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Normal Mode Initialization and the Generation of Gravity Waves by Quasi-Geostrophic Forcing

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  • 1 National Center for Atmospheric Research, Boulder. CO 80307
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Abstract

Several numerical weather prediction models now use nonlinear normal-mode initialization schemes. These schemes describe balanced states which act to limit the initial presence of high-frequency gravity waves and their subsequent growth by internal dynamics. It has been suggested that there may be states that are so balanced that these waves are never excited except through external forcing. These states have been termed “superbalanced” or “belonging to the slow manifold.”

The degrees to which various balance conditions describe solutions to primitive equations are determined using a sparse-spectral model. The degrees of balance are measured in terms of the portion of energy remaining in the unbalanced fields. Time scales of solutions are measured in terms of the power spectra of their normal linear modes. These measures are determined as a function of heating and dissipation rates and Rossby number.

The dynamics of imbalances is examined also. The tendency for an energy-conserving primitive-equation system to equipartition its energy among each independent mode is demonstrated. For non-adiabatic systems, the portion of the fields not described by superbalance conditions is shown to consist primarily of inertial- gravity waves, especially at the largest horizontal scales. These gravity waves occur intermittently and coincide with maxima in the Rossby number and with small-scale energy cascades. They are damped by eddy viscosity.

Mechanisms for generating imbalances are investigated by comparing various filtered versions of the model. Results indicate that high-frequency components of the quasi-geostrophic forcing terms are the, energy source. The gravity waves are amplified further by near-resonant ageostrophic interactions. However, the gravity modes act on the geostrophic field to increase the balance, probably by acting to damp high-frequency eddies. A true slow manifold does not exist in this model for time-mean Ro>0.1.

Abstract

Several numerical weather prediction models now use nonlinear normal-mode initialization schemes. These schemes describe balanced states which act to limit the initial presence of high-frequency gravity waves and their subsequent growth by internal dynamics. It has been suggested that there may be states that are so balanced that these waves are never excited except through external forcing. These states have been termed “superbalanced” or “belonging to the slow manifold.”

The degrees to which various balance conditions describe solutions to primitive equations are determined using a sparse-spectral model. The degrees of balance are measured in terms of the portion of energy remaining in the unbalanced fields. Time scales of solutions are measured in terms of the power spectra of their normal linear modes. These measures are determined as a function of heating and dissipation rates and Rossby number.

The dynamics of imbalances is examined also. The tendency for an energy-conserving primitive-equation system to equipartition its energy among each independent mode is demonstrated. For non-adiabatic systems, the portion of the fields not described by superbalance conditions is shown to consist primarily of inertial- gravity waves, especially at the largest horizontal scales. These gravity waves occur intermittently and coincide with maxima in the Rossby number and with small-scale energy cascades. They are damped by eddy viscosity.

Mechanisms for generating imbalances are investigated by comparing various filtered versions of the model. Results indicate that high-frequency components of the quasi-geostrophic forcing terms are the, energy source. The gravity waves are amplified further by near-resonant ageostrophic interactions. However, the gravity modes act on the geostrophic field to increase the balance, probably by acting to damp high-frequency eddies. A true slow manifold does not exist in this model for time-mean Ro>0.1.

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