Abstract
The theory of point vortices is used to explain the interaction of a surface vortex with subsurface vortices in the framework of a three-layer quasigeostrophic model. Theory and numerical experiments are used to calculate the interaction between one surface and one subsurface vortex. Then, the configuration with one surface vortex and two subsurface vortices of equal and opposite vorticities (a subsurface vortex dipole) is considered. Numerical experiments show that the self-propelling dipole can either be captured by the surface vortex, move in its vicinity, or finally be completely ejected on an unbounded trajectory. Asymmetric dipoles make loop-like motions and remain in the vicinity of the surface vortex. This model can help interpret the motions of Lagrangian floats at various depths in the ocean.
Highlights
The theory of point vortices in a flat liquid layer, going back to the pioneering works of Helmholtz, Kirchhoff, Gröbli, and Thomson (Lord Kelvin) [1–5], arose to a large extent from the need to explain the properties of vortex movements in the atmosphere and ocean
Further development of the theory of point vortices is reflected in monographs and reviews [6–16]
We use a quasigeostrophic model to study the features of the interaction between one vortex of the upper layer and one/two vortices of the middle layer of a three-layer rotating fluid
Summary
The theory of point vortices (vertical vortex lines of finite length) in a flat liquid layer, going back to the pioneering works of Helmholtz, Kirchhoff, Gröbli, and Thomson (Lord Kelvin) [1–5], arose to a large extent from the need to explain the properties of vortex movements in the atmosphere and ocean. Gryanik first generalized the theory of two-dimensional vortices to the case of a two-layer [31] and to an N-layer rotating fluid [32] These works found their application in numerous problems of geophysical content [33–63]. In [66,67], the SEMANE and MEDTOP cruise data were analyzed to study the interactions of intrathermocline vortices with a cyclonic surface vortex; due to intermittent data collection at sea, only a few snapshots of these interactions were obtained. This circumstance is the motivation for Mathematics 2020, 8, 1228; doi:10.3390/math8081228 www.mdpi.com/journal/mathematics.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call