Steady Periodic Water Waves Solutions Using Asymptotic Approach

Sammanfattning: The aim of this work is to study the relation between two invariants of water flow in a channel of finite depth. The first invariant is the height of the water wave and the second one is the flow force. We restrict ourselves to water waves of small amplitude. Using asymptotic technique together with the method of separation of variables, we construct all water waves of small amplitude which are parameterized by a small parameter. Then we demonstrate numerically that the flow force depends monotonically on the height.