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Additional info for Modern Fluid Dynamics. Incompressible flow
However such conditions are not vahd far away from the sphere because there they become v6 R/r 2 « vVo R/r 3 , Le. vov- 1 r « 1. 3], cannot be taken as correct. (Hmt: Compare the size of the transport term u . ) - -- Bibliography. The discussion reported in Sects. 6 follows the ideas in [LL71]. 3 The Rescaling Method and Estimates of the Approximations The procedure illustrated in Sect. 2 to evaluate the orders of magnitude involved in the incompressibility approximations is simple but, in a way, not very systematic.
Hznt: The pressure must be a function 1l"(G). ;. in terms of G along the curve. )). 1) is possible. 1). 1) will hold, cf.
25) while p has to be thought of as no longer related to s or T because (;~)v =-(~~)T =0. 24), in which T depends on time, with the impossibility of such a solution which we have just shown in the case of a compressible fluid. In fact the incompressible fluid is in a suitable sense a limit case of the compressible fluid. In reality a compressible fluid close to an incompressible one (in the sense discussed in Sect. 3) cannot be, from the above discussion, a static thermoconductor and it will start "flowing".