Determine the required stochastic-model parameters from physical flow inputs

Determine rigorous estimates of the Taylor microscale \(\lambda_{T}\), aerodynamic roughness length \(z_{0}\), friction velocity \(u_{\tau}\), and boundary-layer thickness \(\delta\) from the given surface geometry and undisturbed flow velocity, rather than relying on scaling relationships and reasonable guesses.

Background

The stochastic framework requires $\lambda_{T}$, $z_{0}$, $u_{\tau}$, and $\delta$ as baseline inputs for generating uniform momentum zones, vortices, and the correlated two-dimensional velocity field. The paper notes that these quantities are not generally available a priori for a target rough-wall flow and that existing scaling and empirical relationships provide only approximate values.

A rigorous procedure for inferring these parameters from surface geometry and undisturbed flow conditions would make the generative framework more predictive and reduce its dependence on externally prescribed or fitted quantities.