Nonlinear Normal-Mode Balancing and the Ellipticity Condition

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

Using a low-order, spectral, shallow-water model on an f-plane, the conditions under which height-constrained nonlinear normal mode initialization fails and the existence of realizable balancing wind fields are examined. The relationship of this nonrealizability condition and the ellipticity condition for the standard nonlinear balance equation is also examined. A conclusion from this analysis is that non-elliptic geopotential regions must be accompanied by transient gravity wave motion if there is no forcing mechanism.

The low-order results are extended through the use of a global shallow-water model. The relationship between the local f-plane results and the global results is analyzed and a strong correlation between the appearance of non-elliptic geopotential regions and the breakdown of the iteration scheme used in non-linear normal mode balancing is noted.

It is concluded that moderately weak anticyclonic disturbances in equatorial areas may act as regions of energy exchange between rotational and gravitational modes. Also, the climatological existence of these regions implies the necessity forcing to maintain them in the atmosphere and numerical forecast models.

Abstract

Using a low-order, spectral, shallow-water model on an f-plane, the conditions under which height-constrained nonlinear normal mode initialization fails and the existence of realizable balancing wind fields are examined. The relationship of this nonrealizability condition and the ellipticity condition for the standard nonlinear balance equation is also examined. A conclusion from this analysis is that non-elliptic geopotential regions must be accompanied by transient gravity wave motion if there is no forcing mechanism.

The low-order results are extended through the use of a global shallow-water model. The relationship between the local f-plane results and the global results is analyzed and a strong correlation between the appearance of non-elliptic geopotential regions and the breakdown of the iteration scheme used in non-linear normal mode balancing is noted.

It is concluded that moderately weak anticyclonic disturbances in equatorial areas may act as regions of energy exchange between rotational and gravitational modes. Also, the climatological existence of these regions implies the necessity forcing to maintain them in the atmosphere and numerical forecast models.

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