Some Preliminary Comments -- From Euler and Navier Equations to NS-F Full Unsready Equations -- Dimensionless NS-F Equations and Parameters -- The Mathematics of the Rational Asymptotic Modelling -- A Deconstruction Approach for an Unsteady NS-F Fluid Flow at Large Reynolds Number -- Three RAM Applications in Aerodynamics -- The RAM Approach of Bénard Problem -- Two RAM Applications for Atmospheric Motions.

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of  fluid flows modeling on the basis of a typical Navier-Stokes-Fourier  initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff  problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.