We revisited an empirical relationship between the integrated volume depolar- ization ratio, oacc, and the effective multiple scattering factor, -n, on the basis of Monte Carlo simulations of spaceborne lidar backscatter associated with homogeneous wa- ter clouds. The relationship is found to be sensitive to the extinction coefficient and to the particle size. The layer integrated attenuated backscatter is also obtained. Comparisons made between the simulations and statistics derived relationships of the layer integrated depolarization ratio, oacc, and the layer integrated attenuated backscatter, -n, based on the measurement by the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite show that a cloud with a large effective size or a large extinction coefficient has a relatively large integrated backscatter and a cloud with a small effective size or a large extinction coefficient has a large integrated volume depolarization ratio. The present results also show that optically thin water clouds may not obey the empirical relationship derived by Y. X. Hu. and co-authors.

A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associated with the terms of the asymptotic expansions is a well-behaved in??nite system of di??erential equations. An application of those asymptotic expansions of regular solutions is the analysis of the helicity for large times. The dichotomy of the helicity's asymptotic behavior is then established. Furthermore, the relations between the helicity and the energy in several cases are described.

Thèse de doctorat : Mathématiques appliquées : Metz : 2001. / Thèse : 2001METZ026S. Bibliogr. en fin de chaque chapitre.

Reproduction de : Thèse de doctorat : Dynamique des fluides : Toulouse, INPT : 2006. / Titre provenant de l'écran-titre. Bibliogr. 65 réf.

Reproduction de : Thèse doctorat : Mathématiques appliquées : Pau : 2008. / Titre provenant de l'écran titre. Bibliographie.

Kassel, Universiẗat, Diss., 2008.

Zugl.: München, Techn. Univ., Diss., 2009

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 73-77).

Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 2003. / Thesis advisor(s): Kevin D. Jones, Max F. Platzer. Includes bibliographical references (p. 55-56). Also available online.

Thesis--University of Kentucky (M.S.), 2003. / Title from document title page. Document formatted into pages; contains ix, 110 p. : ill. Includes abstract and vita. Includes bibliographical references (p. 99-109).