Three‐dimensional transient rip currents: Bathymetric excitation of low‐frequency intrinsic variability

Abstract

The ROMS‐WEC model [Uchiyama et al., 2010] based on an Eulerian wave‐averaged vortex‐force asymptotic theory of McWilliams et al. (2004) is applied to analyze 3‐D transient wave‐driven rip currents and associated intrinsic very low‐frequency (VLF) variability in the surf zone on a surveyed bathymetry under spatiotemporally uniform offshore incident waves. The 3‐D rip currents are substantially depth‐dependent due to the vertical recirculation, composed of pairs of counter‐rotating longitudinal overturning roll cells that promote surface convergence. The vortex force plays an important role in vorticity budget, preconditioning overall vorticity reduction. These rip currents are intrinsically unstable and contribute about 70% to kinetic energy (KE) as eddy kinetic energy (EKE), consistent with observations. The dominant fluctuation period fits the VLF band, at about 18 min. The current effect on waves (CEW) alters not only the mean rip structure, but also the associated turbulence as the modified cross‐shore EKE profile with considerable accentuation in the inner surf zone. Increased alongshore bathymetric variability proportionally intensifies KE and intrinsic EKE, whereas it reduces the VLF period. With a guide of a pseudo 2D model, we reveal that vortex tilting effect due to the horizontal vorticity inherent in the 3‐D rip currents promotes collapse of the 3‐D eddies through an enhanced forward kinetic energy cascade, leading to short‐lived, laterally‐stretched 3‐D eddies resulting in elongated filaments that decay more quickly than coherent, long‐lived, circular 2‐D eddies.

Extremely Low Frequency (0.1 to 1.0 mHz) Surf Zone Currents

“…There are several hypotheses for the generation of low‐frequency motions in the surf zone. Low‐frequency currents have been observed on bathymetrically alongshore‐inhomogeneous beaches, including those with one or more rip channels (Castelle et al, ; Johnson, ; MacMahan et al, ), and theoretical and numerical simulations of waves propagating across rip channeled surf zone bathymetry often include low‐frequency motions (Bruneau et al, ; Geiman & Kirby, ; Johnson & Pattiaratchi, ; Kennedy et al, ; Reniers et al, ; Uchiyama et al, ). On alongshore uniform beaches, low‐frequency velocity fluctuations have been hypothesized to be generated by instabilities of the alongshore current (Bowen & Holman, ; Oltman‐Shay et al, ; Özkan‐Haller & Kirby, ) and by wave‐group‐induced modulations of sea surface elevation fluctuations (Haller et al, ; Long & Özkan‐Haller, ; MacMahan et al, ).…”

Influences of the Kuroshio on Interisland Remote Connectivity of Corals Across the Nansei Archipelago in the East China Sea

“…The JCOPE2 product is provided as daily-averaged sea surface height (SSH), temperature, salinity, and meridional and zonal horizontal current velocities, which are spatiotemporally projected onto the perimeter of the ROMS-L1 model for the open boundary conditions. The one-way off-line nesting approach described in Mason et al (2010), Uchiyama et al (2014), Uchiyama, McWilliams, et al (2017), Uchiyama, Suzue, et al (2017), Uchiyama, Kanki, et al (2017), Uchiyama et al (2018), Kamidaira et al (2017Kamidaira et al ( , 2018, and Tada et al (2018) is applied to successively decreasing grid spacing from~10 km (JCOPE2) to 3 km (ROMS-L1), and further down to 1 km (ROMS-L2). The parent ROMS-L1 model is designed to encompass a wide area to account for the Kuroshio flowing from the Taiwan Strait, consisting of 768 × 768 horizontal grid cells and 32 vertically stretched terrain-and surface-following s layers (Shchepetkin & McWilliams, 2005).…”

“…The monthly climatology of the major river discharges in Dai et al (2009) was applied for Yangtze River as an additional surface freshwater flux distributed around the river mouth. To improve the reproducibility of the Kuroshio, we introduced a fourdimensional nudging for temperature and salinity with a weak nudging inverse time scale of 1/20 days toward the 10-day averaged JCOPE2 3-D temperature and salinity fields (Uchiyama, McWilliams, et al, 2017). This combination of the data sets and configuration has been exploited for high-resolution modeling of the Kuroshio around Japan extensively with great successes (e.g., Tada et al, 2018;Uchiyama, McWilliams, et al, 2017;Uchiyama, Suzue, et al, 2017).…”

“…To improve the reproducibility of the Kuroshio, we introduced a fourdimensional nudging for temperature and salinity with a weak nudging inverse time scale of 1/20 days toward the 10-day averaged JCOPE2 3-D temperature and salinity fields (Uchiyama, McWilliams, et al, 2017). This combination of the data sets and configuration has been exploited for high-resolution modeling of the Kuroshio around Japan extensively with great successes (e.g., Tada et al, 2018;Uchiyama, McWilliams, et al, 2017;Uchiyama, Suzue, et al, 2017). For further details of the present ROMS-L1 model configuration, readers should refer to Kamidaira et al (2017).…”

Tridimensional nonhydrostatic transient rip currents in a wave-resolving model

“…The theoretical framework from depth-integrated models neglect the effect of vertical shear. Following the advent of robust 3D formulations of wave-averaged equations (McWilliams et al, 2004;Ardhuin et al, 2008), a number of 3D modeling studies have emerged in the last decade (Newberger and Allen, 2007;Uchiyama et al, 2010;Kumar et al, 2012;Marchesiello et al, 2015;Uchiyama et al, 2017;McWilliams et al, 2018;Akan et al, 2020). They show a modulation of nearshore circulation when wave breaking occurs in a shallow surface layer.…”