Introduction --
1. Dimensions, dimensional analysis and similarity --
2. The construction of intermediate-asymptotic solutions using dimensional analysis. Self-similar solutions --
3. Self-similarities of the second kind: first examples --
4. Self-similarities of the second kind: further examples --
5. Classification of similarity rules and self-similarity solutions. A recipe for the application of similarity analysis --
6. Scaling and transformation groups. Renormalization group --
7. Self-similar solutions and travelling waves --
8. Invariant solutions: asymptotic conservation laws, spectrum of eigenvalues, and stability --
9. Scaling in the deformation and fracture of solids --
10. Scaling in turbulence --
11. Scaling in geophysical fluid dynamics --
12. Scaling: miscellaneous special problems.

Publisher Description (unedited publisher data) Counter Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling