Data assimilation for the Navier-Stokes-alpha equations

Korn, Peter

doi:10.1016/j.physd.2009.07.008

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Data assimilation for the Navier-Stokes-alpha equations

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Korn, Peter
Applied Mathematics and Computational Physics (AMCP), Scientific Computing Lab (ScLab), MPI for Meteorology, Max Planck Society;

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Korn, P. (2009). Data assimilation for the Navier-Stokes-alpha equations. Physica D: Nonlinear Phenomena, 238, 1957-1974. doi:10.1016/j.physd.2009.07.008.

Cite as: https://hdl.handle.net/21.11116/0000-000B-4E6E-4

Abstract

The well-posedness of the data assimilation problem for the Navier-Stokes-alpha equations on a bounded three-dimensional domain is investigated. The data assimilation procedures under consideration are the adjoint method of variational data assimilation (4D-Var) and the method of continuous data assimilation. Concerning the adjoint method the existence of optimal initial conditions with respect to an observation-dependent cost functional is proven, the optimizers are characterized by a first-order necessary condition involving the adjoint linearized Navier-Stokes-alpha equations and conditions for the uniqueness of the initial conditions are given. Well-posedness of the continuous data assimilation problem is proven and convergence rates in terms of observational resolution are provided. (C) 2009 Elsevier B.V. All rights reserved.