The Influence of Realistic Dissipation on Planetary Normal Structures

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

The effect of realistic dissipation on the rotational normal modes of a barotropic atmosphere is investigated. Vertical growth of amplitude of the Lamb(10km equivalent depth)modes is found to diminish with increasing meridional index n. The fastest traveling modes are most sensitive to radiative-photo-chemical damping above 4 scale heights. However, with increasing n, thermal and viscous diffusion dissipate more of the energy below this level. The energy flux is virtually attenuated by 8 scale heights. Thus the particular details above this level should have little bearing on the nature of the modes below.

Damping time scales (relaxation periods) are estimated for several modes. These are smallest for wavenumber 1, roughly 10 wave periods, and increase with zonal wavenumber. The role of dissipation in determining these relaxation periods is more than just the local damping of energy. It significantly enhances the “vertical leakage” and thus allows energy to flow more readily to levels of greater dissipation.

In view of the absence of steady forcing mechanisms for these modes, several hypothetical transient situations are examined. The implication of finite relaxation periods to intermittent reinforcement is discussed, and the relative importance of local dissipation versus vertical leakage is considered. Estimates of damping times here together with recent observations of the 5-day wave, suggest that should slower modes, be excited, they would exist only in a transient sense.

The existence of modes ducted horizontally by realistic variations in the mean fields is also considered. If the trapping occurs sufficiently high (greater than the first few scale heights). the, wave duct cannot be excited by forcing near the surface, since the energy flux reaching these levels is minimal. Wave ducting by vertical variations in temperature could be found, but the response associated with such trapping was small and dwarfed by that of the Lamb structure at all heights. The vertical e folding distance for the energy flux is on the order of a few scale heights, over a broad range of disturbance parameters, for vertically propagating rotational modes. Such behavior. suggests that efficiently ducted rotational modes in the atmosphere are unlikely, leaving the Lamb structure as the only plausible rotational normal feature.

Abstract

The effect of realistic dissipation on the rotational normal modes of a barotropic atmosphere is investigated. Vertical growth of amplitude of the Lamb(10km equivalent depth)modes is found to diminish with increasing meridional index n. The fastest traveling modes are most sensitive to radiative-photo-chemical damping above 4 scale heights. However, with increasing n, thermal and viscous diffusion dissipate more of the energy below this level. The energy flux is virtually attenuated by 8 scale heights. Thus the particular details above this level should have little bearing on the nature of the modes below.

Damping time scales (relaxation periods) are estimated for several modes. These are smallest for wavenumber 1, roughly 10 wave periods, and increase with zonal wavenumber. The role of dissipation in determining these relaxation periods is more than just the local damping of energy. It significantly enhances the “vertical leakage” and thus allows energy to flow more readily to levels of greater dissipation.

In view of the absence of steady forcing mechanisms for these modes, several hypothetical transient situations are examined. The implication of finite relaxation periods to intermittent reinforcement is discussed, and the relative importance of local dissipation versus vertical leakage is considered. Estimates of damping times here together with recent observations of the 5-day wave, suggest that should slower modes, be excited, they would exist only in a transient sense.

The existence of modes ducted horizontally by realistic variations in the mean fields is also considered. If the trapping occurs sufficiently high (greater than the first few scale heights). the, wave duct cannot be excited by forcing near the surface, since the energy flux reaching these levels is minimal. Wave ducting by vertical variations in temperature could be found, but the response associated with such trapping was small and dwarfed by that of the Lamb structure at all heights. The vertical e folding distance for the energy flux is on the order of a few scale heights, over a broad range of disturbance parameters, for vertically propagating rotational modes. Such behavior. suggests that efficiently ducted rotational modes in the atmosphere are unlikely, leaving the Lamb structure as the only plausible rotational normal feature.

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