Under some conditions of temperature and flow an ice-water interface in the presence of a turbulent stream has been observed to be unstable. In this paper the source and the conditions for the instability were investigated for a well-defined turbulent boundary-layer flow. It was found that the instability resulted from the interaction that occurs between a wavy surface and a turbulent flow over it. Such an interaction results in a heat transfer variation which is 90 to 180 degrees out of phase with the surface wave shape – a result which is consistent with the calculations of Thorsness & Hanratty (1979a,b).The main factor controlling damping of the instability at an ice-water interface was found to be the rate at which heat is conducted away from the interface into the ice.In the past it has been found that when an ice layer is melting, that is when the heat conduction in the ice is small, the ice surface is highly unstable. In the present study it was found that for a sufficiently large temperature ratio (Tf−Tw)/(T∞−Tf), a steady-state ice layer is also unstable. Furthermore it is predicted, from the present observations, that a growing ice layer with a ratio of ice-side to water-side heat fluxes of up to 2.3 could be unstable.Under sufficiently unstable conditions waves on the ice surface grow to an amplitude at which flow separations occur near the wave crests. This results in a ‘rippled’ ice surface pattern very similar to the patterns observed on mobile bed surfaces (Kennedy 1969) or surfaces which are being dissolved into a flowing stream (Allen 1971). The development of a ‘rippled’ ice surface results in a very substantial increase in the mean heat-transfer rate which would have an important influence on predictions of ice formation in the presence of a turbulent stream.

The Navier-Stokes equations are solved by a numerical method for steady, fully developed, incompressible, laminar flow in curved rectangular channels considering the curvature ratio effect in the formulation. Solutions are obtained for aspect ratios 1, 2, 5 and 0.5 and Dean number ranges from 5 to 715, for example, for the case of square channel. It is found that an additional counter-rotating pair of vortices appears near the central outer region of the channel in addition to the familiar secondary flow at a certain higher Dean number depending on the aspect ratio. This phenomenon is consistent with Dean’s centrifugal instability problem and the secondary flow patterns with two pairs of counter-rotating vortices have not been reported in the past. The correlation equations for the friction factor are developed. The friction factor results are compared with the available theoretical and experimental results for the case of curved square channel and the agreement is found to be good.

The simultaneous effects of curvature, rotation and heating/cooling in channel flow complicate the flow and heat transfer characteristics beyond those observed in the channels with simple curvature or rotation. The phenomena encountered are examined for steady, hydrodynamically and thermally fully developed flow in square channels. The governing equations are solved numerically by using a finite-volume method. Certain hitherto unknown flow patterns are found. And the results show both the nature of the flow transition and the effect of this transition on the distributions of temperature, friction factor and Nusselt number in a square channel.

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