An experimental study of non-linear interaction of velocity fluctuations in the transition region of a two-dimensional wake

Abstract

As an extension of our previous work (Sato & Kuriki 1961), an experimental study was made on the laminar-turbulent transition of a two-dimensional wake, with emphasis on the non-linear interaction of velocity fluctuations. In the natural transition, a sinusoidal velocity fluctuation first appears as a result of the selective amplification of irregular disturbances. When the amplitude of the fluctuation becomes large, a non-linear interaction takes place: higher harmonics of the sinusoidal fluctuation and a slow, irregular fluctuation are generated. The transition into turbulence is gradual, and there are no abrupt ‘breakdowns’.When a sound with two frequencies (f1 and f2) is introduced into the wake, two velocity fluctuations are induced. They are amplified independently when amplitudes are small. If amplitudes exceed certain values, a mutual interaction takes place, and the growth of each component is suppressed by the presence of the other. At the same time, fluctuations with frequencies of f1 − f2, 2(f1 − f2) … and f1 + f2, 2(f1 + f2) … are produced. The behaviour of the slow, irregular fluctuation in the natural transition closely resembles that of the f1 − f2 component. They seem to be produced by the same mechanism.In the transition region of the wake, a small variation in the amplitude of velocity fluctuation is enhanced by the suppression effect, and a small irregularity in the frequency is amplified by the generation of the f1 − f2 component. These are two elementary processes of randomization of regular fluctuations, which lead to the development of turbulence.