In this paper we consider what effect the presence of a nonconstant background current has on the properties of large, fully nonlinear solitary internal waves in a shallow, stratified ocean. In particular, we discuss how the amplitude of the largest nonbreaking wave that it is possible to calculate depends on the background current as well as the nature of the upper bound. We find that the maximum wave amplitude is given by one of three possibilities: The onset of wave breaking, the conjugate flow amplitude or a failure of the wave calculating algorithm to converge (associated with shear instability). We also discuss how wave properties such as propagation speed, half-width, etc. vary with background current amplitude.

Large-amplitude internal waves induce currents and turbulence in the bottom boundary layer (BBL) and are thus a key driver of sediment movement on the continental margins. Observations of internal wave–induced sediment resuspension and transport cover significant portions of the world's oceans. Research on BBL instabilities, induced by internal waves, has identified several mechanisms by which the BBL is energized and sediment may be resuspended. Due to the complexity of the induced currents, process-oriented research using theory, direct numerical simulations, and laboratory experiments has played a vital role. However, experiments and simulations have inherent limitations as analogs for oceanic conditions due to disparities in Reynolds number and grid resolution, respectively. Parameterizations are needed for modeling resuspension from observed data and in larger-scale models, with the efficacy of parameterizations based on the quadratic stress largely determining the accuracy of present field-scale efforts.

The global deglaciation event that followed Last Glacial Maximum was punctuated by a sequence of rapid climate changes. This began with the Laurentide Ice Sheet derived calving event called Heinrich Event 1, continued with the Bølling‐Allerød warming that occurred synchronously with meltwater pulse 1a, and was in turn followed by the Younger‐Dryas abrupt return to cold conditions. Although it has long been believed that these events are consequences of the response of Atlantic meridional overturning circulation to freshwater inputs, it has always been assumed that these inputs were applied directly to the Atlantic Ocean itself. We address the question of how the Atlantic meridional overturning circulation would have responded to the recently hypothesized addition of freshwater into the Arctic Ocean at the time of onset of the Younger‐Dryas, and thereby demonstrate that this response is essentially identical to the response to North Atlantic freshening.

In this paper we discuss numerical simulations of the generation of large-amplitude solitary waves in a continuously stratified fluid by flow over isolated topography. We employ the fully nonlinear theory for internal solitary waves to classify the numerical results for mode-1 waves and compare with two classes of approximate theories, weakly nonlinear theory leading to the Korteweg–deVries and Gardner equations and conjugate flow theory which makes no approximation with respect to nonlinearity, but neglects dispersion entirely. We find that both weakly nonlinear theories have a limited range of applicability. In contrast, the conjugate flow theory predicts the nature of the limiting upstream propagating response (a dissipationless bore), successfully describes the bore's vertical structure, and gives a value of the inflow speed, $c_j$, above which no upstream propagating response is possible. The numerical experiments demonstrate the existence of a class of large-amplitude response structures that are generated and trapped over the topography when the inflow speed exceeds $c_j$. While similar in structure to fully nonlinear solitary waves, these trapped disturbances can induce isopycnal displacements more than 100% larger than those induced by the limiting solitary wave while remaining laminar. We develop a theory to describe the vertical structure at the crest of these trapped disturbances and describe its range of validity. Finally, we turn to the generation of mode-2 solitary-like waves. Mode-2 waves cannot be truly solitary owing to the existence of a small mode-1 tail that radiates energy downstream from the wave. We demonstrate that, for stratifications dominated by a single pycnocline, mode-2 wave dissipation is dominated by wave breaking as opposed to mode-1 wave radiation. We propose a phenomenological criterion based on weakly nonlinear theory to test whether mode-2 wave generation is to be expected for a given stratification.

Abstract. Internal solitary waves are widely observed in both the oceans and large lakes. They can be described by a variety of mathematical theories, covering the full spectrum from first order asymptotic theory (i.e. Korteweg-de Vries, or KdV, theory), through higher order extensions of weakly nonlinear-weakly nonhydrostatic theory, to fully nonlinear-weakly nonhydrostatic theories and finally exact theory based on the Dubreil-Jacotin-Long (DJL) equation that is formally equivalent to the full set of Euler equations. We discuss how spectral and pseudospectral methods allow for the computation of novel phenomena in both approximate and exact theories. In particular we construct markedly different density profiles for which the coefficients in the KdV theory are very nearly identical. These two density profiles yield qualitatively different behaviour for both exact, or fully nonlinear, waves computed using the DJL equation and in dynamic simulations of the time dependent Euler equations. For exact, DJL, theory we compute exact solitary waves with two-scales, or so-called double-humped waves.

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[1] Large-amplitude, vertically trapped internal waves can induce sizable velocities and trigger hydrodynamic instabilities in the bottom boundary layer, thereby contributing to the resuspension of sediments and the maintenance of sediment concentration in the water column. We discuss numerical simulations of several different situations in which the boundary layer in the wave footprint undergoes hydrodynamic instability, with a resultant increase in the incidence of spatiotemporal structures that could facilitate sediment resuspension. For the case of internal solitary waves we provide bounds in parameter space separating regions in which internal waves can be expected to efficiently resuspend sediment from those in which the boundary layer in the wave footprint is both laminar and stable. A notable finding is that the onset of instability is a strong function of the background current. The Lagrangian transport of passive particles due to the instability is explored, and some quantitative measures of the efficiency of the particle transport process are provided. We subsequently discuss the evolution of the power spectra of the bottom shear stress with time and find that while the general characteristics of the instability are robust, lowering either the Reynolds number or the strength of the background current leads to an increase in the typical length scales associated with the mature instability. Finally, we discuss instabilities during the internal wave generation process and alternative instability mechanisms when the bottom is not flat.Citation: Stastna, M., and K. G. Lamb (2008), Sediment resuspension mechanisms associated with internal waves in coastal waters,

[1] In this note we present results on the interaction of fully nonlinear internal solitary waves with the oceanic bottom boundary layer. We show that for fully nonlinear solitary waves it is the interaction of the wave induced velocity field with the upstream boundary layer vorticity that leads to a vortex shedding instability beneath the wave. The vortex shedding provides an efficient mechanism for transporting sediment out of the bottom boundary layer. Bottom boundary stress profiles suggest that the vortex shedding can lead to the resuspension of sediment. In contrast to past studies we find that neither a separation bubble or a wave with a recirculating region are required for vortex shedding to occur.