Turbulent Hydrodynamic Line-Stretching: The Random Walk Limit

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Abstract
Recent results on the central limit theorem for sums of dependent random variables are used to evaluate the asymptotic rates of turbulent stretching of material line and surface elements in the limit t→∞ . The turbulence is assumed to be incompressible and statistically stationary and isotropic, and it is shown that the expectation value of the logarithmic rate of increase of the magnitude of the material elements vanishes at t→∞ . Possibilities for application to weak‐field magnetohydrodynamic turbulence are noted and some associated difficulties are discussed.

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