School of Mechanical Engineering Seminar
Monday, March 18, 2019 at 14:00
Wolfson Building of Mechanical Engineering, Room 206
Nonlinear and linear surface gravity waves
Teodor Vrećica
Yaron Toledo Marine Engineering and Physics lab,
School of Mechanical Engineering, Tel Aviv University
Sea waves have for centuries fascinated scientists, poets, and most who stared over the horizon from a beach. Yet, there are still a large number of wave properties which are not properly understood. They are remarkably similar to various other physical phenomena (e.g. optics, acoustics, plasma waves etc.), but with distinct and important differences. A quick overview of water wave theory will be given with a particular focus on nonlinear interactions and infragravity (IG) waves. Some classical solutions of wave propagation and evolution are presented together with a summary of operational modelling approaches and measurement techniques.
Deterministic and stochastic models of wave evolution, fitting for implementation into operational forecasting models, are derived following the mild-slope approach. Effects of discretization, wave slope, linear and nonlinear bathymetry effects, spectra evolution, and dissipation are discussed and included into the models. One of the main achievements is localization of the nonlinear terms in the stochastic models. This enables it to be implemented in operational wave forecasting models. Two different modes of behavior are identified, one in intermediate water depths, and one in the transition area between intermediate and shallow waters (although the mode depends on the slope as well). A semi local formulation of the coefficient is also derived. Rather than precalculating interaction coefficients it precalculates their change between grid points, which still enables overcoming of Nyquist limitation. The models show good agreements with measurements and allow the extension of operational models to account for nonlinear wave interactions dominant in the nearshore region.
A subclass of surface wave called infragravity (IG) waves are very long waves, which have large wavelengths and propagation speeds compared to wind induced waves, but whose amplitudes are of orders of centimetres. As their strongest generation mechanism is nonlinear wave shoaling, their study was mostly limited to coastal areas. Recently, due to their potential influence on satellite altimetry, there is a renewed interest in IG waves in open oceans. Existing formulations of deep water IG waves account only for generation and reflection from far beaches. By analyzing our ADCP measurements in the Mediterranean, and previous pressure cell measurement campaigns, we found several cases where storms appear to generate IG waves in the deep water. To account for the discrepancies, a new generation method of infragravity waves (related to interaction of wave field with sub-grid oscillations of wind speed) is derived. Initial comparison with measurements shows good agreement.
Issues inherent in most commonly used propagation scheme (ray tracing) for somewhat dispersive long waves are investigated, and alternative approaches are presented. Inclusion of mean and shearing currents and two dimensional bathymetry into time resolving (Boussinesq) and hybrid models is outlined. Advances in interpreting field measurement and incorporating observed spatio-temporal inhomogeneities of the wave field into wave models, understanding of various nonlinear effects in the dispersion relation, and wavelet analysis of sea surface images are also briefly discussed.
