SoSe 20: Mathematical Analysis of Geophysical Models and a Data Assimilation
Rupert Klein, Titi Edriss
Additional information / Pre-requisites
The main lectures will be held in the two weeks: June 26-July 10; accompanying sessions will be organized around it.
Comments
In this course I will be covering three main topics. The first part will be concerning the Navier-Stokes and Euler equations - a quick survey. The second part will discuss the question of global regularity of certain geophysical flows. The third part about a data assimilation algorithm for weather and climate prediction.
The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, which are called the "Primitive Equations", is often prohibitively expensive computationally, and hard to study analytically. In these introductory lectures, aimed toward graduate students and postdocs, I will survey the mathematical theory of the 2D and 3D Navier-Stokes and Euler equations, and stress the main obstacles in proving the global regularity for the 3D case, and the computational challenge in their direct numerical simulations. In addition, I will emphasize the issues facing the turbulence community in their turbulence closure models.
However, taking advantage of certain geophysical balances and situations, such as geostrophic balance and the shallowness of the ocean and atmosphere, I will show how geophysicists derive more simplified models which are easier to study analytically. In particular, I will prove the global regularity for 3D planetary geophysical models and the Primitive equations of large scale oceanic and atmospheric dynamics with various kinds of anisotropic viscosity and di usion. Moreover, I will also show that for certain class of initial data the solutions of the inviscid 2D and 3D Primitive Equations blowup (develop a singularity) in nite time. Furthermore, I will present some recent results concerning the regularity of certain tropical atmospheric models, and the Primitive equations, coupled to microphysics equations of moisture and clouds formation. Finally, I will also discuss some new algorithms for feedback control and data assimilation for the Navier-Stokes equations and other atmospheric and climate models.
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6 Class schedule
Regular appointments