Speaker 1 : Nicholas Pizzo (Scripps Institution of Oceanography, University of California, San Diego)
Date & Time : January 21st (Fri.), 2022 / 9:00-9:40AM (Tokyo (JST))
(--> January 20th (Thu.), 2022 / 4:00-4:40PM (San Diego (PDT)) )
Title : Particle description of the interaction between wave packets and point vortices
Abstract :
This talk explores an idealized model of the ocean surface in which widely separated
surface-wave packets and point vortices interact in two horizontal dimensions. We start
with a Lagrangian which, in its general form, depends on the fields of wave action,
wave phase, stream function and two additional fields that label and track the vertical
component of vorticity. By assuming that the wave action and vorticity are confined to
infinitesimally small, widely separated regions of the flow, we obtain model equations
that are analogous to, but significantly more general than, the familiar system consisting
solely of point vortices. We analyse stable and unstable harmonic solutions, solutions in
which wave packets eventually coincide with point vortices (violating our assumptions),
and solutions in which the wave vector eventually blows up. Additionally, we show that
a wave packet induces a net drift on a passive vortex in the direction of wave propagation
which is equivalent to Darwin drift. Generalizing our analysis to many wave packets and
vortices, we examine the influence of wave packets on an otherwise unstable vortex street
and show analytically, according to linear stability analysis, that the wave-packet-induced
drift can stabilize the vortex street. The system is then numerically integrated for long
times and an example is shown in which the configuration remains stable, which may be
particularly relevant for the upper ocean.