A Numerical Simulation of Amplification of Low-Frequency Planetary Waves and Blocking Formations by the Upscale Energy Cascade

Abstract

In this study, nonlinear numerical simulations of amplification of low-frequency planetary waves and concurrent blocking formations were performed. The simulations are conducted by a barotropic spectral model derived from three-dimensional spectral primitive equations with a basis of vertical structure functions and Hough harmonics. The model is truncated to include only barotropic Rossby components of the atmosphere with simple physics of biharmonic diffusion, topographic forcing, baroclinic instability, and zonal surface stress. These four physical processes are found to be sufficient to produce a realistic and persistent dipole blocking with a sharp transition from zonal to meridional flows on a sphere. Analyzing energetics of blocking formations in the model, we showed an amplification of the meridional dipole mode was confirmed by means of the upscale energy cascade from synoptic disturbances under an environment of persistently amplified wavenumber 2. When the persistent wavenumber 2 exists, synoptic disturbances contribute to amplify the dipole mode of wavenumber 1. In contrast, when the persistent wavenumber 2 is absent, synoptic disturbances contribute to accelerate zonal flow with enhanced wave-mean flow interactions, and wavenumber 1 is not amplified. Therefore, we find that the persistent wavenumber 2 plays a catalytic role in drawing synoptic wave energy and feeding wavenumber 1. The topographic forcing in amplifying wavenumber 2 appears to be necessary for the blocking system in the model, although it is not the main energy source for the system.