In this lecture I am going to present control problems associated with shell models of Turbulence. Shell models of turbulence are simplified caricatures of equations of fluid mechanics in wave-vector representation. They exhibit anomalous scaling and local non-linear interactions in wave number space. We would like to study control problem related to one such widely accepted shell model of turbulence known as sabra shell model. We associate two cost functionals: one ensures minimizing turbulence in the system and the other addresses the need of taking the ow near a priori known state. We derive the optimal controls in terms of the solution of adjoint equation for corresponding linearised problems.

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Last updated: 15 Jun 2019