A Mechanism for Oblique Wave Resornance in the Far Wake

Abstract

There has been some debate recently as to whether the far wake structure downstream of a cylinder is dependant on, or "connected" with the precise details of the near wake structure. Indeed, it has previously been suggested that the far wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that not only the far wake scale but also the frequency are dependant on the near wake. Surprisingly, the characteristic which actually forges a "connection" between the near and far wake is the sensitivity to free stream disturbances. It is these disturbances which are also responsible for the regular 3-D patterns that may be visualised. Observations of a regular "honeycomb" -like 3-D pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale 2-D waves, amplified from the free stream disturbances. In the far wake, we further describe a new mechanism for oblique wave resonance, as follows. In the case of 2-D waves, corresponding to a very small spectral peak in the free stream (fT), interacting (quadratically) with the oblique shedding waves (fK), it appears that the most amplified or resonant frequency in the far wake is a combination-frequency fFW = (fK-fT), which corresponds physically with "oblique resonance waves" of large angle. We present clear visualisation of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary 2-D wave energy by up to two orders of magnitude. Following the discovery of this phenomenon in "natural" far wakes, we subsequently induce oblique wave resonances by acoustic forcing of 2-D waves. A whole set of higher order oblique wave resonances are found, corresponding to frequencies (fK-nfT), where n is an integer. We find from visualisation that, even when the secondary 2-D waves have the same frequency as the oblique waves, it is the oblique waves which are preferentially amplified. Oblique wave angles up to 74 0 have been observed. Simple equations for the oblique waves yield approximate conditions for maximum wake response, with a frequency for peak response given by Fmax = dn - ~, ~, ~ ..... , and an oblique wave angle given by Smax = 2 SK ' where SK is the angle of oblique vortex shedding. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.