Group Velocity of Anisotropic Waves-Part Ⅰ: Mathematical Expression

The group velocity used in meteorology in the last 30 years was derived in terms of conservation of wave energy or crests in wave propagation. The conservation principle is a necessary but not a sufficient condition for deriving the mathematical form of group velocity, because it cannot specify a unique direction in which wave energy or crests propagate. The derived mathematical expression is available only for isotropic waves. But for anisotropic waves, the traditional group velocity may have no a definite direction, because it varies with rotation of coordinates. For these reasons, it cannot be considered as a general expression of group velocity. A ray defined by using this group velocity may not be the trajectory of a reference point in an anisotropic wave train. The more general and precise expression of group velocity which is applicable for both isotropic and anisotropic waves and is independent of coordinates will be derived following the displacement of not only a wave envelope phase but also a     

Large scale perturbations in extratropical atmosphere—Part II: On geostrophic waves

We have examined, in Part I, the propagation mechanism and geostrophic property of classical Rossby waves in a non-divergent barotropic atmosphere. As we found that the non-divergent Rossby waves do not propagate in a hydrostatically equilibrium atmosphere, and do not manifest a good geostrophic property, an alternative large scale circulation pattern of geostrophic waves has been proposed (McHall, 1991a). The propagation mechanism and geostrophic property of these waves are examined in the present study.     

Available equivalent potential energy in moist atmospheres

Summary The equivalent potential energy of the moist atmosphere is defined as the sum of its total potential energy and latent heat. The available equivalent potential energy is the amount of equivalent potential energy available for conversion into kinetic energy. For the isolated moist atmospheres, we may find the equivalent lowest state which is the limit of the states attained through all the actual processes involving water condensation and possesses the least equivalent potential energy. Thus, the maximum available equivalent potential energy with respect to the equivalent lowest state can be estimated for any provided initial state. This study may extend the understanding for the development of precipitation systems in the moist atmosphere.With 5 Figures     

An Introduction to the New Book-GEOSTROPHIC WAVE CIRCULATIONS

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INSTABILITY PROPERTIES OF ATMOSPHERIC DISTURBANCES

There are some basic problems in previous theoretical studies of baroclinic instability.The derived criticalbaroclinity was considerably lower than the time averaged mean meridional temperature gradient,especially in the lowertroposphere.Also,the linear mechanism of baroclinic disturbance development which is noted restricted by the criticalbaroclinity was not studied sufficiently.The realistic critical baroclinity and disturbance development are discussed inthis study.It will be shown that the critical condition of instability and typical time and space scales of disturbances de-pend on three-dimensional structures of atmosphere and sphericity of the earth,other than the horizontal temperaturegradient alone.The variant behaviour of atmospheric disturbances depends highly on their specific scales that may bedescribed by the same theoretical model.Thus,there would be no substantial differences in the basic instability mecha-nism of many disturbances including the polar lows and explosive cyclones.     

Wintertime stratospheric anomalies— Part II: Sudden warmings

The process of stratospheric sudden warmings from development of planetary waves to the sudden cooling after reversal of mean zonal circulation will be studied with the primitive equations of heat and momentum balances. It will be explained that the sudden warmings may occur only in the polar regions of winter stratosphere where zonal mean temperature decreases poleward. The heating rate in the order of major warmings is produced by developed planetary waves in the stratospheric breaking layers. The particular perturbation structure characterized by large amplitude of wave 1 together with minimum of wave 2 discovered by Labitzke (1977) is crucial for initiation of major warmings. The cooling by the same mechanism can be produced in the regions with reversed mean temperature gradient.     

Group velocity of anisotropie waves—Part II: Conservative properties

It has been argued in Part I that traditional expression of multidimensional group velocity used in meteorology is only applicable for isotropic waves. While for anisotropic waves, it cannot manifest propagation of waves group along the trajectory of a reference wave point, and varies with rotation of coordinates. The general mathematical ex-pression of group velocity which may be used also for anisotropic waves has been derived in Part I. It will be proved that the mean wave energy, momentum and wave action density are all conserved as a wave group propagates at the general group velocity. Since general group velocity represents the movement of a reference point in either isotropic or anisotropic wave trains, it may be used to define wave rays. The variations of wave parameters along the rays in a slowly varying environment are represented by ray-tracing equations. Using the general group velocity, we may de-rive the anisotropic ray-tracing equations, which give the traditional ray-tracing equations for isotropic waves.     

Large scale perturbations in extratropical atmosphere—Part I: On rossby waves

This study reexamines the propagation mechanism and geostrophic property of the classical two-dimensional Rossby waves in a non-divergent barotropic atmosphere. It will be found that propagation of large scale atmospheric waves depends crucially on horizontal divergence. A small Rossby number in Rossby waves is not sufficient for the waves to have a small ageostrophic component, because the two-dimensional classical Rossby waves do not manifest the geostrophic balance as good as observed in the atmosphere.     

Planetary stationary waves in the atmosphere Part I: Orographic stationary waves

It is proposed that the orographic stationary waves are required by long-term balance of momentum in the at-mosphere with zonally asymmetric orographic forcing, This hypothesis may be confirmed successfully with the theo-retical model of geostrophic waves. In the Part I, we will explain the observed phase distributions of orographic sta-tionary waves at middle and high latitudes of the Northern Hemisphere, according to the long-term balance of zonal momentum over the stationary orographic forcing. It is revealed that the geographic distribution of stationary waves depends not only on local topgraphy but also on mean circulation fields and angular momentum flux in the atmos-phere. So these waves cannot be simulated by the models in a restricted area.