Breaking of Internal Kelvin Waves Shoaling on a Slope

Abstract

In stratified flow, breaking of internal waves over slopes induces resuspension of bottom sediments and transport of mass. When internal waves shoal and break, flow dynamics and mass transport differ significantly according to whether the Coriolis force is included or neglected. Despite its importance, the currents generated by breaking internal Kelvin waves remain uninvestigated. Therefore, this study considers breaking of internal waves over a uniform slope under Coriolis with equivalent upper-and lower-layer depths. Laboratory experiments, using a 6.0-m rotating tank, were undertaken to visualize currents using particle image velocimetry. Experimental data validated a three-dimensional fluid dynamics model, in which a phase-averaged velocity (residual jet) was simulated to occur at the lateral wall (to the right) of the progressive internal Kelvin waves in the breaking zone, with the generation of an oblique downslope return flow (downdraft) under Coriolis. The geostrophic balance drove the residual jet, and the equation for estimating the residual current, due to the jet, was formulated and was discussed by referring a coastal jet in Lake Erie. The results provide insight on mass transport in lakeshore and coastal zones. Plain Language Summary The key idea of the present study is the "residual jet" which occurs at the lateral wall on the right side of the progressive internal Kelvin waves due to breaking over a uniform slope. We conducted laboratory experiments by using a rotating tank, and internal Kelvin wave breaking was visualized by using particle image velocimetry (PIV) method. Also, using a three-dimensional fluid dynamics model, a residual jet was demonstrated to occur with the generation of an oblique downdraft running down the slope under Coriolis, which was verified through the laboratory experiments. We found that the geostrophic balance drives a residual jet, and the equation for estimating the residual current, due to the jet, was formulated and was discussed by referring a coastal jet in Lake Erie. Therefore, the paper will provide the oceanography communities with a new understanding of the effect of internal Kelvin wave breaking, and the associated residual currents, on long-term mass transport.

Influence of Thermal Stratification on Seasonal Net Ecosystem Production and Dissolved Inorganic Carbon in a Shallow Subtropical Lake

“…To estimate the residence time in YYL, we performed three‐dimensional hydrological simulations using a three‐dimensional environmental model, Fantom, which is based on object‐oriented programming methods (Laniak et al., 2013; Maruya et al., 2010; Nakamoto et al., 2013; Nakayama et al., 2014, 2016; Nakayama, Sato, et al., 2020; Nakayama, Shintani, et al., 2020). To evaluate bathymetry's effects on the flow field and residence time, we used a Fantom to simulate the bottom slope in a z coordinate system with partial cells (Adcroft, 1997).…”

A Spatially Integrated Dissolved Inorganic Carbon (SiDIC) Model for Aquatic Ecosystems Considering Submerged Vegetation

“…Therefore, we extend the above analysis to develop a spatially (horizontally) integrated DIC (SiDIC) numerical model suitable for shallow water areas, which is able to clarify the vertical and temporal changes of DIC. The base model is a three-dimensional environmental model, Fantom (Nakayama, Sato, et al, 2020;Nakayama et al, 2014Nakayama et al, , 2016. The governing equation is the Navier-Stokes equation, and object-oriented programming is used.…”

“…(2009) have shown that much of the Earth’s carbon is captured and stored naturally as “blue carbon” in oceanic and coastal ecosystems, with vegetated habitats, such as mangroves and submerged aquatic vegetation (SAV), accounting for more than 50% of all carbon storage in ocean sediment. Previous studies have shown that SAV enhances the stratification of the water column (Nakayama, Sato, et al., 2020), suppressing vertical water exchange in shallow water areas (Ghisalberti & Nepf, 2006, 2009). When stratification occurs, large amounts of dissolved inorganic carbon (DIC) can accumulate in the deeper layers of an aquatic ecosystem because the dampening of vertical mixing prevents the flux of carbon between the upper and lower layers (Lin et al., 2021, 2022).…”

“…of the water column (Nakayama, Sato, et al, 2020), suppressing vertical water exchange in shallow water areas (Ghisalberti & Nepf, 2006. When stratification occurs, large amounts of dissolved inorganic carbon (DIC) can accumulate in the deeper layers of an aquatic ecosystem because the dampening of vertical mixing prevents the flux of carbon between the upper and lower layers (Lin et al, 2021(Lin et al, , 2022.…”

3D Flow Structures During Upwelling Events in Lakes of Moderate Size

“…The tilting of the thermocline promotes mixing, specifically in the littoral zone (MacIntyre & Jellison, 2001), along with littoral‐pelagic mass exchange (Rao & Schwab, 2007). During relaxation, when upwelling winds weaken, complex phenomena characterize the nearshore area as internal waves may interact with lake morphometry, resulting in internal wave shoaling and breaking (Horn et al., 2001; Nakayama et al., 2020).…”