms responsible for instability and the subsequent transition to turbulence. Using numerical simulations, we demonstrate the existence of a mode of instability due to internal solitary wave propagation over broad topography that is fundamentally different from the two dominant paradigms of flow separation over sharp topography and global instability in the wave footprint that occurs over a flat bottom observed at high Reynolds number. We discuss both the two and three-dimensional evolution of the instability on experimental scales. The instability takes the form of a roll up of vorticity near the crest of the topography. As this region is unstratified in our simulations, little three-dimensionalization is observed. However, the instability-induced currents provide an efficient means to modulate across boundary layer transport. We subsequently extend the results to the field scale and discuss both the aspects of the instability that are consistent across scales and those that are different.

Large amplitude internal waves in naturally occurring stratified fluids induce currents throughout the water column and hence have the potential to drive instability, and turbulent transition within, and hence material exchange across the bottom boundary layer. In the presence of broad, small amplitude topography, waves of depression have been shown to induce a vortex roll-up instability that has the potential for cross-bottom boundary layer transport through the generation of coherent vortices. At the same time, the three-dimensionalization associated with the instability is weak. We demonstrate that the presence of a near-bottom stratification provides a means for an enhanced rate of three-dimensionalization. For solitary waves of elevation, which do not yield a coherent response in the absence of a near-bottom stratification, the presence of a near-bottom stratification leads to a local hydraulic response, or a gravity-current-like intrusion, as the wave passes over the topography. This feature forms on the lee slope of the topography, propagates with the wave for some time, and provides a coherent pathway for material to be transported a distance of 1.5 times the topography amplitude into the water column in laboratory-scale simulations. Evidence of coherent structures in the turbulent flow in this region is presented.

Numerical simulations are used to investigate waves generated by flow over crater topography of diameter 100 km in an idealized atmosphere. The atmosphere is stratified with a constant buoyancy frequency profile and the background wind is constant. This study describes the development of a low-level jet along the upstream crater slope and its interaction with the cooler air within the crater valley. This interaction results in a hydraulic jump–like structure that acts as a modified topography, forcing a beam of secondary waves. The hydraulic jump is formed by a retreating gravity current as the cool air within the crater readjusts after the initial tilting of potential temperature contours. A two-dimensional simulation is used to compare features such as wave overturning in two and three dimensions. Several variations on the atmosphere’s profile are considered, including an atmosphere with reduced constant stratification and an atmosphere that is unstratified within the crater. These results indicate that the stratification within the crater is an important component in the development of the hydraulic jump. Also, several topographic modifications are included, such as a crater with no rims and a crater with reduced diameter. These comparisons reveal that the crater rims have little impact on the general wave pattern and that the crater curvature can influence wave breaking and lateral deflections. In addition, cases with rotation break the symmetry and induce more overturning in one-half of the crater.

It is well-known that in certain parameter regimes, the steady flow of a density stratified fluid over topography can yield large amplitude internal waves. We discuss an embedded boundary method to solve the Dubreil-Jacotin-Long (DJL) equation for steady-state, supercritical flows over topography in an inviscid, stratified fluid. The DJL equation is equivalent to the full set of stratified steady Euler equations and thus the waves we compute are exact nonlinear solutions. The numerical method presented yields far better scaling with increase in grid size than other iterative methods that have been used to solve this equation, and this in turn allows for a more thorough exploration of parameter space. For waves under the Boussinesq approximation, we contrast the properties of trapped waves over hill-like and valley-like topography, finding that the symmetry of freely propagating solitary waves when the stratification is reflected across the middepth is not present for trapped waves. We extend the derivation of the DJL equation to the non-Boussinesq case and discuss the effect of the new, non-Boussinesq terms on the structure of the trapped waves, finding that the sharp transition between large and small amplitude waves observed under the Boussinesq approximation is much more gradual when the Boussinesq approximation is relaxed. Finally, we demonstrate the existence of asymmetric steady states over hill-like topography where the flow is subcritical upstream of the topography but transitions to supercritical somewhere over the hill. Waves in this new class of exact solutions are related to so-called downstream recovery jumps predicted on the basis of hydrostatic (shallow water) theories, but when breaking does not occur the recovery jump does not stop propagating downstream and an asymmetric state across the topography maximum is reached for long times.