Analytic expression for the short-time rate of growth of the intermaterial contact perimeter in two-dimensional chaotic flows and Hamiltonian systems

This article derives an analytic expression for the short- or intermediate-time behavior of the moment hierarchy of finite-time Liapunov exponents (stretching exponents) for two-dimensional periodically forced Hamiltonian systems and incompressible time-periodic fluid flows. As a result, the exponent characterizing the apparent short-time exponential growth of the intermaterial contact perimeter for two-dimensional systems can be predicted from the statistical properties of the invariant stretching distribution. The analysis as a whole is in fact grounded on an analytic expression for the high stretching tail of the invariant distribution of the finite-time Liapunov exponents. The asymptotic behavior of the moment hierarchy of the stretching field is also addressed in order to highlight the role of the dynamic heterogeneity accounted for by the variance of the stretching exponents.