Reduced models to analyze the different regimes of the flow past a circular cylinder

Abstract

This study concerns the flow past a circular cylinder in the range from the stationary regime until the observation of the first chaotic traits. The aim is to study the transitions of the flow regarded as a dynamical system passing through bifurcations as one increases its parameter, the Reynolds number.The proposed methodology considers the phenomenon as composed by a reduced set of coherent structures or modes that interact dynamically with the extern environment and with each other. These structures belong to the spectrum of the linearized Navier-Stokes operator and are identified in oscillatory solutions that are numerically obtained. The linear behavior of the modes is defined by its stability and oscillatory character and describes its interaction with the extern environment. The sequel is given by the projection of the Navier-Stokes onto the bases of identified modes that gives rise to the nonlinear reduced models of the phenomenon.The numerical integration of the reduced models is very simple and allows one to evaluate the nonlinear interaction between the modes in order to elucidate the underlying mechanism of the asymptotic solutions. However, the usage of reduced models goes far beyond the theoretical comprehension of the phenomenon and can reach some serious applications in engineering, where simplified calculators for the flow past bluff bodies are important tools to design certain structures. A leading example in the national engineering comes from the oil industry, which is continuously forced to advance its exploitation capacity over deep sea, where some gigantic structures are placed to resist the strong currents of our coast under the action of the vortex induced vibration phenomenon.