Energy spectra of flow past a circular cylinder

Abstract

Unsteady flow past a circular cylinder is computed for 100≤Re≤10⁷. A stabilized finite element formulation is utilized to solve the incompressible flow equations in the primitive variables form. Close to the cylinder and in the wake region, the finite element mesh has very high resolution. The phenomenon of drag crisis (sudden drop in drag v/s Re at Re~2×10⁵) is captured by the present, two-dimensional, computations. With an increase in Re the transition point of the shear layer, separated from the cylinder surface, moves up-stream. Our computations indicate that at the critical Re the instability reaches the point of flow separation and energizes the local flow causing it to re-attach. Energy spectra for these highly resolved flows at various Re are computed and the effect of various parameters involved in their calculation is investigated. It is found that despite the high shear in the flow, the kinetic energy shows the same structure as observed for 2D isotropic turbulence. For large Re flows it is found that the energy, E(k), varies as k^-5/3 below the energy injection wave number and as k^-3 for higher wave numbers.