Applied Mathematics Seminars: Determining Modes of the 2D Navier-Stokes Equations on the Beta-Plane
10 February 2017 14:00 in CM219
The Navier-Stokes equations describe the motion of fluids, with the two and three dimensional cases exhibiting certain very different characteristics. Kolmogorov's 1941 theory regarding the energy cascade in 3D turbulence and its 2D enstrophy analogue by Kraichnan in 1967 suggest that the behaviour of a fluid can be described by finite degrees of freedom, despite it being described by a PDE which is, fundamentally, infinite-dimensional. To develop this idea further, the idea of determining modes was introduced by Foias et al in 1983.
The beta-plane approximation is applied to simulate the effect that the earth's rotation has on the 2D NSE, where the rotation varies linearly with the latitude. Physical arguments and numerics indicate that the flow in such a simulation will be come zonal with time. Al-Jaboori and Wirosoetisno (2011) proved that the flow becomes more zonal with stronger rotation.
In this talk, I will introduce the concepts of determining modes and the beta-plane approximation, go over developments and improvements that have been made and cover some results that we have made by combining these two ideas.
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