Transition to Turbulence in a Fluid Flow

Abstract

We have used the technique of laser Doppler velocimetry to study the flow of a fluid contained between concentric cylinders with the inner cylinder rotating. It is convenient to describe the flow as a function of the (dimensionless) Reynolds number R, which can be defined as R = ω_cylr_i (r_o-r_i)/υ, where ω_cyl is the angular frequency of the inner cylinder, r_i and r_o are the radii of the inner and outer cylinders respectively, and υ is the kinematic viscosity. For small R the flow is purely azimuthal, but as TAYLOR [1] showed in 1923, above a critical Reynolds number R_c the simple azimuthal flow is no longer stable and there is a transition to a flow with a horizontal vortex pattern superimposed on the azimuthal flow. A photograph of the flow with the Taylor vortices is shown in Fig.1(a); the flow pattern is rendered visible by a suspension of small flat flakes [2] which align with the flow. The Taylor vortex flow has been extensively studied in recent years by DONNELLY [3], KOSCHMIEDER [4], SNYDER [5], and others. At a higher, well defined R there is a transition from the time-independent Taylor vortex flow to a time-dependent flow with transverse waves superimposed on the horizontal vortices, as shown in Fig.1(b) and (c). Although the wavy flow has been observed in many experiments, the most thorough study has been the photographic investigations of COLES [6], who found that as R was increased beyond the onset of the wavy regime, the flow became noisier and noisier and ultimately turbulent (see Fig.1(d)).