Georgia Institute of Technology College of Sciences

The ocean and atmosphere are density stratified fluids. A wide variety of gravity waves propagate in their interior, redistributing energy and mixing the fluid, affecting global climate balances.  Stratified fluids with narrow regions of rapid density variation with respect to depth (pycnoclines) are often modelled as layered flows. We shall adopt this model and examine horizontally propagating internal waves within a three-layer fluid, with a focus on mode-2 waves which have oscillatory vertical structure and whose observations and modelling have only recently started. Mode-2 waves (typically) occur within the linear spectrum of mode-1 waves (i.e. they travel at lower speeds than mode-1 waves), and thus mode-2 solitary waves are  generically associated with an unphysical resonant mode-1 infinite oscillatory tail. We will show that these tail oscillations can be found to have zero amplitude, thus resulting in families of localised solutions (so called embedded solitary waves) in the Euler equations. This is the first example we know of embedded solitary waves in the Euler equations, and would imply that these waves are longer lived that previously thought.