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This paper presents a class of turbulence models written in terms offractional partial differential equations (FPDEs) with stochastic loads. Everysolution of these FPDE models is an incompressible velocity field and thedistribution of solutions is Gaussian. Interaction of the turbulence with solidwalls is incorporated through the enforcement of various boundary conditions.The various boundary conditions deliver extensive flexibility in the near-wallstatistics that can be modelled. Reproduction of both fully-developedshear-free and uniform shear boundary layer turbulence are highlighted as twosimple physical applications; the first of which is also directly validatedwith experimental data. The rendering of inhomogeneous synthetic turbulenceinlet boundary conditions is an additional application, motivated bycontemporary numerical wind tunnel simulations. Calibration of model parametersand efficient numerical methods are also conferred upon.

A fractional PDE model for turbulent velocity fields near solid walls