The force exerted on an object immersed in a flowing turbulent fluid is considered as a zero-memory, nonlinear transformation of the bivariate Gaussian process whose components are the fluid particle velocities and local accelerations that would be present at the location of the object if the object were not disturbing the fluid. A model often used in applications is assumed and the probability density and the moment generating function are derived and investigated. The covariance between the forces at two space-time points in the presence of a space-varying mean flow is developed and a series approximation outlined. Under suitable restrictions the partial sums of the series are used to obtain an easily computed approximation to the spectral density of the force at a fixed space location.
"Random Hydrodynamic Forces on Objects." Ann. Math. Statist. 38 (1) 37 - 51, February, 1967. https://doi.org/10.1214/aoms/1177699057