The basic scaling law

Scaling law theories are especially concerned with transitions from one regime to another. Suppose there exists a transition at some critical value x of the parameter x where the variable 5 changes its form. Then the fundamental postulate of scaling law theory is that S can be written  

Obviously, So is the form adopted by S in regime (i). Such a transition is represented schematically in Fig. 4.10. Note that whilst scaling law theory can 

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Equation (13) gives the basic scaling law for dissipation. But if a more rigorous treatment is applied, we obtain [7] ... 

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