In this study, we consider how the wave number selection in spherical Couette flow, in the transition to azimuthal waves after the first instability, occurs in the presence of noise. The outer sphere was held stationary, while the inner sphere rotational speed was increased linearly from a subcritical flow to a supercritical one. In a supercritical flow, one of two possible flow states, each with different azimuthal wave numbers, can appear depending upon the initial and final Reynolds numbers and the acceleration value. Noise perturbations were added by introducing small disturbances into the rotational speed signal. With an increasing noise amplitude, a change in the dominant wave number from m to m ± 1 was found to occur at the same initial and final Reynolds numbers and acceleration values. The flow velocity measurements were conducted by using laser Doppler anemometry. Using these results, the role of noise as well as the behaviour of the amplitudes of the competing modes in their stages of damping and growth were determined.

The flow in a turbulent mixing layer resulting from two parallel different velocity streams, that were brought together downstream of a jagged partition was investigated experimentally. The trailing edge of the partition had a short triangular ‘chevron’ shape that could also oscillate up and down at a prescribed frequency, because it was hinged to the stationary part of the partition to form a flap (fliperon). The results obtained from this excitation were compared to the traditional results obtained by oscillating a two-dimensional fliperon. Detailed measurements of the mean flow and the coherent structures, in the periodically excited and spatially developing mixing layer, and its random constituents were carried out using hot-wire anemometry and stereo particle image velocimetry.The prescribed spanwise wavelength of the chevron trailing edge generated coherent streamwise vortices while the periodic oscillation of this fliperon locked in-phase the large spanwise Kelvin–Helmholtz (K-H) rolls, therefore enabling the study of the inter- action between the two. The two-dimensional periodic excitation increases the strength of the spanwise rolls by increasing their size and their circulation, which depends on the input amplitude and frequency. The streamwise vortices generated by the jagged trailing edge distort and bend the primary K-H rolls. The present investigation endeavours to study the distortions of each mode as a consequence of their mutual interaction. Even the mean flow provides evidence for the local bulging of the large spanwise rolls because the integral width (the momentum thickness, θ), undulates along the span. The lateral location of the centre of the ensuing mixing layer (the location where the mean velocity is the arithmetic average of the two streams,y0), also suggests that these vortices are bent. Phase-locked and ensemble-averaged measurements provide more detailed information about the bending and bulging of the large eddies that ensue downstream of the oscillating chevron fliperon. The experiments were carried out at low speeds, but at sufficiently high Reynolds number to ensure naturally turbulent flow.

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Unsteady axially symmetric flows of a viscous incompressible liquid in a spherical layer, which are formed by modulation of the rotation rate of one of the spherical boundaries, are considered. The wave struc tures of such flows are investigated by the method based on determination of the instantaneous difference in phases between the sphere velocity and the azimuthal velocity at each flow point. The steady state character of the distribution of the instantaneous phase difference in the meridional plane of flows is established. The possibility of applying the method at very low vibrational amplitudes is shown.

The results of an experimental investigation of unsteady viscous incompressible flows in a spherical gap, when the rotation velocity of one sphere varies in accordance with the harmonic law, while that of the other sphere remains constant, are presented. The modulation amplitudes and frequencies are small compared with the mean rotation velocities of the spheres. Transition to chaos is studied in a layer, whose thickness is equal to the inner sphere radius, in the case of counter rotation of the spherical boundaries. A periodic flow generated as a result of the mutual synchronization of the frequencies of a three-frequency regime preceding that under study at lower Reynolds numbers is taken as the original state. It is shown that certain properties of turbulent flows near the threshold of their formation essentially depend on the modulation frequency. Keywords: transitions to chaos, spherical layer, periodic variation in the sphere rotation velocities, properties of turbulent flows.A distinctive feature of certain large-scale geophysical processes, such as flows in the liquid core of the Earth, the atmosphere, and oceans, is the combination of the spherical geometry and rotation, including the case of nonuniform rotation. The rotation effect on flows with the spherical geometry can be accounted for in the model spherical Couette flow, which represents a shear flow of a viscous incompressible fluid generated in the case of rotation of the spherical boundaries about the common axis. Under steady boundary conditions the steady flow is determined by three similarity criteria, namely, the Reynolds numbers Re i = Ω i r 2 i /ν and the relative layer thickness σ = (r 2 − r 1 )/r 1 . Here, r i and Ω i are the radii and the rotation velocities of the inner and outer spheres (i = 1, 2), and ν is the kinematic viscosity of the fluid in the layer.

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