Abstract
We discuss some aspects of the velocity field and particle trajectories beneath periodic traveling equatorial surface waves over a flat bed in a flow with uniform underlying currents. The system under study consists of the governing equations for equatorial ocean waves within a non-inertial frame of reference, where Euler’s equation of motion has to be suitably adjusted, in order to account for the influence of the earth’s rotation.
Highlights
Irrotational flows of symmetric periodic traveling water waves over a flat bed are well-studied; from a theoretical point of view [4,10,19], numerically [1,9,11] and experimentally [23].This paper deals with some qualitative properties of certain geophysical waves, which are not governed by Euler’s equations of motion, but by suitable extensions that account for the influence of the earth’s rotation
More precisely we study irrotational flows and particle paths beneath symmetric periodic traveling surface waves in regions close to the equator
The corresponding boundary conditions on the free surface and on the flat bed are given by v = (u − c)ηx on y = η(x), P
Summary
Irrotational flows of symmetric periodic traveling water waves over a flat bed are well-studied; from a theoretical point of view [4,10,19], numerically [1,9,11] and experimentally [23]. In the case of equatorial surface waves, which propagate practically unidirectionally in the East–West direction due to the prevailing wind pattern (known as trade winds), it is justifiable to consider the f -plane approximation for two-dimensional flows instead of the full geophysical governing equations in three dimensions. This reduction and the simplifying assumption of irrationality, implying that underlying currents are uniform, make it possible to analyze qualitative properties of the flow with the aid of well-known tools from complex and harmonic analysis, and conformal mapping theory.
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