Mathematical Geosciences Seminar - Marek Stastna

Marek Stastna, Department of Applied Mathematics, University of Waterloo, Canada

Large amplitude internal solitary waves in the presence of shear: theory, data and high resolution simulations

Large amplitude internal solitary waves in the ocean can be described by a number of theories. In this talk I will review results pertinent to waves in the presence of a background shear. As the gold standard, I will use the Dubreil-Jacotin-Long (DJL) equation which is equivalent to the full stratified Euler equations and hence yields exact internal solitary waves. I will use the DJL equation to demonstrate that the presence of a background current changes wave structure, and can change the type of upper bound on wave amplitude. I will discuss sensitivity to background current showing that internal solitary waves are more sensitive to currents oriented with the direction of wave propagation. I will survey instances of strong shear where the DJL solution fails to match field measurements, and discuss what types of waves form from initial disturbances for such situations. In the second half of the talk, I will discuss the formation and evolution of internal solitary waves with subsurface cores since these depend on the presence of a background shear current for their existence and require large numerical simulations to achieve accurate representation. Here again I will contrast simulations with field measurements.

Passcode for this talk is math-geo