Question: What can low-dimensional deterministic mechanisms tell us about high-dimensional chaotic and stochastic systems ?
Our group uses low-dimensional deterministic and chaotic vortex-dynamics models of the Euler and Navier-Stokes equations to shed light on turbulent fluid dynamics with the goal of understanding fluid mixing in the atmosphere and oceans
Vortex dynamics is a branch of dynamical systems theory in much the same spirit as the N-body problem in celestial mechanics. Despite the fact that problems in celestial mechanics have historically been among the key driving forces in progress in dynamics, research in this area has fallen out of favor and celestial mechanics is no longer taught as a standard part of the applied mathematics curriculum. Vortex dynamics, by contrast, is a lively and active research topic that uses techniques that have widespread applicability to many general problems in dynamics and applied mathematics. Our group has focused mostly on developing the N-vortex problem from a dynamical systems perspective, to gain insights into more general classical Hamiltonian systems, and also as a low-dimensional approximation to the Euler equations from fluid dynamics to develop intuition into the complex mechanisms at work in the rich field of turbulence theory.
You can read more about this topic in my book. Here are four papers to read where you can learn more about our approach. See full publication list for others.
- PK Newton, Point vortex dynamics in the post-Aref era, Fluid Dynamics Research 46(3) 031401 (2014)
- PK Newton, H Shokraneh, Interacting dipole pairs on a rotating sphere, Proc. Roy. Soc. A 464 1525-1541 (2008)
- R Kidambi, PK Newton, Streamline topologies for integrable vortex motion on a sphere, Physica D: Nonlinear Phenomena 140 (1-2) 95-125 (2000)
- R Kidambi, PK Newton, Motion of three point vortices on a sphere, Physica D: Nonlinear Phenomena 116 (1-2) 143-175 (1998)
