Using symbolic expressions to get the Taylor expansion of the Lagrangian auto-covariance function

Eduardo S. Schneider, Craig L. Zirbel


This work describes how we derived symbolic expressions for the Taylor coefficients of the Lagrangian auto-covariance function for a two-dimensional, mean-zero, homogeneous, steady, and incompressible random velocity field which is written as a sum of many Fourier modes. Additionally, we wrote code to calculate these coefficients exactly and produce executable code which quickly calculates the first terms of the Taylor expansion of the Lagrangian auto-covariance function.


Velocity field, Lagrangian auto-covariance, Taylor expansion, passive tracer transport

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