On Laminar Wakes Behind a Circular Cylinder in Stratified Fluids

Finite-difference techniques based on boundary-fitted coordinates have been developed to study the flow of a stably stratified viscous fluid past a circular cylinder. A time-dependent approach is used and an implicit solution is applied in the implementation of vorticity-stream function formulation. All field equations are approximated using central differences and solved simultaneously at each time step by the SOR iteration. Results show that the stratification tends to retard the vortex shedding from the two sides of the cylinder and to narrow down the wake behind the cylinder. With increasing stratification, the drag exerted by the fluid on the cylinder at first decreases and then increases. These solutions also indicate that the periodic configurations of the oscillatory character of the wake flow decrease with the increase of stratification.

Frequency selection and asymptotic states in laminar wakes

A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.