Elena Sanina

Numerical modeling of 3D fully nonlinear potential periodic waves

A simple and exact numerical scheme for long-term simulations of 3D potential fully nonlinear periodic gravity waves is suggested. The scheme is based on the surface-following nonorthogonal curvilinear coordinate system. Velocity potential is represented as a sum of analytical and nonlinear components. The Poisson equation for the nonlinear component of velocity potential is solved iteratively. Fourier transform method, the second-order accuracy approximation of vertical derivatives on a stretched vertical grid and the fourth-order Runge–Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. A one-processor version of the model for PC allows us to simulate evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of nonlinear 2D surface waves, generation of extreme waves, and direct calculations of nonlinear interactions.

A comparison of methods for estimating directional spectra of surface waves

Three methods of estimating the directional spectra of water waves are intercompared. The Maximum Likelihood Method (MLM) and the Maximum Entropy Method (MEM) require stationarity of the time series and yield only the frequency-direction spectra. The Wavelet Directional Method (WDM) does not require stationarity and also yields the wave number-direction spectra and is suitable for event analysis. The comparison includes three cases of wind-generated waves on a large lake and two cases of model-generated waves with different directional spreading. The comparisons of the frequency-direction spectra show that the Wavelet Directional Method yields the best estimates of the directional spectra.

Calibration and Cross Validation of a Global Wind and Wave Database of Altimeter, Radiometer, and Scatterometer Measurements

AbstractA combined satellite dataset consisting of nine altimeter, 12 radiometer, and two scatterometer missions of wind speed and wave height is calibrated in a consistent manner against NDBC data and independently validated against a separate buoy dataset. The data are investigated for stability as a function of time. Instances where there are discontinuities or drift in the data are identified and accounted for in the calibration. The performance of each of the instruments at extreme values is investigated using quantile–quantile comparisons with buoy data. The various instruments are cross validated at matchup locations where satellite ground tracks cross. The resulting calibrated and cross-validated dataset is believed to represent the largest global oceanographic dataset of its type, which includes multiple instrument types calibrated in a similar fashion.

Statistics of wave kinematics in random directional wave fields

In this dissertation, we present the analysis of long-term wave simulations performed using fully nonlinear potential deep water wave model. The results of the simulations are compared with the spectra obtained using a variety of directional methods and are discussed in the context of their applications. Further investigation of the numerical model is conducted by comparing the Gaussian spectra development with that detected previously using other methods. The instabilities of unidirectional waves with noisy initial spectra resulting in a lateral modulation of wave crests are discussed. The short-crestedness of a wave field is investigated in terms of the three-dimensional steepness defined as the vector whose magnitude is equal to the average steepness calculated along the vector direction in a horizontal plane. Several statistical characteristics of the surface elevation field and wave spectrum development such as a non-uniformity of the wave spectrum and a migration of its peaks are discussed. The emergence of coherent structures on the ocean surface closely related to the tendency of high waves to occur in groups is analysed. Various features of the identified groups such as velocity of the groups, their lengths, lifetime and steepness are studied. A general analysis of the number of detected groups is also performed for the computed wave fields. In order to quantify the spatial and temporal wave group characteristics the space-time autocorrelation functions of the surface elevation envelopes are constructed and discussed.