The Nonlinear Effects of Orographic and Momentum Forcing in a Low-Order, Barotropic Model

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  • 1 European Centre for Medium Range Weather Forecasts, Reading, England
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Abstract

An analysis of a low-order barotropic system with orographic and momentum forcing is presented. The low-order expansion of the streamfunction is performed on a spherical geometry, the expansion functions thus being spherical harmonics. Two purely zonal components and two wave components with the same zonal wavenumber but different orders, or latitudinal wavenumbers, are described by the model. The nonlinear terms appearing in the six ODE's governing the time evolution of the system give rise to bifurcations into multiple steady-state solutions.

In order to retain as many nonlinear terms as possible, however, one must be careful in the choice of components. An analysis of the different possibilities is presented and two examples having somewhat different properties are investigated. Three of the components are the same in each example, while the three others differ in their symmetry properties around the equator.

For the example which is believed to be most representative of realistic conditions, it is shown that a combination of orographic forcing and zonally asymmetric momentum forcing is required to obtain multiple steady-state solutions for realistic parameter values. The forcing must exceed certain critical values for a bifurcation from one to three steady states to appeal. A stability investigation of the steady-state triplets shows that two are stable while one is unstable. Examining the energetics of the two stable steady states for a situation which corresponds to a wintertime forcing pattern, it is shown that one of the stable steady states is much more zonal than the other. The non-zonal circulation is similar to a “blocked” flow. Another significant difference in the energetics between the two flow types is the intensity of the energy transfer between zonal and eddy kinetic energy. Comparisons with observational studies of “blocked” and zonal flow confirms that this is a characteristic feature of the observed energetics.

Abstract

An analysis of a low-order barotropic system with orographic and momentum forcing is presented. The low-order expansion of the streamfunction is performed on a spherical geometry, the expansion functions thus being spherical harmonics. Two purely zonal components and two wave components with the same zonal wavenumber but different orders, or latitudinal wavenumbers, are described by the model. The nonlinear terms appearing in the six ODE's governing the time evolution of the system give rise to bifurcations into multiple steady-state solutions.

In order to retain as many nonlinear terms as possible, however, one must be careful in the choice of components. An analysis of the different possibilities is presented and two examples having somewhat different properties are investigated. Three of the components are the same in each example, while the three others differ in their symmetry properties around the equator.

For the example which is believed to be most representative of realistic conditions, it is shown that a combination of orographic forcing and zonally asymmetric momentum forcing is required to obtain multiple steady-state solutions for realistic parameter values. The forcing must exceed certain critical values for a bifurcation from one to three steady states to appeal. A stability investigation of the steady-state triplets shows that two are stable while one is unstable. Examining the energetics of the two stable steady states for a situation which corresponds to a wintertime forcing pattern, it is shown that one of the stable steady states is much more zonal than the other. The non-zonal circulation is similar to a “blocked” flow. Another significant difference in the energetics between the two flow types is the intensity of the energy transfer between zonal and eddy kinetic energy. Comparisons with observational studies of “blocked” and zonal flow confirms that this is a characteristic feature of the observed energetics.

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