Reduced-order Galerkin models of plane Couette flow
André V. G. Cavalieri, Petrônio A. S. Nogueira
Abstract
Reduced-order models for plane Couette flow are obtained by Galerkin projection of the Navier-Stokes equations onto the leading controllability modes of the linearized system. Nonlinear dynamical systems so constructed, with various degrees of truncation, are numerically stable and reproduce statistics of minimal turbulent Couette flow at Reynolds numbers 500 and 1200 for different choices of modal bases. A closure model was not included to the Galerkin system, suggesting that this is not essential for the stability of such models, at least for the flow at hand.
Topics & Concepts
Galerkin methodCouette flowMathematicsNonlinear systemFlow (mathematics)TurbulenceTaylor–Couette flowProjection (relational algebra)Plane (geometry)Reynolds numberTruncation (statistics)Closure (psychology)Stability (learning theory)Mathematical analysisClassical mechanicsMechanicsPhysicsGeometryComputer scienceEconomicsQuantum mechanicsAlgorithmMachine learningStatisticsMarket economyFluid Dynamics and Turbulent FlowsFluid Dynamics and Vibration AnalysisModel Reduction and Neural Networks