Research papersTidally influenced alongshore circulation at an inlet-adjacent shoreline
Highlights
► Tidal forcing is found to be an important contribution to the surfzone alongshore force balance adjacent to an inlet. ► Tides result in a barotropic pressure gradient and alter the wave field through depth changes and wave–current interaction. ► Tidal modulation of the surfzone alongshore force balance can result in changes in the direction of surfzone alongshore flow.
Introduction
Wave driven alongshore circulation at sandy beaches has been extensively investigated and linked to the transport of sediments and pollutants (e.g. Bowen, 1969, Komar and Inman, 1970, Longuet-Higgins, 1970, Thornton and Guza, 1986, Feddersen et al., 1998, Chen et al., 2003, Feddersen and Guza, 2003, Apotsos et al., 2008, Clark et al., 2010, and many more). Similarly, detailed analyses have been conducted describing flow, forcing, and sediment transport through and adjacent to tidal inlets (e.g. O'Brien, 1969, Hayes, 1980, Hench and Luettich, 2003, Elias et al., 2006, van der Vegt et al., 2006, Vennell, 2006, Olabarrieta et al., 2011). However, given the common occurrence of tidal inlets along wave dominated coast, surprisingly few analyses have been conducted investigating hydrodynamics at inlet adjacent sandy beaches where surfzone alongshore circulation may be impacted by both wave and tidal processes. One such example is the analysis of Davis and Fox (1981) who investigated circulation using field measurements and a numerical model in and around Matanzas River, Florida (USA). They concluded that impacts of the inlet and tidal circulation on the open coast surfzone circulation were extremely limited in spatial extent, with tidal currents being undetectable 500 m from the inlet. Here, we investigate the role of tidal forcing in altering and otherwise influencing alongshore circulation within the surfzone at an energetic shoreline adjacent to a much larger tidal inlet.
Numerical results are presented from Ocean Beach in San Francisco, CA (USA) a 7 km long stretch of sandy beach located immediately south of the Golden Gate, the sole entrance to San Francisco Bay. Tidal flux is large through the Golden Gate, with a tidal prism of approximately 2×109 m3 (Barnard et al., 2007, Dallas and Barnard, 2011), two orders of magnitude larger than Matanzas River described by Davis and Fox (1981). Recently Shi et al. (2011) conducted a numerical investigation of alongshore momentum balances at Ocean Beach for storm conditions (offshore significant wave height (Hs) of 3.5 m) and determined that refraction of waves across an ebb-tidal delta that attaches to the coast at Ocean Beach introduces an alongshore pressure gradient that can dominate the alongshore forcing. They also concluded that the tidal pressure gradient, resulting from tidal flow through the inlet, was not large enough to alter the spatial variability in forcing introduced by the heterogeneous wave field. However, the focus of their analysis was on the role of the heterogeneous wave field and they did not present a quantitative analysis of the relative contributions of tidal and wave forcing to the overall force balance. Their analysis of the tidal pressure gradient was also limited to a single time during the ebb which, as will be shown here, is not representative of the entire tidal cycle. In the present analysis we extend their results by specifically investigating tidal contributions to surfzone alongshore forcing, through the tidal pressure gradient and also through tidal influences on the wave field, using numerically computed alongshore momentum balances from 24 climatologically derived wave conditions over a 24.8 h representative tidal cycle.
Section snippets
Study location
Ocean Beach in San Francisco, CA (USA) is a 7 km stretch of sandy beach that makes up the western flank of the City of San Francisco (Fig. 1). The proximity of Ocean Beach to the Golden Gate subjects this area to strong alongshore tidal currents, up to ∼1 m/s at the north end of Ocean Beach in ∼10 m depth (Barnard et al., 2007). Wave propagation is impacted both by interaction with these strong tidal currents and by the San Francisco Bar, a ∼150 km2 ebb-tidal delta located immediately outside of
Governing alongshore dynamics
In the surfzone, the time-averaged (over many wave periods), depth-integrated alongshore momentum balance can be written as (e.g. Feddersen et al., 1998):where the left hand side (LHS) of the equation is the local acceleration and advective acceleration terms ( is the water density, η is the water surface deviation from still water, h is still water depth, u and v are the depth and time-averaged current velocities in the
Numerical model
The numerical hydrodynamic model, Delft3D-FLOW (Lesser et al., 2004) coupled with the wave model SWAN (Holthuijsen et al., 1993, Booij et al., 1999, Ris et al., 1999) was used to simulate the hydrodynamics and produce alongshore momentum balances. Delft3D solves the unsteady shallow-water equations in two or three dimensions on a staggered Arakawa-C grid (Lesser et al., 2004). In addition to the forces applicable to nearshore flows (i.e. those in (1)), Delft3D also includes the Coriolis force,
Model calibration and validation
Detailed calibration and validation of both the flow and wave models is also presented in Elias and Hansen (in press) and is briefly summarized here. Propagation of tides within the circulation model was calibrated using 39 active and historic NOAA tidal stations on the open coast and inside San Francisco Bay. After calibration the largest tidal constituents show good agreement at tidal stations within the Golden Gate inlet and at Pt. Reyes (Fig. 1A and C, Table 1, amplitude differences <0.03
Model input reduction
Our approach here is not to specifically investigate a particular time period but rather to determine, using a representative set of conditions and tidal forcing, whether or not tidal forcing is of a large enough magnitude to have an impact on the surfzone alongshore force balance. Therefore, the observed wave climate and tidal cycle was synthesized into representative conditions. The wave climate was distilled into 24 cases that represent 14 years of offshore buoy observations and the full
Alongshore momentum balances
To understand the underlying physics of the modeled flows for each of the 24 simulations, the influence of the heterogeneous wave field on the flow and ultimately the role of tidal forcing within the surfzone, alongshore momentum balances for each of the 24 wave cases were investigated. In this paper we use a modified version of the open source Delft3D-Flow (version 4.00.06.705:813) that saves all the terms of the governing momentum equations as output, including all terms in (1). For each wave
Discussion
Shi et al. (2011) found that alongshore variability in wave heights introduced by wave refraction across the ebb-tidal delta offshore of the Golden Gate results in an alongshore pressure gradient that can be the dominant term of the alongshore momentum balance, a conclusion that is supported by our simulations. However, they also concluded that the tidal pressure gradient was not large enough to modify the spatial variability in forcing introduced by the inhomogeneous wave field. If we run our
Conclusions
A high-resolution coupled flow and wave numerical model was used to investigate the role of tidal forcing in driving and modifying alongshore flows within the surfzone along a 7 km stretch of shoreline adjacent to a major inlet. The 24 most frequently occurring wave cases were derived from 14 years of offshore buoy records and a 24.8 h representative tide was developed from the calibrated tidal constituents. For each of the 24 wave cases the model was run for one representative tidal cycle.
Acknowledgments
This work was funded by the U.S. Geological Survey and U.S. Army Corps of Engineers. We thank Alex Apotsos and Joe Long for reviewing an initial draft of this manuscript as well as two anonymous reviewers for their suggestions.
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