By Masaki Satoh
General move types (GCMs), which outline the elemental dynamics of atmospheric movement, are these days utilized in a number of fields of atmospheric technological know-how akin to climate forecasting, weather predictions and environmental estimations. the second one variation of this well known paintings has been up-to-date to incorporate contemporary development of excessive solution international modeling. It additionally comprises for the 1st time features of high-resolution worldwide non-hydrostatic types that the writer has been learning because the booklet of the 1st version. a few highlighted effects from the Non-hydrostatic ICosahedral Atmospheric version (NICAM) also are incorporated. the writer outlines the theoretical innovations, basic versions and numerical equipment for modeling the overall circulate of the ambience. focusing on the actual mechanisms chargeable for the advance of large-scale flow of the ambience, the e-book bargains entire assurance of an incredible and speedily constructing approach utilized in the atmospheric technology. Dynamic interpretations of the atmospheric constitution and their facets within the normal stream version are defined step via step.
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Additional resources for Atmospheric Circulation Dynamics and General Circulation Models
5 Enthalpy balance and Bernoulli’s theorem From the transformation between enthalpy and kinetic energy, we obtain Bernoulli’s theorem. 3), the change in enthalpy h is expressed as du d(pvs ) du dvs dp dh = + = +p + vs . 43) into this, we obtain the equation of enthalpy dh dp = + ε − ∇ · F ene . 34), we obtain ρ ρ d dt v2 +h 2 = ∂p ∂ − ρv · ∇Φ + (σ vi ) − ∇ · F ene . 66) 20 [Ch. 51). 47). 66) becomes v2 +σ 2 d dt = 0. 67) That is, the sum of kinetic energy and static energy is conserved along ﬂuid motion.
We then derive the momentum equation in a rotating frame. We deﬁne the angular velocity of the rotating frame by Ω, which is constant irrespective of time. We also designate a quantity in the inertial frame by a subscript a and that in the rotating frame by a subscript r. A time derivative of a vector A is transformed as dA dt = a dA dt + Ω × A. 26) Sec. 2] Conservation laws and basic equations 15 where v a is velocity in the inertial frame and v r is velocity in the rotating frame. 28) is the distance to the axis of rotation.
3 Conservation of energy The conservation of energy is expressed as the balance equation for total energy. For application to the atmosphere, total energy per unit volume ρetot can be deﬁned as the sum of kinetic energy 12 ρv 2 , potential energy ρΦ (or ρΦr in the case of the rotating frame), and internal energy ρu, where u is the speciﬁc internal energy per unit mass: 1 2 ρv + ρΦ + ρu. 32) that is, there is no source of total energy. 33) 16 [Ch. 1 Basic equations where F etot designates the ﬂux density vector of total energy.