Applied/ACMS/absS23

ACMS Abstracts: Spring 2023

Paul Milewski (Bath)

Title: Embedded solitary internal waves

Abstract: The ocean and atmosphere are density stratified fluids. Stratified fluids with narrow regions of rapid density variation with respect to depth (pycnoclines) are often modelled as layered flows. In this talk we shall examine horizontally propagating internal waves within a three-layer fluid, with a focus on mode-2 waves which have oscillatory vertical structure. Mode-2 nonlinear waves (typically) occur within the linear spectrum of mode-1 waves (i.e. they travel at lower speeds than mode-1 waves), and are hence generically associated with an unphysical resonant mode-1 oscillatory tail. We will present evidence 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.