Trimodal steady water waves

Abstract

We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a combination of three different Fourier modes, giving rise to a rich and complex variety of wave patterns. The bifurcation argument is based on a blow-up technique, taking advantage of three parameters associated with the vorticity distribution, the strength of the background stream, and the period of the wave.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-014-0812-3

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