By Masaki Satoh

General stream versions (GCMs), which outline the basic dynamics of atmospheric flow, are these days utilized in a number of fields of atmospheric technological know-how corresponding to climate forecasting, weather predictions and environmental estimations. the second one version of this popular paintings has been up-to-date to incorporate contemporary growth of excessive solution worldwide modeling. It additionally comprises for the 1st time features of high-resolution worldwide non-hydrostatic types that the writer has been learning because the ebook of the 1st version. a few highlighted effects from the Non-hydrostatic ICosahedral Atmospheric version (NICAM) also are incorporated. the writer outlines the theoretical options, uncomplicated versions and numerical tools for modeling the final movement of the ambience. focusing on the actual mechanisms accountable for the improvement of large-scale movement of the ambience, the ebook deals accomplished assurance of an immense and swiftly constructing method utilized in the atmospheric technological know-how. Dynamic interpretations of the atmospheric constitution and their features within the basic stream version are defined step by means of step.

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**Example text**

6) vλ is the longitudinal component of velocity. 2 shows the relation between the angular momentum vector l and its axial component lz . 5. 2 The circulation theorem Integration of the equation of motion along a closed curve gives the circulation theorem. Circulation can be related to vorticity. We use both the velocity in the inertial frame v a and that in the rotating frame v r to explain the circulation theorem. We refer to a quantity in the inertial frame with a subscript a and that in the rotating frame with r.

39) where the subscript k denotes each component of dry air. 04 J kg−1 K−1 . It is easy to see that the internal energy and the enthalpy of ideal gas depend only on temperature. 43) ∂h ∂p = −T 2 v T = 0. 44) p In practice, we can assume that the speciﬁc heat is constant irrespective of temperature in the atmosphere. 45) that is, Cv is also constant. 46) where we have assumed that the internal energy at T = 0 K is zero. We often use the ratio of the two speciﬁc heats γ and the ratio of the gas constant to the speciﬁc heat at constant pressure κ: γ ≡ Cp , Cv κ ≡ Rd = 1 − γ −1 .

55) Hence, we have the divergence equation as dD dt = |ω|2 + v · ∇2 v − ∇2 v2 +Φ −∇· 2 ∇p ρ + ∇ · f. 29). 56) that ∇· dv r dt = dD v2 − |ω r |2 − v r · ∇2 v r + ∇2 r . 57) We also have ∇ · (2Ω × v r ) = −2Ω · ω r . 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).