  This paper presents a class of turbulence models written in terms of
fractional partial differential equations (FPDEs) with stochastic loads. Every
solution of these FPDE models is an incompressible velocity field and the
distribution of solutions is Gaussian. Interaction of the turbulence with solid
walls is incorporated through the enforcement of various boundary conditions.
The various boundary conditions deliver extensive flexibility in the near-wall
statistics that can be modelled. Reproduction of both fully-developed
shear-free and uniform shear boundary layer turbulence are highlighted as two
simple physical applications; the first of which is also directly validated
with experimental data. The rendering of inhomogeneous synthetic turbulence
inlet boundary conditions is an additional application, motivated by
contemporary numerical wind tunnel simulations. Calibration of model parameters
and efficient numerical methods are also conferred upon.
