EFFECTS OF MANIFOLDS AND CORNER SINGULARITIES ON STRETCHING IN CHAOTIC CAVITY FLOWS

It has been assumed that the stretching field in chaotic flows evolves as the result of a random multiplicative process [F. J. Muzzio, C. Me neveau, P. D. Swanson and J. M. Ottino, Scaling and multifractal prope rties of mixing in chaotic flows, Phys. Fluids A, 4, 1439-1456, (1992) ; F. J. Muzzio, P. D. Swanson and J. M. Ottino, partially mixed struct ures produced by multiplicative stretching in chaotic flows, Int. J. B ifurc. Chaos, 2, 37-50 (1992)]. This assumption has been used to deriv e an asymptotic scaling formalism of distributions of stretching value s that has useful predictive capabilities. Deviations from this scalin g were thought to be limited to cases with regular islands. However, a s is shown in this paper for the chaotic cavity flow, deviations from the proposed scaling can also occur for globally chaotic flows as a re sult of the joint action of unstable manifolds of hyperbolic periodic point and of singularities at the corners of the cavity. A detailed ex amination of random multiplicative stretching, the conditions necessar y for its validity, and the intensity of manifold interaction effects is performed here for the cavity flow.