By Masaki Satoh

General stream versions (GCMs), which outline the elemental dynamics of atmospheric flow, are these days utilized in a variety of fields of atmospheric technological know-how resembling climate forecasting, weather predictions and environmental estimations. the second one version of this popular paintings has been up to date to incorporate fresh growth of excessive solution international modeling. It additionally comprises for the 1st time points of high-resolution worldwide non-hydrostatic versions that the writer has been learning because the e-book of the 1st variation. a few highlighted effects from the Non-hydrostatic ICosahedral Atmospheric version (NICAM) also are integrated. the writer outlines the theoretical ideas, uncomplicated types and numerical tools for modeling the final move of the ambience. targeting the actual mechanisms accountable for the advance of large-scale stream of the ambience, the e-book bargains entire assurance of a major and speedily constructing strategy utilized in the atmospheric technological know-how. Dynamic interpretations of the atmospheric constitution and their features within the normal stream version are defined step by means of step.

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**Example text**

Second, the circulation theorem is derived through the balance of momentum of forces along the boundary of a ﬁnite domain. In the limit of an inﬁnitesimal domain, the circulation theorem reduces to vorticity equations. Third, the equation of potential vorticity is derived from vorticity equations and the equation of a scalar quantity, such as potential temperature. Under an appropriate condition, potential vorticity is a materially conserved quantity. At the end of this section, the divergence equation is introduced as a pair of vorticity equations.

58) Thus, the divergence equation in the rotating frame is written as dD dt = (ω r + 2Ω) · ω r + v r · ∇2 v r − ∇2 −∇ · ∇p ρ + ∇ · f. 59) is a prognostic equation for the divergence of the three-dimensional velocity ﬁeld. In practice, this form of the equation is rarely used. Instead, an equation for the horizontal divergence of two-dimensional velocity is usually used for the governing equations of atmospheric general circulation models (see Chapter 20). Nevertheless, we should point out the relevance of the threedimensional divergence equation to the sound wave.

52) where p0 is a reference pressure at which potential temperature becomes equal to temperature. Normally, p0 = 1,000 hPa is used. The adiabatic process often appears in atmospheric motions. In the adiabatic process, the change in thermodynamic variables occurs at constant entropy. 32). 33), is expressed as γd ≡ ∂T ∂p = s 1 . 58) Sec. 2] Conservation laws and basic equations 11 or the change in the potential temperature is ρ dθ θ = 1 dp − dρ. 56), in the adiabatic process ds = dθ = 0, pressure and density are related as p = const.