Detection of ocean waves using satellite altimetry: Application to equatorial Kelvin waves

A new method for wave motion detection from satellite altimetric measurements of sea surface height is presented. The essence of the approach is to construct a two‐dimensional traveling‐wave Fourier series representation of the amplitude field within a prespecified oceanic region. The method employs an iterative, nonlinear least‐squares technique based on the Marquardt‐Levenberg algorithm to solve for model parameters describing characteristic features of the evolving wave system. The Marquardt‐Levenberg Fourier series (MLFS) algorithm was applied to Kelvin waves active during the 1986–1987 El Nino event in the equatorial Pacific ocean using GEOSAT Exact Repeat Mission altimetry data. Characteristics of the wave system were found to be in essential agreement with earlier field measurements and the observations of Cheney and Miller (1987) obtained using time series developed from GEOSAT data. The advantage of the present detection scheme lies in its speed and ability to determine a wave system's dispersion relation over a finite range of wavenumbers, and hence the group velocity of that system.     

Non-hydrostatic pressure in σ-coordinate ocean models

Numerical ocean modelling is computationally very demanding. Traditionally, the hydrostatic approximation has been applied to reduce the computational burden. This approximation is valid in large scale studies with coarse grid resolution. With faster computers and gradually smaller grid sizes, we may expect that more studies will be performed with non-hydrostatic ocean models. In recent papers several methods for including non-hydrostatic pressure in σ-coordinate models have been suggested. In this paper the sensitivity of the non-hydrostatic pressure field, the velocity fields, and the density fields to changes in the method for computing non-hydrostatic pressure in σ-coordinate ocean models is addressed.The first test case used involves the propagation and breaking of an internal wave at an incline in a tank. The other test case concerns tidally driven flow over a sill in a stratified fjord. The results from our numerical exercises suggest that the velocity and density fields are very robust to the model choices investigated here. The differences between the model results are of the same order as the uncertainty due to the internal pressure gradient error, and they are smaller than an estimate of the uncertainty due to subgrid scale closure.     

Utilization of the energy in ocean waves

The characteristics of ocean wind waves place certain constraints upon devices designed to convert their energy to a useful form. Here we consider the nature of these constraints and the theoretical analysis of a wave power generator that conforms to the design criteria. We also present the results of field tests with several models of the wave power generator. The experimental results support the theory and indicate that such a wave pump is suitable for power generation in a variety of circumstances.     

On the growth of ocean waves

The availability of 10 h of continuous, uninterrupted field measurements of wind waves recorded in the western Pacific and containing a complete wave growth episode, has provided a distinct opportunity for us to make a novel, unprecedented examination of detailed wave growth processes. We found that the significance of the size of data used in the measurement, which can only be addressed with continuous and uninterrupted measurements, reflected the ineptness of the conventional approach toward further detailed understanding of realistic wave growth processes, as the conventional 20 min data size essentially stamped out any dynamics with time scale below 20 min. While our conventional understanding and modeling were generally operative and useful, they left no real vestige on time localized mechanisms such as wave grouping or wave breaking processes all with time scales much less than 20 min.     

Modelling ocean waves in ice-covered seas

Over the past decade there has been a rapid growth of interest in wave propagation through ice covers. This paper summarizes the author’s observation of the modeling efforts on this topic. Models can be theory-based, data-driven, or a combination of the two. A pure data-driven model relies on a large amount of observations and is only becoming available recently. Theory-based models on the other hand have a long history. They are always a simplified version of the reality. As our knowledge grows, theories become more complicated. A theory for waves-in-ice that captures all possible processes does not exist. However, when integrated with observation through calibration, these combined theory + data-based models may be used with some confidence. In this paper, different models, their basic concepts, their calibration and validation are discussed. The present theory-based models do not have the correct spectral attenuation trend as observed from field or laboratory experiments. Hence, through calibration they may fit different parts of the wave spectra but not all. Pure data-driven models can reproduce the correct trend, but its dependability outside the situation where the data are collected is uncertain. In addition to offering tools to forecast waves-in-ice, these model building and validating efforts point to missing mechanisms that should be carefully studied. Despite the many challenges towards building a satisfactory general waves-in-ice model, significant progress has been made for models that work reasonably well in the marginal ice zone. We anticipate much more data will become available in the coming years to help us improve the existing models.     

Energy budget of surface waves in the global ocean

Mechanical energy input from atmosphere and losses from wave-breaking dissipation of sea surface waves are estimated by a direct scheme. This scheme is based on the integration in the wavenumber space of the wind input and breaking dissipation source functions of the MASNUM wave model. The global amount of wind energy input, averaged in 2005, is about 57 TW, and the wave-breaking dissipation summed in deep-water is about 33 TW, over a half of the wind energy input. The residual may be dissipated by beach processes. Global distributions of the energy input and breaking dissipation concentrate in the westerlies of the Southern Hemisphere.     

On ensemble prediction of ocean waves

The numerical ensemble prediction is a well accepted method for improving the performance of atmospheric models. In the context of ocean wave modeling little has been researched or documented about this technique. An essential study of the method of ensemble prediction applied to deep water waves has been carried out. A framework is defined for obtaining perturbations of the directional wave spectra and for employing an ensemble of wind fields generated by an atmospheric model. The third-generation global wave model WAM is used with real atmospheric conditions to investigate the effect on wave predictions of perturbed initial conditions and atmospheric forcing. Due to spectral shape stabilisation, perturbing wave initial conditions has limited utility in ensemble prediction. However, the members could be used in wave data assimilation schemes in an interactive way. Using ensembles of the atmospheric condition can generate diverging solutions, justifying the ensemble procedure by itself. In the cases studied, it is observed that the ensemble mean outperformed the other members. The solution behaviour suggests using a lower-order approximation of the model to generate ensemble members with less computational cost.     

Non-linear effects in the packets of internal waves in the ocean

The mechanisms for the generation of mean density and current velocity fields in a medium with a vertical shear, conditioned by the non-linearity of packets of internal waves are analysed. Modulation instability of internal waves is studied allowing for the earth's rotation. A non-linear Schrödinger's equation for the evolution of the envelope has been derived. Also corrections to the mean density and current velocity in the approximation, quadratic by the wave's amplitude, non-oscillating on the wave's time scale have been obtained. The longitudinal modulation conditions have been analysed.Translated by V. Puchkin. UDK 551.466.8.     

The mixing mechanism in the formation of ocean shear waves

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Generation of internal waves in a three-layer ocean

Within the framework of the linear theory of long waves taking into account the action of the Coriolis force, we solve the problem of generation of internal waves by a barotropic tide impinging on a bottom irregularity of the sea-ridge type. The cross section of the ridge is assumed to be rectangular and the stratification of the ocean is regarded as stepwise with two thermoclines (three-layer model). We study the dependences of the characteristics of generated waves on the parameters of stratification and the period of the impinging barotropic tide. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

The role of surface waves in the ocean mixed layer

Previously, most ocean circulation models have overlooked the role of the surface waves. As a result, these models have produced insufficient vertical mixing, with an under - prediction of the ,nixing layer （ML） depth and an over - prediction of the sea surface temperature （SST）, particularly during the summer season. As the ocean surface layer determines the lower boundary conditions of the atmosphere, this deficiency has severely limited the performance of the coupled ocean - atmospheric models and hence the climate studies. To overcome this shortcoming, a new parameterization for the wave effects in the ML model that will correct this systematic error of insufficient mixing. The new scheme has enabled the mixing layer to deepen, the surface excessive heating to be corrected, and an excellent agreement with observed global climatologic data. The study indicates that the surface waves are essential for ML formation, and that they are the primer drivers of the upper ocean dynamics; therefore, they are critical for climate studies.     

A mathematical representation of random gravity waves in the ocean

We give a mathematical representation of random ocean surface waves in the gravity-wave regime. The so-called random gravity waves are treated as an asymptotic phenomenon when the wind pressure acting on the surface and the dissipation become negligible. We adopt a phenomenological model for the wind pressure such that it excites a surface consisting of wind-driven sea and swell. Starting from the Navier-Stokes equations, we derive a general system of the first-order perturbation equations governing the surface waves, and solve them with this wind pressure as the excitation. The resulting solution is decomposed into a part which is asymptotically dominant and another which is asymptotically negligible. The former consists of two groups: one which is a sum of superpositions of uncorrelated plane waves having approximate dispersion relations and the other a sum of random plane waves with their wavenumbers and frequencies approximately satisfying the dispersion relation. They correspond to the dominant parts of the wind-driven sea and the swell, respectively. Finally, we derive a limiting form of the directional-frequency spectrum in the gravity-wave regime.     

Prediction of ocean waves based on the single-parameter growth equation of wind waves

A method for the prediction of ocean waves was developed on the basis of the single-parameter growth equation of wind waves, proposed byToba (1978) on the basis of similarity in growing wind waves. The applicability of the method to actual problems was tested by hindcasting the wave characteristics with the method, for two cases with differing time and space scales, one in Kii Channel Approach, Japan, and the other in the North Atlantic Ocean. The results showed that the present method can predict waves within an error of 1.3 m in wave heights, which ranged from 3 to 12 m.     

Models of radar imaging of the ocean surface waves

A number of models which would explain ocean wave imagery taken with a synthetic aperture imaging radar are analyzed analytically and numerically. Actual radar imagery is used to support some conclusions. The models considered correspond to three sources of radar backscatter cross section modulation: tilt modulation, roughness variation, and the wave orbital velocity. The effect of the temporal changes of the surface structure, parametric interactions, and the resulting distortions are discussed.     

Instability analysis of three-dimensional ocean shear waves

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