Class: MW 1330-1445 Pearson 106

Instructor: Dr. James T. Kirby
Ocean Engineering Laboratory 205
831-2438
kirby@udel.edu

Required Text: none. Text for course is available online, and a file of references will be maintained in the Ocean Engineering Lab conference room.

• Introduction and review of governing equations. Scaling the boundary value problem for water waves.
• Introduction to perturbation methods for nonlinear problems.
• Weakly dispersive shallow water waves. Boussinesq and Korteweg-deVries equations. Solitary and cnoidal waves. Kadomtsev-Petviashvili equation and short-crested waves.
• Evolution of shallow water waves in variable depth. Evolution of the spectral wave field.
• Stokes Waves: Regular waves to second order. Higher order theories. Fourier series solutions for regular waves.
• Capillary waves, Wilton's ripple and resonant interaction.
• Slowly modulated Stokes waves: The Schrodinger equation.
• Random Stokes waves: the second order forced sea and resonant interaction.

• Modulated Stokes waves: narrow banded spectra and the nonlinear Schrodinger equation.
• Long waves: resonant forcing of edge waves.
• Fully nonlinear waves: Numerical solution of the transient problem.
• Parametric forcing, cross waves, and an introduction to chaotic dynamics.

Grading: About 40% of the semester grade will be based on assigned homeworks. In addition, each student will be required to prepare a term paper, which will count for most of the remainder of the grade. These may be in the nature of a review of a topic not fully covered in class. They may be more concentrated efforts dealing with a specific problem, and, if so, students are allowed (indeed, encouraged) to treat a problem within the scope of their thesis research. The efforts may be theoretical, numerical or, in the event that tank setups permit, experimental. People may work alone, or, if the scope of a project warrants it, in groups of two.