Merrick C. Haller

Boussinesq modeling of a rip current system

In this study, we use a time domain numerical model based on the fully nonlinear extended Boussinesq equations [Wei et al., 1995] to investigate surface wave transformation and breaking-induced nearshore circulation. The energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves. Wave run-up on the beach is simulated using a moving shoreline technique. We employ quasi fourth-order finite difference schemes to solve the governing equations. Satisfactory agreement is found between the numerical results and the laboratory measurements of Haller et al. [1997], including wave height, mean water level, and longshore and cross-shore velocity components. The model results reveal the temporal and spatial variability of the wave-induced nearshore circulation, and the instability of the rip current in agreement with the physical experiment. Insights into the vorticity associated with the rip current and wave diffraction by underlying vortices are obtained.

Quasi-three-dimensional modeling of rip current systems

[1] The focus of the paper is the analysis of the flow in rip current systems generated by channels in longshore bars on a beach. The horizontal variations of rip current systems are described through the use of the quasi-three-dimensional nearshore circulation model SHORECIRC. Model predictions are compared to laboratory measurements of waves and current velocities throughout the entire rip current system and show reasonable agreement. The rips in the two channels are found to behave differently because of the depth variation across the basin. It is found that higher bottom stress leads to more stable flow where the rip current meanders less and fewer eddies are generated. The wave current interaction creates forcing which reduces the distance rip currents flow offshore and can lead to a slow pulsation of the rip current. This pulsation is in addition to the instabilities of a jet which can also be present in rip currents. The three dimensionality of the rip current system is found to have a significant effect on the overall circulation patterns. INDEX TERMS: 4255 Oceanography: General: Numerical modeling; 4512 Oceanography: Physical: Currents; 4546 Oceanography: Physical: Nearshore processes; KEYWORDS: rip currents, nearshore circulation, numerical modeling, waves

Rip current instabilities

A laboratory experiment involving rip currents generated on a barred beach with periodic rip channels indicates that rip currents contain energetic low-frequency oscillations in the presence of steady wave forcing. An analytic model for the time-averaged flow in a rip current is presented and its linear stability characteristics are investigated to evaluate whether the rip current oscillations can be explained by a jet instability mechanism. The instability model considers spatially growing disturbances in an offshore directed, shallow water jet. The effects of variable cross-shore bathymetry, non-parallel flow, turbulent mixing, and bottom friction are included in the model. Model results show that rip currents are highly unstable and the linear stability model can predict the scales of the observed unsteady motions.

Remote Sensing of the Nearshore

The shallow waters of the nearshore ocean are popular, dynamic, and often hostile. Prediction in this domain is usually limited less by our understanding of the physics or by the power of our models than by the availability of input data, such as bathymetry and wave conditions. It is a challenge for traditional in situ instruments to provide these inputs with the appropriate temporal or spatial density or at reasonable logistical or financial costs. Remote sensing provides an attractive alternative. We discuss the range of different sensors that are available and the differing physical manifestations of their interactions with the ocean surface. We then present existing algorithms by which the most important geophysical variables can be estimated from remote sensing measurements. Future directions and opportunities will depend on expected developments in sensors and platforms and on improving processing algorithms, including data assimilation formalisms.

Ocean Wavenumber Estimation From Wave-Resolving Time Series Imagery

We review several approaches that have been used to estimate ocean surface gravity wavenumbers from wave-resolving remotely sensed image sequences. Two fundamentally different approaches that utilize these data exist. A power spectral density approach identifies wavenumbers where image intensity variance is maximized. Alternatively, a cross-spectral correlation approach identifies wavenumbers where intensity coherence is maximized. We develop a solution to the latter approach based on a tomographic analysis that utilizes a nonlinear inverse method. The solution is tolerant to noise and other forms of sampling deficiency and can be applied to arbitrary sampling patterns, as well as to full-frame imagery. The solution includes error predictions that can be used for data retrieval quality control and for evaluating sample designs. A quantitative analysis of the intrinsic resolution of the method indicates that the cross-spectral correlation fitting improves resolution by a factor of about ten times as compared to the power spectral density fitting approach. The resolution analysis also provides a rule of thumb for nearshore bathymetry retrievals-short-scale cross-shore patterns may be resolved if they are about ten times longer than the average water depth over the pattern. This guidance can be applied to sample design to constrain both the sensor array (image resolution) and the analysis array (tomographic resolution).

Comparison of radar and video observations of shallow water breaking waves

Simultaneous microwave and video measurements of shallow water breaking waves are presented. A comparison of the data from the two sensors shows that short-duration spikes in the measured X-band radar cross section are highly correlated with the presence of breaking waves in the video imagery. In addition, the radar backscatter from shallow water breaking events is responsible for 40% to 50% of the total cross section, which is a much larger contribution than typically observed for deepwater breaking events. Based on estimates of the area of individual breaking regions determined from digitized video images, the radar cross section per unit area of the turbulent breaking region is shown to be well approximated by a value of -1.9 dB at 31/spl deg/ grazing. Finally, there are some differences between the radar and video signals that suggest that microwave radar may be less sensitive than video techniques to relict foam not associated with active wave breaking. In general, the results indicate that radar is a very good detector of shallow water breaking waves and suggest that radar can be used for the measurement of the spatial and temporal variations of wave breaking.

Optical and Microwave Detection of Wave Breaking in the Surf Zone

Synchronous and colocated optical and microwave signals from waves in the surf zone are presented and analyzed. The field data were collected using a high-resolution video system and a calibrated horizontally polarized marine radar during the decaying phase of a storm. The resulting changes in the received signals from varying environmental conditions were analyzed. The analysis of the optical signal histograms showed functional shapes that were in accordance with the expected imaging mechanisms from the breaking and nonbreaking waves. For the microwave returns, the histogram shape showed a little dependence on the environmental parameters and exhibited an inflexion point at high returned power that is attributed to a change in the scattering mechanism. The high intensity signals were clearly associated with active wave breaking. However, with either sensor, it can be difficult to effectively isolate the wave breaking signature from other sources, such as a remnant foam or the highly steepened nonbreaking waves. A combined method was developed using the joint histograms from both sensors, and it is shown to effectively discriminate between active breaking, remnant foam, and steepened waves. The new separation method allows a further analysis of the microwave scattering from the breaking waves and a better quantification of the length scales of the breaking wave roller and the spatial/temporal distribution of wave breaking and wave dissipation in the surf zone.

Rip Current Observations via Marine Radar

New remote sensing observations that demonstrate the presence of rip current plumes in X-band radar images are presented. The observations collected on the Outer Banks (Duck, North Carolina) show a regular sequence of low-tide, low-energy, morphologically driven rip currents over a 10-day period. The remote sensing data were corroborated by in situ current measurements that showed depth-averaged rip current velocities were 20e40cm=s whereas significant wave heights were Hs 50:5e1m. Somewhat surprisingly, these low-energy rips have a surface signature that sometimes extends several surf zone widths from shore and persists for periods of several hours, which isin contrastwith recent rip current observations obtained with Lagrangian drifters. These remote sensing observations provide a more synoptic picture of the rip current flow field and allow the identification of several rip events that werenot captured by thein situ sensors and times of alongshoredeflection oftherip flowoutsidethesurfzone.Thesedataalsocontainaripoutbreakeventwherefourseparateripswereimagedovera1-kmstretchofcoast. For potential comparisons of the rip current signature across other radar platforms, an example of a simply calibrated radar image is also given. Finally,insituobservationsoftheverticalstructureoftheripcurrent flowaregiven,andathresholdoffshorewindstress(.0:02m=s 2 )isfoundto preclude the rip current imaging. DOI: 10.1061/(ASCE)WW.1943-5460.0000229.

Asymmetry in Directional Spreading Function of Random Waves due to Refraction

In this study, a more general directional spreading function is developed that allows for asymmetric directional distributions. For multidirectional random waves that approach the shore obliquely over a planar slope, we demonstrate that directional asymmetry is generated due to wave refraction. The asymmetry created by refraction increases with the offshore peak wave direction. The present spreading function is compared to a preexisting symmetric spreading function and is shown to better capture changes in the directional distribution that occur in a refracting, random wave field. Finally, the new asymmetric spreading function is compared to a long time series of wave directional spectra measured at a nearshore field site. The results demonstrate that refraction-induced asymmetry is common in the nearshore and the asymmetric spreading function gives an improved analytic representation of the overall directional distribution as compared to the symmetric function.

Surf zone bathymetry and circulation predictions via data assimilation of remote sensing observations

Bathymetry is a major factor in determining nearshore and surf zone wave transformation and currents, yet is often poorly known. This can lead to inaccuracy in numerical model predictions. Here bathymetry is estimated as an uncertain parameter in a data assimilation system, using the ensemble Kalman filter (EnKF). The system is tested by assimilating several remote sensing data products, which were collected in September 2010 as part of a field experiment at the U.S. Army Corps of Engineers Field Research Facility (FRF) in Duck, NC. The results show that by assimilating remote sensing data alone, nearshore bathymetry can be estimated with good accuracy, and nearshore forecasts (e.g., the prediction of a rip current) can be improved. This suggests an application where a nearshore forecasting model could be implemented using only remote sensing data, without the explicit need for in situ data collection.