Linear Instability with Ekman and Interior Friction. Part II: Initial Value Analysis

Abstract

Normal-mode and nonmodal growth are investigated using initial value models. The initial value problems for the Eady and a generalized Eady model (the G model) are solved with no friction and with both Ekman and interior friction. The nonmodel growth is described as either a superposition of eigenmodes or as a transfer between the ?thermal? and relative vorticity parts of quasigeostrophic potential vorticity. When all the eigen-modes are neutral, the growth rate (σH>) of enstrophy is zero, though the growth rate of energy (σE>) and amplitude (σL>) may be positive. For an initial condition having large upstream tilt and constant amplitude, a period of large initial growth in the energy and amplitude is followed by either oscillatory growth and decay (when all eigenmodes are neutral) or asymptotes to a rate given by the most unstable normal mode. In Part I, the authors show that interior friction strongly damps the continuum eigenmodes; however, nonmodal growth can still be significant even when interior friction is present in the Eady model. In the more realistic G model, less overlap between the eigenmodes is found and consequently the nonmodal growth by superposition is reduced compared to the Eady model studied previously by others.