Surfzone-inner shelf interaction analyzed witha quintuple nested high resolution ocean model
Hideki Kaida 1 and Yusuke Uchiyama 11

Department of Civil Engineering, Kobe University, Japan
Abstract

Observational studies have recently rediscovered that littoral currents play a crutial role in the interaction between
surfzone and inner shelf (e.g., Lentz et al., 2008). A synoptic, detailed numerical experiment is conducted to pursue thisproblem with a multi-nested coupling system consisting of ROMS-WEC (Uchiyama et al., 2010), SWAN and WRF athorizontal resolutions down to 20 m. Both the Eulerian and Lagrangian analyses clearly indicate that wave-driven threedimensional currents significantly enhance horizontal and vertical mixing and dispersion. Lagrangian particle tracking
exhibits that rip currents and undertows induce vertical secondary flow that plunges those particles downwards beyond thepycnocline, leading to markedly increased initial dilution and thus much faster relative dispersion tendency.
Keywords – Surfzone-shelf interaction, multiple nesting approach, atmosphere-wave-ocean coupling
1 Introduction
Recent observations have suggested that wave-induced threedimensional littoral currents are substantially important formaterial transport between surfzone and inner shelf (e.g., Lentz
et al., 2008). The surfzone acts as a barrier by cross-shore
vertical recirculation due to breaking wave-induced flow to form
an isolated water mass called ‘sticky water’ (Wolanski, 1994).
However, a 3-D modeling framework that solves both thelittoral and inner shelf currents concurrently has not been fully
established, and therefore modeling studies for the surfzoneinner shelf interaction lags behind observational ones. In thepresent study, we examine the surfzone-inner shelf interaction
using a high resolution 3-D ocean model with wave effects
based on the novel ROMS-WEC framework (Uchiyama et al.,2010), that relies on an Eulerian wave-averaged vortex-force
formalism, at a horizontal resolution of 20 m, coupled with anoperational spectral wave model SWAN and a regional
atmospheric model WRF to render an atmosphere-wave-oceaninteraction.
2 Numerical Model
In order to properly represent both the surfzone and innershelf dynamics, a quintuple nested configuration is developedwith ROMS and ROMS-WEC. A winter-spring storm season atSanta Monica Bay, CA, USA, is chosen for the experiment toaccount for stormy rough waves. The innermost (the fifth nest)
solution at a horizontal resolution of 20 m (hereinafter L5, Fig.
1), that enables us to consider surfzone dymanics, is used for thefollowing analyses. The present ROMS configuration consistsof five nested domains with an offline, one-way nesting
technique that downscales from 5 km horizontal resolution for
the U.S. West Coast (L1) to L5 domain through L2, L3 and L4
intermediate domains at 1 km, 250 m and 75 m respectively.
The outermost boundary condition is provided by a global
oceanic reanalysis data set, SODA 2.0.4, to convey the basinscale oceanic signals adequately. L5 is forced by the 2-hourly
averaged L4 output inclusive of tidal signals as a boundary
condition projected onto the L5 perimeters in time and spaceSea surface wind stress, heat and radiation fluxes are given by adouble nested WRF downscaling result with the innermost
horizontal resolution of 6 km. Surface waves are considered inROMS-L3, L4 and L5 by an offline coupling with a triple
nested SWAN solution running on the corresponding ROMSgrids. The computational period for L5 is from February 2008 toApril 2008 when northwesterly swells are predominant.

Fig. 1. Snapshot of surface normalized relative vorticity
for L5. Left: full L5 model domain, right: nearshore zoom-in
corresponding to the black frame in the left panel.

Fig. 2. Cross-shore profiles of kinematic wave dissipation
rate εb [m 3/s3] at y = 18 km from the L5 SWAN solution.
Red line: εb for the strongest rip currents.

Fig. 3.  Sequential plots of surface normalized relativevorticity (a-c, g-i) and density anomaly σt [kg/m 3] averaged
alongshore within the control volume L (d-f, j-l). Panels a-f:case A (with wave breaking), panels g-l: case B (withoutwave breaking, viz., εb = 0).
Table 1  Computational configurations for three
dimensional Lagrangian particle tracking experiment.
Case No.

εbA1
A2
B1
B2

ONONOFFOFF

Particle release position and numberof particles N released from each site
Inside the surfzone, N = 600
Outside the surfzone, N = 1660
Inside the surfzone, N = 600
Outside the surfzone, N = 1660

3 Sensitivity test with/without breaker effectA snapshot of normalized relative vorticity in L5 shows anexample of offshore-directed strong rip currents erupting fromthe surfzone (Fig. 1). These rip currents are driven by strong
wave breaking on the alongshore-variable topography (Fig.2).
We loosely define a breaking point as an interface with themaximum εb to consider cross-shore water/material exchange
between the onshore surfzone and the offshore inner-shelf withrespect to this breaking point. To quantify the contribution ofwave-driven littoral currents due to wave breaking to the crossshore material transport between them, we take an advantage ofthe vortex-force based ROMS-WEC. A comparative test run iscarried out to eliminate only the breaker effect among the otherwave effects such as vortex force and Bernoulli head, byvanishing εb. Case A stands for a control run where εb isconsidered, while εb vanishes in case B.  We confirm that nullεb is almost fully accepted in the model within a few hours aftervanishing εb, and 4 days later case B successfully eliminates
littoral currents while retaining the offshore overall flow field ascompared to that for case A (not shown).
4 Eulerian view: stratification
We focus on the energetic rip event that mostly develops from
2/28 15:00 to 2/29 16:00. A control volume L (17,875 m ≤ y ≤18,125m) is defined to examine the alongshore-averaged
vertical structure of water density anomaly σt. From a calm
littoral current situation under a mild wave condition to an earlystage of development of the rip currents (left and middle panels
in Fig. 3), deep dense water is brought up to the surface in bothcases. When rip currents develop (right panel in Fig. 3), most of
the lighter water mass still remains near the shoreline in case B,
although it disappears in the surfzone in case A. This suggeststhat the barrier structure around the surfzone is more easily
destroyed through cross-shore mixing between the surfzone andthe offshore enhanced by the rip currents. In other words, wave-Fig. 4.  Temporal evolution of alongshore integrated
Lagrangian PDFs of the particles on 2/28/2008. Left: 1 hour,middle: 3 hours, right: 10 hours after the release. Yellow curvesin each panel indicate the KPP-estimated surface boundary(mixed) layer depth.
induced cross-shore currents diminish the isolated water massformed around the surfzone.
5 Lagrangian view: particle tracking
An offline, 3-D Lagrangian passive particle tracking using thesimulated L5 flow field is conducted to assess effects of littoral
currents on cross-shore mixing and dispersal. Among several
different cases we have conducted, four typical cases for theduration of the strongest rip currents are presented as listed inTable 1. In cases A1 and B1, all the particles are released in thesurfzone. Alongshore-integrated Lagrangian PDF in Fig. 4
illustrates that littoral currents transport the particles laterally to
finally dilute out of the surfzone for case A1, whereas someparticles remain in the surfzone if εb vanishes (case B1). Theparticles released in the offshore (cases A2 and B2) behave
differently, while littoral currents bring them back to thesurfzone due to horizontally circulating littoral cell structurewith a substantial influence of the vertical shear associated with3-D littoral currents. As a consequent, littoral currents have apronounced impact on enhancing the cross-shore dispersion ofthe particles, consistently with the Eulerian result in Sec. 4.
References[1] Letnz, S. J., M. Fewings, P. Howd, J. Fredericks, and K. Hathaway,
Observations and a model of undertow over the inner continental
shelf., J. Phys. Oceanogr, Vol.38, pp.2341-2357, 2008.
[2] Uchiyama,Y., J. C. McWilliams and A.F. Shchepetkin, Wavecurrent interaction in an oceanic circulation model with a vortex
force formalism: Application to the surf zone, Ocean Modell., Vol.
34:1-2, pp. 16-35, 2010.
[3] Wolanski, E., Physical Oceanographic Processes of the Great
Barrier Reef, CRC Press, Boca Raton, Florida, 194 pp, 1994.