Nonlinear ocean waves and surface currents: A theoretical investigation

This thesis contains two parts. In the first part the nonlinear ocean waves and in the second part Eulerian surface currents are studied.;The action balance equation which describes the evolution of wave variance spectrum plays a central role in modern wave modelling. It gives the statistical description of the time evolution of sea waves, which has many applications. The general expression for the source function, in action balance equation consists of three terms representing input energy from wind, the nonlinear transfer and energy dissipation by white capping. The shape and rate of evolution of wind sea spectrum is controlled by the term of nonlinear transfer. The first part of this study is mainly concerned with the approximate solutions of nonlinear transfer action functions that satisfy a set of first order ordinary differential equations. The JONSWAP spectrum is used as initial conditions to solve this problem. Three analytical methods due to Picard, Bernoulli and Adomian and one numerical integration method using fourth order Runge-Kutta scheme are used to compute the nonlinear transfer action functions. The results obtained from these four methods are compared in graphical forms and we have found excellent agreement among them.;The second part of this study is devoted mainly to the determination of the analytic solutions for the Eulerian currents present in ocean circulation. A variety of solutions that satisfy a required boundary and initial conditions are obtained. A Laplace transform method with convolution integral concept is used as a solution technique. Some solution are graphically illustrated, and physical meaning are described.