A shallow water spectral wave model

A shallow water spectral wave prediction model based on a numerical solution of the radiative transfer equation is presented. The model is second generation and uses a simple yet effective representation for the nonlinear source term. In addition, the model pays particular attention to the shallow water processes of refraction, shoaling, bottom friction, and wave breaking. The flexibility of the model is demonstrated by an intercomparison with field data from a number of tropical cyclones. The turning winds from such storms provide a demanding test of model physics. The comparisons are in both deep and shallow water

Directional spectra of hurricane wind-waves

A comprehensive directional wave buoy data set showing the directional wave spectrum during the passage of a number of hurricanes is presented. The data confirm remote sensing measurements, showing that waves in the forward quadrants of the storm are dominated by swell radiating out from the intense wind regions to the right of the storm centre. The data show that for almost all quadrants of the storm, the dominant waves are remotely generated swell. The directional spectra are composed of swell at low frequency (the dominant waves) and locally generated waves above approximately three times the spectral peak frequency. There is, however, no tendency for the spectrum to become bi-modal in either frequency or direction. Rather, the spectra are directionally skewed, with a smooth directional transition from low frequency to high frequency. As for uni-directional wind field cases, the spectra are narrowest at the spectral peak frequency and broaden at frequencies above and below the peak. Despite the fact that much of the wave field is dominated by swell, the spectral width, as a function of non-dimensional frequency is very similar to that reported for uni-directional wind fields. The one-dimensional spectrum can be approximated by the parametric form proposed by Donelan et al. (1985). The parameters defining the spectrum also follow the same functional dependence as that reported for uni-directional winds. The fact that both the one-dimensional and directional spectra are very similar to spectra reported under simple uni-directional winds is interpreted as being a result of the shape stabilization effects of non-linear interactions. The data exhibit these same functional forms at low frequencies where they can be receiving no significant local input from the wind. This result indicates that the spectral shape is being controlled almost completely by the non-linear interactions with input and dissipation terms of lesser importance. This result indicates that input and dissipation are important in determining the total quantity of energy in the wave field, but appear to play only a minor role in determining the spectral shape

An estimate of the Geosat altimeter wind speed algorithm at high wind speeds

Existing wind speed algorithms for satellite altimeters have been developed from data in the range 0 to 20 m/s. At higher wind speeds the available algorithms diverge alarmingly. By comparing Geosat altimeter values of the radar cross section with model predictions of the surface winds during satellite overpasses of tropical cyclones, a wind speed algorithm valid for wind speeds between 20 and 40 m/s is developed. There is, however, considerable scatter in these data. An error analysis shows that this observed scatter is consistent with the accuracy to which the tropical cyclone wind fields can be inferred. An approximately linear dependence of the radar cross section on wind speed is, however, clearly evident within these data. At the lower limit of its applicability (U 10 = 20 m/s), these data are consistent with the previously derived algorithms. At its upper limit (U 10 = 40 m/s), mean squared slope values inferred from the radar cross section are consistent with the theoretical upper limit

Predicting the breaking onset of surface water waves

Why do ocean waves break? Understanding this important and obvious property of the ocean surface has been elusive for decades. This paper investigates causes which lead deep-water two-dimensional initially monochromatic waves to break. Individual wave steepness is found to be the single parameter which determines whether the wave will break immediately, never break or take a finite number of wave lengths to break. The breaking will occur once the wave reaches the Stokes limiting steepness. The breaking probability and the location of breaking onset can be predicted, properties of incipient breakers measured. Potential applications to field conditions are discussed

Design of an integrated shallow water wave experiment

The experimental design and instrumentation for an integrated shallow-water surface gravity wave experiment is discussed. The experiment required the measurement of the water surface elevation, meteorological parameters, and directional spectra at a number of locations on a shallow lake. In addition, to acquire data under a wide range of conditions, an experimental period of three years was required. A system of telephone and radio modem links were installed to enable real-time monitoring of instrument performance at eight separate measurement locations on the lake. This system also enabled logging sessions to be optimized to ensure the maximum possible data return from this extended experimentIEEE Oceanic Engineering Societ

A three-dimensional analysis of marine radar images for the determination of ocean wave directionality and surface currents

A series of spatial wave images recorded by a conventional marine radar is analyzed to determine the three-dimensional E(kx, ky, ω) spectrum. In the absence of a surface current the spectral energy in this three-dimensional wave number frequency space will lie on a shell defined by the dispersion relationship. Any deviation from the expected dispersion relationship can be interpreted as being due to a current induced Doppler shift of the wave frequency. A least squares curve fitting technique is used to determine the surface current required to account for the observed Doppler shift. A comparison of the radar determined spectra and surface currents with ground truth data indicates that the radar system and analysis technique produces results consistent with conventional instrumentation

Wave-driven flow over shallow reefs

Long-term (1 month) observations of waves and currents over a natural reef are presented which show a strong correlation between offshore rms incident wave height and cross-reef currents at subtidal frequencies. The energy spectrum of the cross-reef currents shows a significant peak at twice the semidiurnal tidal frequency, while the spectrum of sea surface elevation over the reef flat shows no corresponding peak. Furthermore, experimental results reported by Gourlay (1993) show setup over the reef occurs in the absence of a beach, and the cross-reef transport decreases with an increase in the sea surface slope across the reef flat due to an increase in setup at the top of the reef face. Analytic solutions for flow forced by wave breaking over an idealized reef explain the above features of cross-reef flows in the absence of a beach. Through the surf zone on the reef face the cross-reef gradient in the radiation stress due to wave breaking is partitioned between balancing an offshore pressure gradient associated with setup over the reef and forcing a mean flow across the reef. Over the reef flat, where the depth is constant, there is no forcing due to wave breaking and the flow is driven by a pressure gradient which results from the setup through the surf zone. The magnitude of the setup through the surf zone is such that the transport across the reef flat matches the transport through the surf zone which is forced by the gradient in the radiation stress. Solutions are presented for general reef geometry, defined by the reef width and slope of the seaward reef face, and incident wave forcing, defined by the depth at the breakpoint and the depth of water over the reef. As the depth over the reef goes to zero, the solutions converge to the plane beach solutions described by Longuet-Higgins and Stewart (1964), wave setup is maximized, and the cross-reef transport is zero. In other cases the relative magnitudes of the setup and the cross-reef transport depend on the geometry of the reef and the incident wave forcing

Fine scale inhomogeneity of wind-wave energy input, skewness, and asymmetry

Analysis of measured sea and lake wind wave data reveals large variability of the wind energy input, as well as the waves skewness and asymmetry. The spatial and temporal third moments alternate in sign over a few wave periods and over a few wavelengths, respectively. Simulation through a 2D Wave Boundary Layer model in which the air flow is modeled by 2nd order Reynolds equations (Chalikov, 1998) conforms to these findings and exposes a rich structure. We found clear correlation of the variations of the skewness and the asymmetry with the wind input

Comparison of wind speed and wave height trends from twentieth-century models and satellite altimeters

The trends in marine 10-m wind speed U10 and significant wave height Hs found in two century-long reanalyses are compared against a model-only integration. Reanalyses show spurious trends due to the assimilation of an increasing number of observations over time. The comparisons between model and reanalyses show that the areas where the discrepancies in U10 and Hs trends are greatest are also the areas where there is a marked increase in assimilated observations. Large differences in the yearly averages call into question the quality of the observations assimilated by the reanalyses, resulting in unreliable U10 and Hs trends before the 1950s. Four main regions of the world’s oceans are identified where the trends between model and reanalyses deviate strongly. These are the North Atlantic, the North Pacific, the Tasman Sea, and the western South Atlantic. The trends at +24-h lead time are markedly weaker and less correlated with the observation count. A 1985–2010 comparison with an extensive dataset of calibrated satellite altimeters shows contrasting results in Hs trends but similar U10 spatial trend distributions, with general agreement between model, reanalyses, and satellite altimeters on a broad increase in wind speed over the Southern Hemisphere.publishedVersio