Stability and dynamics of solitary gravity-capillary waves

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Gravity-capillary waves are waves on the water's surface when the effects of both gravity and surface tension are similar in magnitude. These waves have a wavelength of approximately 1-2 cm. It is at this length scale, for example, that the initiation of the generation of wind ripples occurs and it is these waves that can be detected by some forms of remote sensing radars used to study the surface of the ocean and for detecting oil spills. We shall study these waves in the nonlinear regime, where solitary waves play an important role in the dynamics. We will use both the full equations of fluid dynamics and also derive and validate model equations that are simpler given that in complex flows, the full equations are computationally diffucult to solve.