Turbulent channel flow simulations in convecting reference frames

We perform finite-difference numerical simulations of turbulent channel flow in stationary and moving reference frames. The flow statistics computed in the stationary frame exhibit significant discrepancies with respect to reference spectral data in terms of energy spectra and convection velocity of disturbances, especially in the near-wall region. On the other hand, simulations performed in a reference frame moving with the bulk flow velocity suffer from this shortcoming to a much lesser extent. We propose an explanation of these observations by assuming the scalar Burgers’ equation as working model. The analysis highlights the lack of Galilean invariance of finite-difference schemes, which exhibit a leading dispersive error in the presence of bulk advection. The numerically computed energy spectra exhibit the same features as the channel spectra, supporting the notion that dispersive effects are responsible for the blockage of the mechanism of energy cascade to high wavenumbers.