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A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the nonlinear shallow water equations to study the nearshore dynamics of infragravity (IG) waves. Based on simulations of waves on a relatively moderate and mild beach slope with a non-hydrostatic wave-flow model (SWASH), the new theory shows that spatial gradients in IG energy flux are nearly completely balanced by the combined effect of bottom stresses and predominantly nonlinear triad interactions. The new balance confirms many features of existing weakly nonlinear theories, and yields an improved description in the inner surfzone where waves become highly nonlinear. A gain of IG energy flux throughout the shoaling and outer surfzones is driven by triad interactions between IG waves and pairs of sea-swell (SS) waves. The IG energy flux decreased in the inner surfzone, primarily through an energy cascade to the swell-band and superharmonic frequencies where wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. The IG wave breaking, characterized by triads between three IG or two IG waves and one SS wave, was significant only deep inside the surfzone of the mild slope. Even though IG waves broke on the mild slope, nonlinear interactions between IG waves and pairs of SS waves were responsible for at least half of the net IG flux loss., Environmental Fluid Mechanics

A fully nonlinear non-dispersive energy balance for surfzone waves is derived based on the nonlinear shallow water equations to study the nearshore dynamics of infragravity (IG) waves. Based on simulations of waves on a relatively moderate and mild beach slope with a non-hydrostatic wave-flow model (SWASH), the new theory shows that spatial gradients in IG energy flux are nearly completely balanced by the combined effect of bottom stresses and predominantly nonlinear triad interactions. The new balance confirms many features of existing weakly nonlinear theories, and yields an improved description in the inner surfzone where waves become highly nonlinear. A gain of IG energy flux throughout the shoaling and outer surfzones is driven by triad interactions between IG waves and pairs of sea-swell (SS) waves. The IG energy flux decreased in the inner surfzone, primarily through an energy cascade to the swell-band and superharmonic frequencies where wave energy is ultimately dissipated. Dissipation by bottom friction was weak on both slopes. The IG wave breaking, characterized by triads between three IG or two IG waves and one SS wave, was significant only deep inside the surfzone of the mild slope. Even though IG waves broke on the mild slope, nonlinear interactions between IG waves and pairs of SS waves were responsible for at least half of the net IG flux loss., Environmental Fluid Mechanics

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Geophysical Research: Oceans 121 (2016): 7819–7844, doi:10.1002/2016JC011922., A 9 km long tracer plume was created by continuously releasing Rhodamine WT dye for 2.2 h during ebb tide within the southern edge of the main tidal channel at New River Inlet, NC on 7 May 2012, with highly obliquely incident waves and alongshore winds. Over 6 h from release, COAWST (coupled ROMS and SWAN, including wave, wind, and tidal forcing) modeled dye compares well with (aerial hyperspectral and in situ) observed dye concentration. Dye first was transported rapidly seaward along the main channel and partially advected across the ebb-tidal shoal until reaching the offshore edge of the shoal. Dye did not eject offshore in an ebb-tidal jet because the obliquely incident breaking waves retarded the inlet-mouth ebb-tidal flow and forced currents along the ebb shoal. The dye plume largely was confined to <4 m depth. Dye was then transported downcoast in the narrow (few 100 m wide) surfzone of the beach bordering the inlet at 0.3 inline image driven by wave breaking. Over 6 h, the dye plume is not significantly affected by buoyancy. Observed dye mass balances close indicating all released dye is accounted for. Modeled and observed dye behaviors are qualitatively similar. The model simulates well the evolution of the dye center of mass, lateral spreading, surface area, and maximum concentration, as well as regional (“inlet” and “ocean”) dye mass balances. This indicates that the model represents well the dynamics of the ebb-tidal dye plume. Details of the dye transport pathways across the ebb shoal are modeled poorly perhaps owing to low-resolution and smoothed model bathymetry. Wave forcing effects have a large impact on the dye transport., Littoral Geosciences and Optics Division of the Office of Naval Research as part of the Tidal Inlets and River Mouths Directed Research Initiative

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Geophysical Research: Oceans 121 (2016): 7819–7844, doi:10.1002/2016JC011922., A 9 km long tracer plume was created by continuously releasing Rhodamine WT dye for 2.2 h during ebb tide within the southern edge of the main tidal channel at New River Inlet, NC on 7 May 2012, with highly obliquely incident waves and alongshore winds. Over 6 h from release, COAWST (coupled ROMS and SWAN, including wave, wind, and tidal forcing) modeled dye compares well with (aerial hyperspectral and in situ) observed dye concentration. Dye first was transported rapidly seaward along the main channel and partially advected across the ebb-tidal shoal until reaching the offshore edge of the shoal. Dye did not eject offshore in an ebb-tidal jet because the obliquely incident breaking waves retarded the inlet-mouth ebb-tidal flow and forced currents along the ebb shoal. The dye plume largely was confined to <4 m depth. Dye was then transported downcoast in the narrow (few 100 m wide) surfzone of the beach bordering the inlet at 0.3 inline image driven by wave breaking. Over 6 h, the dye plume is not significantly affected by buoyancy. Observed dye mass balances close indicating all released dye is accounted for. Modeled and observed dye behaviors are qualitatively similar. The model simulates well the evolution of the dye center of mass, lateral spreading, surface area, and maximum concentration, as well as regional (“inlet” and “ocean”) dye mass balances. This indicates that the model represents well the dynamics of the ebb-tidal dye plume. Details of the dye transport pathways across the ebb shoal are modeled poorly perhaps owing to low-resolution and smoothed model bathymetry. Wave forcing effects have a large impact on the dye transport., Littoral Geosciences and Optics Division of the Office of Naval Research as part of the Tidal Inlets and River Mouths Directed Research Initiative

Our long-term goals include developing and field-testing numerical models of shallow water breaking waves and wave-driven processes, including currents, and tracer transport and dispersion. Improved prediction of the fate of terrestrial runoff pollution and other substances (e.g. fine sediment, chemicals) sometimes present in very shallow water.

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-207TR, 2016-03-19

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-207TR, 2016-03-19

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.

Author Posting. © American Meteorological Society, 2014. 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 31 (2014): 1410–1421, doi:10.1175/JTECH-D-13-00230.1., Aerial images are used to quantify the concentration of fluorescent Rhodamine water tracing (WT) dye in turbid and optically deep water. Tracer releases near the shoreline of an ocean beach and near a tidal inlet were observed with a two-band multispectral camera and a pushbroom hyperspectral imager, respectively. The aerial observations are compared with near-surface in situ measurements. The ratio of upwelling radiance near the Rhodamine WT excitation and emission peaks varies linearly with the in situ dye concentrations for concentrations <20 ppb (r2 = 0.70 and r2 = 0.85–0.88 at the beach and inlet, respectively). The linear relationship allows for relative tracer concentration estimates without in situ calibration. The O(1 m) image pixels resolve complex flow structures on the inner shelf that transport and mix tracer., We thank ONR and NSF for funding this work., 2014-12-01

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.

Author Posting. © American Meteorological Society, 2014. 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 31 (2014): 1410–1421, doi:10.1175/JTECH-D-13-00230.1., Aerial images are used to quantify the concentration of fluorescent Rhodamine water tracing (WT) dye in turbid and optically deep water. Tracer releases near the shoreline of an ocean beach and near a tidal inlet were observed with a two-band multispectral camera and a pushbroom hyperspectral imager, respectively. The aerial observations are compared with near-surface in situ measurements. The ratio of upwelling radiance near the Rhodamine WT excitation and emission peaks varies linearly with the in situ dye concentrations for concentrations <20 ppb (r2 = 0.70 and r2 = 0.85–0.88 at the beach and inlet, respectively). The linear relationship allows for relative tracer concentration estimates without in situ calibration. The O(1 m) image pixels resolve complex flow structures on the inner shelf that transport and mix tracer., We thank ONR and NSF for funding this work., 2014-12-01

Our long-term goals include developing and field-testing numerical models of shallow water breaking waves and wave-driven processes, including currents, and tracer transport and dispersion. Improved prediction of the fate of terrestrial runoff pollution and other substances (e.g. fine sediment, chemicals) sometimes present in very shallow water.

Our long-term goals include developing and field-testing numerical models of shallow water breaking waves and wave-driven processes, including currents, and tracer transport and dispersion. Improved prediction of the fate of terrestrial runoff pollution and other substances (e.g. fine sediment, chemicals) sometimes present in very shallow water. The objective of this project, to measure mixing and transport in a small tidal inlet, was achieved in the RIVET 1 experiment. During RIVET I, we measured transport and dispersion from within the New River Inlet to 2-3 km offshore and alongshore, at different tidal stages. Analysis of this diverse data set of waves, currents, stratification, Lagrangian drifter, and dye-tracers has begun.

Long-term objectives are developing and field testing numerical models of shallow water breaking waves and wave-driven processes including mixing, currents, and transport and dispersion of tracers. Calibrated models will provide improved prediction of the fate of tracers (e.g. pollution, fine sediment, chemicals) in very shallow water. Objectives during the past year included continued analysis of existing data sets, and extending our existing field capability in preparation for participation in the tidal inlet/river mouth DRI.

Long-term objectives are developing and field testing numerical models of shallow water breaking waves and wave-driven processes including mixing, currents, and transport and dispersion of tracers. Calibrated models will provide improved prediction of the fate of tracers (e.g. pollution, fine sediment, chemicals) in very shallow water., FY10 Annual Reports of S & T efforts sponsored by the Ocean Battlespace Sensing S & T Department of the Office of Naval Research., The original document contains color images.

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): C11027, doi:10.1029/2011JC007210., A model that accurately simulates surf zone waves, mean currents, and low-frequency eddies is required to diagnose the mechanisms of surf zone tracer transport and dispersion. In this paper, a wave-resolving time-dependent Boussinesq model is compared with waves and currents observed during five surf zone dye release experiments. In a companion paper, Clark et al. (2011) compare a coupled tracer model to the dye plume observations. The Boussinesq model uses observed bathymetry and incident random, directionally spread waves. For all five releases, the model generally reproduces the observed cross-shore evolution of significant wave height, mean wave angle, bulk directional spread, mean alongshore current, and the frequency-dependent sea surface elevation spectra and directional moments. The largest errors are near the shoreline where the bathymetry is most uncertain. The model also reproduces the observed cross-shore structure of rotational velocities in the infragravity (0.004 < f < 0.03 Hz) and very low frequency (VLF) (0.001 < f < 0.004 Hz) bands, although the modeled VLF energy is 2–3 times too large. Similar to the observations, the dominant contributions to the modeled eddy-induced momentum flux are in the VLF band. These eddies are elliptical near the shoreline and circular in the mid surf zone. The model-data agreement for sea swell waves, low-frequency eddies, and mean currents suggests that the model is appropriate for simulating surf zone tracer transport and dispersion., This research was supported by SCCOOS, CA Coastal Conservancy, NOAA, NSF, ONR, and CA Sea Grant., 2012-05-18

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., 2012-05-18

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., 2012-05-18

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): C11027, doi:10.1029/2011JC007210., A model that accurately simulates surf zone waves, mean currents, and low-frequency eddies is required to diagnose the mechanisms of surf zone tracer transport and dispersion. In this paper, a wave-resolving time-dependent Boussinesq model is compared with waves and currents observed during five surf zone dye release experiments. In a companion paper, Clark et al. (2011) compare a coupled tracer model to the dye plume observations. The Boussinesq model uses observed bathymetry and incident random, directionally spread waves. For all five releases, the model generally reproduces the observed cross-shore evolution of significant wave height, mean wave angle, bulk directional spread, mean alongshore current, and the frequency-dependent sea surface elevation spectra and directional moments. The largest errors are near the shoreline where the bathymetry is most uncertain. The model also reproduces the observed cross-shore structure of rotational velocities in the infragravity (0.004 < f < 0.03 Hz) and very low frequency (VLF) (0.001 < f < 0.004 Hz) bands, although the modeled VLF energy is 2–3 times too large. Similar to the observations, the dominant contributions to the modeled eddy-induced momentum flux are in the VLF band. These eddies are elliptical near the shoreline and circular in the mid surf zone. The model-data agreement for sea swell waves, low-frequency eddies, and mean currents suggests that the model is appropriate for simulating surf zone tracer transport and dispersion., This research was supported by SCCOOS, CA Coastal Conservancy, NOAA, NSF, ONR, and CA Sea Grant., 2012-05-18

The factors contributing to the timing and intensity of phytoplankton blooms ("red tides") in very shallow water are poorly understood. Here, the sudden and brief (3h) appearance at the surface of an alongshore-parallel band of red tide is described. The bloom, near Huntington Beach CA, was dominated by the locally common red-tide forming dinoflagellate Lingulodinium polyedrum (F. Stein). Surface chlorophyll-a (Chl a) and temperature (T) were mapped with a novel GPS-tracked jetski. The surface red-tide band, with maximum Chl a~7 microgram L-1, was visible for more than 3h, was located 500 m from shore (~8m water depth), was ~200m wide and extended ~1km alongshore. The subsurface bloom, with maximum Chl a > 30 microgram L-1, developed farther offshore, near the 17-deg C isotherm over 4-7 days prior to the surface appearance. A few hours before the surface band appeared, an intense Chl a> patch was observed in 13m total depth in the mid-water column trough of a shoreward-propagating supertidal internal wave. The Chl a> patch intensification was consistent with dinoflagellate vertical swimming interacting with the wave-driven circulation. In shallow water (<12 m depth), vertical mixing, attributed to internal wave breaking, brought the Chl a patch to the surface. Warm water in very shallow water (depth < 5 m) apparently blocked the Chl a patch from entering the surfzone. These observations highlight the role of small-scale physical and biological processes in determining the spatial and temporal characteristics of nearshore red tide blooms., Submitted for publication to Limnology and Oceanography, 2010.