The effects of near-bottom stratification on internal wave induced instabilities in the boundary layer

Abstract

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.

Observations of Enhanced Sediment Transport by Nonlinear Internal Waves

“…Past laboratory and numerical studies of NLIW‐BBL interaction (Boegman & Stastna, 2019, and references therein) have almost exclusively been initialized with zero or weak near‐bed stratification (Harnanan et al, 2017, is a notable exception, though their boundary‐layer rollup dynamic differs significantly from our observations). The vortex shedding, which occurs in these simulations, has thus been effectively unconstrained until the main thermocline.…”

“…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.…”

Vortex generation due to internal solitary wave propagation past a sidewall constriction

“…2017; Harnanan et al. 2017). Temporal discretization was accomplished by a third-order multistep method with adaptive time step.…”

“…This can be contrasted with the more commonly studied situation of cross-BBL transport, in which an adjustment occurs only at depth (Boegman & Stastna 2019) or at shear layers (Xu, Stastna & Deepwell 2019). The only possible exception is the case of ‘local hydraulics’ observed by Harnanan, Stastna & Soontiens (2017) for instabilities below an ISW of elevation within a secondary, near-bottom stratified layer. However, even for this case the wave-induced flow remains consistent along the topography.…”