The goal of this course is to acquire knowledge about the fundamental aspects of the water wave’s phenomena and mastering of mathematical methods for modeling these flows present in a variety of practical problems.

Students are trained to develop mathematical models of water waves with contemporary and scientific methods. Also they are prepared to solve the relevant problems by analytical and numerical methods.

Theoretical lessons incorporate the basic laws that describe the water wave’s phenomenon which includes several specific studies of the linear and nonlinear waves. Linear problems include description of waves on sloping beaches, as well as the phenomenon of edge waves. Some general ideas associated with ray theory are developed also and its results are applied to variable depth, ship waves, and waves on currents. Under the nonlinear problems, the application to waves on a sloping beach is extended in order to include the effects of nonlinearity. The Stokes expansion which produces higher approximations to the classical linear wave is described also. The fully nonlinear solitary wave is considered too. Explanation of the analogy between nonlinear water waves and (nonlinear) gas dynamics is given.

Practical lessons contain application of analytical and numerical results for different models of linear and nonlinear water waves.

Passed exam in Fluid mechanic and Thermodynamics.

Course handouts.

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 20

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 10
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 50

A Modern Introduction to the Mathematical Theory of Water Waves, R. S. Johnson, Cambridge University Press, October 28, 1997; Linear Water Waves: A Mathematical Approach, N. Kuznetsov, V. Maz'ya, B. Vainberg, Cambridge University Press; 1 edition (August 19, 2002)