Interaction of a mode-2 internal solitary wave with narrow isolated topography

Abstract

Numerical and experimental studies of the transit of a mode-2 internal solitary wave over an isolated ridge are presented. All studies used a quasi-two-layer fluid with a pycnocline centred at the mid-depth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode-2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by non-dimensionalizing the wave amplitude by the lower layer depth, a/ . A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/ . a) ddeepwel@uwaterloo.ca

Shoaling mode-2 internal solitary-like waves

“…The combined numerical and laboratory investigation undertaken in the Deepwell et al (2017) study provided, for the first time, clear indications of flow separation and vortex formation on the upward boundary slope of the topography as a characteristic property of shoaling mode-2 waves of large and moderate amplitude. The numerical modelling study by Cheng et al (2017) considered the distortion caused to mode-2 waves by passage over a combined slope-shelf topography placed in a channel having the same dimensions and gate release wave generation mechanism in the experiments described by Carr et al (2015); Deepwell et al (2017) and the present investigation. Test runs conducted by Cheng et al (2017) to replicate the laboratory study by Carr et al (2015) for constant depth conditions showed excellent agreement between numerical simulations and laboratory data.…”

“…In practice, such smoothing does not modify the ISWs generated, but does decrease the amount of turbulence near the release location. The code has been found to do an excellent job in reproducing experimental results, for example in propagation of mode-2 ISWs over isolated topography (Deepwell et al 2017).…”

“…There is already a substantial literature on the modelling of mode-2 waves for cases of constant depth and many of these studies (Davis & Acrivos 1967;Maxworthy 1980;Kao & Pao 1980;Stamp & Jacka 1995;Terez & Knio 1998;Schmidt 1998;Stastna & Peltier 2005;Gavrilov & Lyapidevski 2009;Salloum et al 2012;Olsthoorn et al 2013;Brandt & Shipley 2014;Carr et al 2015;Deepwell & Stastna 2016;Cheng et al 2018) have contributed significantly to our understanding of the generation mechanisms of mode-2 waves, their structural, stability and kinematic properties and their ability to transport mass. Much recent interest has focussed on the effects of bottom topography upon the above properties, with laboratory and computational studies being undertaken by Gavrilov & Lyapidevski (2011); Guo & Chen (2012); Yuan et al (2018); Cheng et al (2017) for slope-shelf topography and Deepwell et al (2017) for the case of a train of mode-2 ISWs encountering a narrow, two-dimensional, Gaussian-profile ridge. The combined numerical and laboratory investigation undertaken in the Deepwell et al (2017) study provided, for the first time, clear indications of flow separation and vortex formation on the upward boundary slope of the topography as a characteristic property of shoaling mode-2 waves of large and moderate amplitude.…”

“…Much recent interest has focussed on the effects of bottom topography upon the above properties, with laboratory and computational studies being undertaken by Gavrilov & Lyapidevski (2011); Guo & Chen (2012); Yuan et al (2018); Cheng et al (2017) for slope-shelf topography and Deepwell et al (2017) for the case of a train of mode-2 ISWs encountering a narrow, two-dimensional, Gaussian-profile ridge. The combined numerical and laboratory investigation undertaken in the Deepwell et al (2017) study provided, for the first time, clear indications of flow separation and vortex formation on the upward boundary slope of the topography as a characteristic property of shoaling mode-2 waves of large and moderate amplitude. The numerical modelling study by Cheng et al (2017) considered the distortion caused to mode-2 waves by passage over a combined slope-shelf topography placed in a channel having the same dimensions and gate release wave generation mechanism in the experiments described by Carr et al (2015); Deepwell et al (2017) and the present investigation.…”

Internal Wave Observations Off Saba Bank

“…However, in quasi-mode-2 models such appearance was mostly found in shallower waters of < 200 m under the ridge-top crest and only at near-buoyancy frequencies, during ebb-flow. Most observations and modeling show high-frequency solitary waves in quasi-mode-2 that may occur every tidal period (e.g., Ramp et al, 2012;Deepwell et al, 2017;Xie et al, 2017). To our knowledge only once actual quasi-mode-2 internal tides were suggested to exist (Farmer and Smith, 1980).…”