The Linear Stability of Finite Amplitude Surface Waves on a Linear Shearing Flow

We give some instability characteristics of two-dimensional finite amplitude surface waves on a linear shearing flow to three-dimensional infinitesimal rotational disturbances using a numerical method. We have found three kinds of instabilities: two of them are related with four- and five-wave resonances and the rest is intrinsically caused by a shearing flow. The growth rates of instabilities associated with four- and five-wave resonances are larger than those without a shearing flow for the same wave steepness.