No abstract

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.

No abstract

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.