Spectral approximation methods for non equilibrium transport in turbulent channel flows using fADE

In this work, the study of suspended sediment transport under unsteady, uniform and non equilibrium condition is extended using space fractional diffusion equation (fADE) with parameter α. Semi analytical solutions of this space fADE with realistic boundary conditions are obtained using spectral method developed on Chebyshev orthogonal polynomials. Solutions obtained from this method are compared with previous analytical solutions for the case α=2 and satisfactory results are obtained. Apart from these, the effect of non-locality on non equilibrium transport of particles is discussed and it is found that in unsteady condition sediment concentration increases when α<2 except for near bed region. Whereas sediment concentration increases over the full water depth under steady condition when α<2. Also in unsteady condition, the increase of sediment diffusivity increases the sediment concentration except for the near bed region. This new analytical technique shows that new kind of solutions can be generated using Chebyshev orthogonal polynomials.