Wind-Induced Changes to Shoaling Surface Gravity Wave Shape

Unforced shoaling waves experience growth and changes to wave shape. Similarly, wind-forced waves on a flat-bottom likewise experience growth/decay and changes to wave shape. However, the combined effect of shoaling and wind-forcing on wave shape, particularly relevant in the near-shore environment, has not yet been investigated theoretically. Here, we consider small-amplitude, shallow-water solitary waves propagating up a gentle, planar bathymetry forced by a weak, Jeffreys-type wind-induced surface pressure. We derive a variable-coefficient Korteweg-de Vries-Burgers (vKdV-B) equation governing the wave profile's evolution and solve it numerically using a Runge-Kutta third-order finite difference solver. The simulations run until convective prebreaking -- a Froude number limit appropriate to the order of the vKdV-B equation. Offshore winds weakly enhance the ratio of prebreaking height to depth as well as prebreaking wave slope. Onshore winds have a strong impact on narrowing the wave peak, and wind also modulates the rear shelf formed behind the wave. Furthermore, wind strongly affects the width of the prebreaking zone, with larger effects for smaller beach slopes. After converting our pressure magnitudes to physically realistic wind speeds, we observe qualitative agreement with prior laboratory and numerical experiments on breakpoint location. Additionally, our numerical results have qualitatively similar temporal wave shape to shoaling and wind-forced laboratory observations, suggesting that the vKdV-B equation captures the essential aspects of wind-induced effects on shoaling wave shape. Finally, we isolate the wind's effect by comparing the wave profiles to the unforced case. This reveals that the numerical results are approximately a superposition of a solitary wave, a shoaling-induced shelf, and a wind-induced, bound, dispersive, and decaying tail.Comment: Added discussion of asymptotic regime (section 2F), discussion of perturbed KdV (section 4B), and minor corrections; 23 pages, 10 figure

The effect of wave breaking on surf-zone turbulence and alongshore currents : a modeling study

Author Posting. © American Meteorological Society, 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 35 (2005): 2187–2203, doi:10.1175/JPO2800.1.The effect of breaking-wave-generated turbulence on the mean circulation, turbulence, and bottom stress in the surf zone is poorly understood. A one-dimensional vertical coupled turbulence (k–ε) and mean-flow model is developed that incorporates the effect of wave breaking with a time-dependent surface turbulence flux and uses existing (published) model closures. No model parameters are tuned to optimize model–data agreement. The model qualitatively reproduces the mean dissipation and production during the most energetic breaking-wave conditions in 4.5-m water depth off of a sandy beach and slightly underpredicts the mean alongshore current. By modeling a cross-shore transect case example from the Duck94 field experiment, the observed surf-zone dissipation depth scaling and the observed mean alongshore current (although slightly underpredicted) are generally reproduced. Wave breaking significantly reduces the modeled vertical shear, suggesting that surf-zone bottom stress cannot be estimated by fitting a logarithmic current profile to alongshore current observations. Model-inferred drag coefficients follow parameterizations (Manning–Strickler) that depend on the bed roughness and inversely on the water depth, although the inverse depth dependence is likely a proxy for some other effect such as wave breaking. Variations in the bed roughness and the percentage of breaking-wave energy entering the water column have a comparable effect on the mean alongshore current and drag coefficient. However, covarying the wave height, forcing, and dissipation and bed roughness separately results in an alongshore current (drag coefficient) only weakly (strongly) dependent on the bed roughness because of the competing effects of increased turbulence, wave forcing, and orbital wave velocities.This work was funded by NSF, ONR, and NOPP

Modeling surf zone tracer plumes : 2. Transport and dispersion

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 116 (2011): C11028, doi:10.1029/2011JC007211.Five surf zone dye tracer releases from the HB06 experiment are simulated with a tracer advection diffusion model coupled to a Boussinesq surf zone model (funwaveC). Model tracer is transported and stirred by currents and eddies and diffused with a breaking wave eddy diffusivity, set equal to the breaking wave eddy viscosity, and a small (0.01 m2 s−1) background diffusivity. Observed and modeled alongshore parallel tracer plumes, transported by the wave driven alongshore current, have qualitatively similar cross-shore structures. Although the model skill for mean tracer concentration is variable (from negative to 0.73) depending upon release, cross-shore integrated tracer moments (normalized by the cross-shore tracer integral) have consistently high skills (≈0.9). Modeled and observed bulk surf zone cross-shore diffusivity estimates are also similar, with 0.72 squared correlation and skill of 0.4. Similar to the observations, the model bulk (absolute) cross-shore diffusivity is consistent with a mixing length parameterization based on low-frequency (0.001–0.03 Hz) eddies. The model absolute cross-shore dispersion is dominated by stirring from surf zone eddies and does not depend upon the presence of the breaking wave eddy diffusivity. Given only the bathymetry and incident wave field, the coupled Boussinesq-tracer model qualitatively reproduces the observed cross-shore absolute tracer dispersion, suggesting that the model can be used to study surf zone tracer dispersion mechanisms.This research was supported by SCCOOS, CA Coastal Conservancy, NOAA, NSF, ONR, and CA Sea Grant.2012-05-1

Direct estimation of the Reynolds stress vertical structure in the nearshore

Author Posting. © American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Atmospheric and Oceanic Technology 24 (2007): 102-116, doi:10.1175/JTECH1953.1.Measurements of the vertical Reynolds stress components in the wave-dominated nearshore are required to diagnose momentum and turbulence dynamics. Removing wave bias from Reynolds stress estimates is critical to a successful diagnosis. Here two existing Reynolds stress estimation methods (those of Trowbridge, and Shaw and Trowbridge) for wave-dominated environments and an extended method (FW) that is a combination of the two are tested with a vertical array of three current meters deployed in 3.2-m water depth off an ocean beach. During the 175-h-long experiment the instruments were seaward of the surfzone and the alongshore current was wind driven. Intercomparison of Reynolds stress methods reveals that the Trowbridge method is wave bias dominated. Tests of the integrated cospectra are used to reject bad Reynolds stress estimates, and the Shaw and Trowbridge estimates are rejected more often than FW estimates. With the FW method, wave bias remains apparent in the cross-shore component of the Reynolds stress. However, the alongshore component of Reynolds stress measured at the three current meters are related to each other with a vertically uniform first EOF containing 73% of the variance, indicating the presence of a constant stress layer. This is the first time the vertical structure of Reynolds stress has been measured in a wave-dominated environment. The Reynolds stress is, albeit weakly, related to the wind stress and a parameterized bottom stress. Using derived wave bias and bottom stress parameterizations, the effect of wave bias on Reynolds stress estimates is shown to be weaker for more typical surfzone conditions (with both stronger waves and currents than those observed here).Funded by NSF, ONR, and NOPP

Surfzone to inner-shelf exchange estimated from dye tracer balances

Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 120 (2015): 6289–6308, doi:10.1002/2015JC010844.Surfzone and inner-shelf tracer dispersion are observed at an approximately alongshore-uniform beach. Fluorescent Rhodamine WT dye, released near the shoreline continuously for 6.5 h, is advected alongshore by breaking-wave- and wind-driven currents, and ejected offshore from the surfzone to the inner-shelf by transient rip currents. Novel aerial-based multispectral dye concentration images and in situ measurements of dye, waves, and currents provide tracer transport and dilution observations spanning about 350 m cross-shore and 3 km alongshore. Downstream dilution of near-shoreline dye follows power law decay with exponent −0.33, implying that a tenfold increase in alongshore distance reduces the concentration about 50%. Coupled surfzone and inner-shelf dye mass balances close, and in 5 h, roughly half of the surfzone-released dye is transported offshore to the inner-shelf. Observed cross-shore transports are parameterized well ( inline image, best fit slope inline image) using a bulk exchange velocity and mean surfzone to inner-shelf dye concentration difference. The best fit cross-shore exchange velocity inline image is similar to a temperature-derived exchange velocity on another day with similar wave conditions. The inline image magnitude and observed inner-shelf dye length scales, time scales, and vertical structure indicate the dominance of transient rip currents in surfzone to inner-shelf cross-shore exchange during moderate waves at this alongshore-uniform beach.National Science Foundation Graduate Research Fellowship Grant Number: DGE1144086, California Sea Grant Number: R/CONT-207TR2016-03-1

Episodic vertical nutrient fluxes and nearshore phytoplankton blooms in Southern California

Author Posting. © Association for the Sciences of Limnology and Oceanography, 2012. This article is posted here by permission of Association for the Sciences of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography 57 (2012): 1673-1688, doi:10.4319/lo.2012.57.6.1673.Three distinct phytoplankton blooms lasting 4–9 d were observed in approximately 15-m water depth near Huntington Beach, California, between June and October of 2006. Each bloom was preceded by a vertical NO3 flux event 6–10 d earlier. NO3 concentrations were estimated using a temperature proxy that was verified by comparison with the limited NO3 observations. The lower–water-column vertical NO3 flux from vertical advection was inferred from observed vertical isotherm displacement. Turbulent vertical eddy diffusivity was parameterized based on the observed background (< 0.3 cycles h−1) stratification and vertical shear in the horizontal currents. The first vertical nitrate flux event in June contained both advective and turbulent fluxes, whereas the later two events were primarily turbulent, driven by shear in the lower part of the water column. The correlation between the NO3 flux and the observed chlorophyll a (Chl a) was maximum (r2 = 0.40) with an 8-d lag. A simple nitrate–phytoplankton model using a linear uptake function and driven with the NO3 flux captured the timing, magnitude, and duration of the three Chl a blooms (skill = 0.61) using optimal net growth rate parameters that were within the expected range. Vertical and horizontal advection of Chl a past the measurement site were too small to explain the observed Chl a increases during the blooms. The vertical NO3 flux was a primary control on the growth events, and estimation of both the advective (upwelled) and turbulent fluxes is necessary to best predict these episodic blooms.California Sea Grant, National Oceanic and Atmospheric Administration, California Coastal Conservancy, National Science Foundation, and the Office of Naval Research supported this research