A quantitative analysis of the dissipation inherent in semi-Lagrangian advection

Semi-Lagrangian advection schemes are known to be dissipative because of the interpolation required to estimate the values of the flow fields at each parcel's departure point. The amplification factors of first-, second-, third-, and fourth-order Lagrangian interpolation schemes are used to calculate the dissipative decay time scale and the resulting effective eddy viscosity as functions of wavelength and residual Courant number. The dissipation inherent in the semi-Lagrangian advection can then be compared to more traditional forms of dissipation, such as Laplacian or biharmonic eddy viscosity. The correspondence between semi-Lagrangian advection and more traditional Eulerian techniques is emphasized. The dependence of the dissipation upon the time step and grid spacing is also discussed, with a view of selecting the discretionary parameters to meet conservation criteria.