By Masaki Satoh

General stream versions (GCMs), which outline the elemental dynamics of atmospheric flow, are these days utilized in numerous fields of atmospheric technology akin to climate forecasting, weather predictions and environmental estimations. the second one variation of this popular paintings has been up to date to incorporate contemporary growth of excessive answer international modeling. It additionally comprises for the 1st time facets of high-resolution international non-hydrostatic types that the writer has been learning because the ebook of the 1st variation. a few highlighted effects from the Non-hydrostatic ICosahedral Atmospheric version (NICAM) also are incorporated. the writer outlines the theoretical techniques, basic versions and numerical tools for modeling the overall circulate of the ambience. focusing on the actual mechanisms accountable for the advance of large-scale movement of the ambience, the booklet deals finished insurance of a major and quickly constructing procedure utilized in the atmospheric technological know-how. Dynamic interpretations of the atmospheric constitution and their features within the common circulate version are defined step via step.

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If viewed in a rotating frame, the effect of a component of a rigid body rotation is counted as a potential force due to the centrifugal potential and can be included as part of the geopotential. 2, geostrophic balance and thermal wind balance are described. Geostrophic balance is defined as a static balance with wind fields in the rotating frame. Thermal wind balance is the corresponding balance of vorticity. In the following two sections, the stability of these balanced states is examined. 3. 4 on the assumption that the perturbation has a two-dimensional axisymmetric flow.

Thus, the baroclinic term increases circulation toward the anti-clockwise direction. 11) is the dissipation term due to friction. This term does not necessarily weaken circulation in general. 3 Vorticity equations The circulation theorem is given by integration of the equation of motion along a closed curve. In this subsection, vorticity equations are derived as a derivative form of the circulation theorem. 2); that is ρ ∂ vi + vj ∂j vi ∂t = ∂j σij − ρ∂i Φ. 20) Sec. 3] Angular momentum, vorticity, and divergence 25 where vorticity is written as ωi = εijk ∂j vk ; that is v2 .

3 vorticity equations are derived by applying the rotation operator to the equation of motion. As a counterpart to vorticity equations, the divergence equation can be derived by applying the divergence operator to the equation of motion. The divergence of velocity is defined as D ≡ ∂i vi = ∇ · v. 22) yields ∂D ∂t = −∂i (εijk ωj vk ) + ∂i 1 ∂j σij ρ − ∂i2 Φ + v2 2 . 54) The first term on the right-hand side is rewritten as ∂i (εijk ωj vk ) = −ωj2 + εijk (∂i ωj )vk = −ωj2 − (∂i ∂i vk )vk + (∂k ∂i vi )vk = −|ω|2 − v · ∇2 v + v · ∇D.

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