Topographically generated internal waves and boundary layer instabilities

Abstract

Flow over topography has been shown to generate finite amplitude internal waves upstream, over the topography and downstream. Such waves can interact with the viscous bottom boundary layer to produce vigorous instabilities. However, the strength and size of such instabilities depends on whether viscosity significantly modifies the wave generation process, which is usually treated using inviscid theory in the literature. In this work, we contrast cases in which boundary layer separation profoundly alters the wave generation process and cases for which the generated internal waves largely match inviscid theory. All results are generated using a numerical model that simulates stratified flow over topography. Several issues with using a wave-based Reynolds number to describe boundary layer properties are discussed by comparing simulations with modifications to the domain depth, background velocity, and viscosity. For hill-like topography, three-dimensional aspects of the instabilities are also discussed. Decreasing the Reynolds number by a factor of four (by increasing the viscosity), while leaving the primary two-dimensional instabilities largely unchanged, drastically affects their three-dimensionalization. Several cases at the laboratory scale with a depth of 1 m are examined in both two and three dimensions and a subset of the cases is scaled up to a field scale 10-m deep fluid while maintaining similar values for the background current and viscosity. At this scale, increasing the viscosity by an order of magnitude does not significantly change the wave properties but does alter the wave’s interaction with the bottom boundary layer through the bottom shear stress. Finally, two subcritical cases for which disturbances are able to propagate upstream showcase a set of instabilities forming on the upstream slope of the elevated topography. The time scale over which these instabilities develop is related to but distinct from the advective time scale of the waves. At a non-dimensional time when instabilities have formed in the field scale case, no instabilities have yet formed in the lab scale case.

Observations of Enhanced Sediment Transport by Nonlinear Internal Waves

“…It is generally thought that GI requires a threshold strength of APG (Diamessis & Redekopp, 2006), and this is influenced by wave shape and amplitude (Stastna & Lamb, 2008). The waves in previous GI studies have largely focused on large‐amplitude steady soliton solutions to either WNL (e.g., Diamessis & Redekopp, 2006) or fully nonlinear equations (Stastna & Lamb, 2002, 2008) (a recent notable exception is Soontiens et al, 2015, who demonstrated instability under relatively low‐amplitude developing waves near to their generation source). While our NLIWs were large amplitude, they were complex, time‐evolving wave trains and not well described by such steady equations.…”

“…Beyond mobilization of bed load, Bogucki et al (1997) observed the potential for NLIWs to eject sediments high in the water column, and Bogucki and Redekopp (1999) subsequently proposed that this was due to a global instability (GI) mechanism. This GI mechanism has motivated nearly two decades of laboratory (Aghsaee & Boegman, 2015; Carr et al, 2008) and numerical (Aghsaee et al, 2012; Diamessis & Redekopp, 2006; Stastna & Lamb, 2002) studies and, more recently, studies into other novel NLIW‐induced instabilities (Harnanan et al, 2015, 2017; Olsthoorn & Stastna, 2014; Soontiens et al, 2015).…”

“…The fate of a GI as it ultimately decays into turbulence is also poorly understood as numerical simulations are, with the notable exception of Sakai et al (2020), typically halted before the wave‐induced stirring cascades energy to fine‐scale motions. Further, only the studies of Harnanan et al (2015, 2017), Sakai et al (2020), and Soontiens et al (2015) are 3‐D, as required to resolve a turbulent cascade.…”

Neutral and stratified turbulent boundary layer flow over low mountains

“…The fact that some wave drag in the boundary layer can be significant was also recognized by [16] and earlier by [17]. Beyond the drag itself, the contribution of boundary layer waves to turbulent exchange is also recognized in oceanography and for sediment suspension [18,19].…”

Calculation of internal-wave-driven instability and vortex shedding along a flat bottom

“…Local instability made by internal solitary waves interacting with a variable bottom topography may exhibit jet-like roll-up of vorticity near the crest of the topography, as calculated in two and three dimensions at moderate Reynolds number by Harnanan, Soontiens & Stastna (2015) and Harnanan, Stastna & Soontiens (2017). Re-suspension or entrainment of internal solitary waves interacting with a bottom topography was modelled numerically by Olsthoorn &Stastna (2014), andWaite (2015) calculated the viscous bottom boundary layer effects on the generation of internal solitary waves at topography and the related instabilities in the case of a background current.…”