On radiating baroclinic instability of zonally varying flow

Abstract

The baroclinic instability characteristics of zonally varying flow are examined in a quasigeostrophic, two-layer, beta-plane model. The most unstable eigenmode is determined numerically by solving a one-dimensional initial value problem. Emphasis is placed on determining how the basic state vertically averaged wind, U_B, local maximum in vertical wind shear, ΔU_T, and length of the locally unstable region, λ_L, combine to yield local instabilities whose energy fluxes radiate deep into the locally neutral far field. The existence of such zonally radiating instabilities (RIs), which represent a transition between trapped and global instabilities, requires that λ_L not exceed some critical value and that ΔU_T/U_B lie within a certain range. In sharp contrast to the trapped and global instabilities, the RIs have horizontal wavelengths that increase dramatically with distance from the locally unstable region. If λ_L and ΔU_T/U_B are both sufficiently small, the local instability that emerges is characterized by a vertical asymmetry in its horizontal spatial structure; the disturbance in the upper layer has a longer zonal wavelength than its counterpart in the lower layer. For slowly varying basic states, analysis of the local disturbance energetics reveals that the baroclinic energy conversion predominates within the locally unstable region. For basic states that vary rapidly in the downstream direction, the barotropic energy conversion associated with the horizontal deformation field may predominate over the baroclinic conversion depending on the relative importance of ΔU_T and U_B. For RIs, the energy budget outside the locally unstable region is primarily due to the advection of total energy and the convergence of mechanical energy flux. Calculations of the basic state tendencies show that the net effect of the local (trapped or radiating) instabilities is to redistribute energy from the baroclinic to the barotropic component of the basic state flow. The fluxes produced by the trapped modes reduce the vertical shear downstream of the jet center, while the fluxes produced by the radiating modes reduce the vertical shear both downstream and near the jet center.