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Down all material functions of the n-th order fluid in terms of the material coefficients bo.. 12). Then the required expressions follows from their definitions in terms of g' (see table 1). 17) where the scalar invariants for each specific flow are in table 1. 3). The same is valid for the limit for vanishing strain rate of the out-of-plane normal stress difference in PCF and PEF (see eqs. 16) turns out to be also the slope at £=0 of the viscosity in 3DEF with reversed sign (its numerical value is shown in figure 4).

Their idea has been later on incorporated in more refined bulk perturbation schemes derived or not from an hamiltonian (see ref. 18,19 and ref. 20 for the non hamiltonian version). e. the exact analogue of the perturbation field we used to create an electrical current). The perturbation was later on slightly modified by Evans22 to conserve the net linear momentum of the system. e. there is no function A, eq. 2), such that C j = (aAldpj) and Dj= aAldrj ). t to the perturbation of eq. 3) is automatically obeyed by hamiltonian perturbations and does not seem to be physically restrictive 23 ).

Such a curvature is consistent with a general class of multiplicative cascade models which Mandelbrot (1974b, 1976) called 'weighted curdling models' because they do not have the black and white character of the Novikov-Stewart model. But here again, it was desirable to reinterpret the models in terms of pure inertial range quantities. This was done by Parisi & Frisch (1985) and led to the multifractal model as formulated in Section 3, in which a central role is played by the Legendre transformation.

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Aircraft Profile No. 30: The North American F-100 Super Sabre by Ray Wagner

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