ScalingThe author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists. |
Contents
Introduction | 1 |
Dimensional analysis and physical similarity | 12 |
Selfsimilarity and intermediate asymptotics | 52 |
intermediateasymptotic solution | 65 |
Complete and incomplete similarity Selfsimilar | 82 |
Scaling and transformation groups | 94 |
Selfsimilar phenomena and travelling waves | 109 |
Scaling laws and fractals | 123 |
Scaling laws for turbulent wallbounded shear | 137 |
| 164 | |
| 171 | |
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Common terms and phrases
arguments assumed Barenblatt basic bisectrix boundary conditions boundary layer Chapter Chorin and Prostokishin concentrated flooding conservation law considered const constant corresponding density depend determined dimension function dimensional analysis dimensional parameters dimensionless parameters drag example experimental data Figure fluid formulation fractal curves fractal dimension function f fundamental units G.I. Taylor governing parameters groundwater idealized problem incomplete similarity independent dimensions initial condition intermediate asymptotics K´arm´an large Reynolds numbers length scale LMT class mass mathematical motion neglected obtained ordinary differential equation original system parameters l+1 parameters with independent phenomena phenomenon pipe Prandtl properties prototype relation renormalization group scaling law 8.26 segment length self-similar solutions self-similar variables separatrices shock wave similarity parameters stratum system of units transformation group travelling waves turbulent unit of length universal logarithmic law velocity distribution viscosity Zeldovich