System of equations that this laboratory is able to perform:Free-surface potential flow Euler equations, Whitham-Boussinesq Equations, Boussinesq Equation, KdV Equation, among other variations and extensions of these equations.
Types of waves that we can study in this lab: solitary waves, dispersive shock waves, soliton waves, tsunami waves, periodic waves, traveling waves, longitudinal waves, transverse waves, trapped waves.
Topographies that may be of interest to geophysical phenomena: Topographies of larger order depth variation, beach-type topographies, channels of bounded cross-section, channels of unbounded cross-section, periodic and/or rapid depth variations, continental shelves.
Theoretical and methodological tools for the analysis of the phenomena we wish to study and for the creation of numerical codes: Infinite-dimensional Hamiltonian systems, Spectral Analysis, Dispersive Shock Wave Adjustment Method, Asymptotic methods, spectral and pseudospectral methods, finite difference methods, Cartesian and curvilinear coordinate systems, DtN operator spectrum calculation for different topographies.
Examples of ocean phenomena and processes where these equations and methodologies can be applied: Internal waves in stratified fluids (concentration on waves in the pycnocline), vertical modes, Lee waves (standing waves in meteorology), waves in a pond, seiches in a body of water, breaking waves on beaches, the phenomenon of dead water, surface wave radiation due to topography, non-linear wave effects in the presence of variable topography.
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