By Gallavotti G.
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Compute S (S = 6π, Stokes formula). 2: General and incompressible equations. 1] can be acceptable. e. v0 ν −1 R ≪ 1 which is read, see the coming sections, by saying that the “Reynolds’ number” is small. e. v0 ν −1 r ≪ 1. 3], cannot be taken as correct. ) Bibliography: The discussion reported in (D,E,F) follows the ideas in [LL71]. 3: Approximations estimates. 3 The rescaling method and estimates of the approximations. 2 to evaluate the orders of magnitude involved in the incompressibility approximations is simple but, in a way, not very systematic.
E. solutions in which the thermodynamic functions depend only on z. We shall denote them s = s0 (z), T = T (z), p = p(z), ε = ε(z) and ρ = ρ(z), (ρ = r(p, s)). 6) which is an ordinary differential equation for p(z) determining it once the data p(0) = p0 and the function s = s0 (z) are known. 8) Or, in other words if G(x) is bounded below, otherwise the equation does not admit hydrostatic solutions. 11) Hence it is possible that a gas in which temperature is not constant stays in a “stratified equilibrium”.
Check this statement by finding and consulting some geophysical data. 4: Elements of hydrostatics 41 considered as incompressible. 2 one sees that density variations on the scale l over which sensible variations of pressure occur are such that: ∆ρ ≃ cgl2 , where c is the sound velocity. Take, in the case of air, c ≃ 103 km/h. e. ≃ 104 m. 11) to evaluate the height from a measurement of pressure. For larger heights ρ cannot any more be considered as constant and to compute the height z in terms of p it becomes necessary to know also how temperature changes with height.
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