Estimation of energy dissipation caused by odd order difference schemes for an unstable planetary boundary layer

Abstract

AbstractNumerical error by an odd order difference approximation in the advection term dissipates energy in the resolved motion. We propose a method to estimate the energy dissipation rate derived from the numerical error to clarify its effect on the energy budget. The energy dissipation rate in Large‐Eddy Simulations for an ideal unstable boundary layer is analysed. The proposed method reveals that the imbalance of the energy budget can be ascribed to the non‐conservative property with respect to kinetic energy of the discretised advection terms, while the net energy dissipation in the resolved field is almost insensitive to the origins of the energy dissipation. However, the magnitude of the momentum and temperature fluxes is sensitive to the difference scheme; the numerical error in the advection term reduces these fluxes in the resolved part. A subgrid scheme should be designed so as to compensate decrease of the resolved flux when an odd order difference is applied to the advection term.