The energy cascade process in turbulent flows is studied. Kolmogorov inertial range theories are critically reviewed and the multifractal characterization is discussed. Multiplicative cascade models are compared to the energy dissipation field (EDF) measured in the atmosphere. Landau's objection to the 1941 Kolmogorov theory is extended to the predictions of statistical fluid mechanics. The hypothesis $ rm Delta v( lambda L) { buildrel{d} over=} lambda sp{1/3} Delta v(L)$ is rejected with a statistical test. The moments $ rm langle( log varepsilon(L)) sp{p} rangle,$ where $ varepsilon$(L) denotes the EDF averaged over a volume of size L, are shown to be gaussian. For the EDF: Convergence tests showed that the exponents $ tau$(q) were not reliable for q $<$ 0; the correlations obey $ rm langle( mu sb{x}( delta)) sp{p}( mu sb{x+ delta}( delta)) sp{q} rangle propto delta sp{ gamma(p,q)}$ but $ gamma$ does not always equal the value obtained with a multinomial measure; a privileged scale ration r $ approx$ 1/2 is suggested by the prefactor oscillations of the correlation function. The implications of these results for the modelling of the EDF are discussed.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.74674 |
| Date | January 1991 |
| Creators | Saucier, Antoine |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001238483, proquestno: AAINN67833, Theses scanned by UMI/ProQuest. |
Page generated in 0.0018 seconds