Cancellation of vorticity in steady-state non-isentropic flows of complex fluids

In steady-state non-isentropic flows of perfect fluids there is always thermodynamic generation of vorticity when the difference between the product of the temperature with the gradient of the entropy and the gradient of total enthalpy is different from zero. We note that this property does not hold in general for complex fluids for which the prominent influence of the material substructure on the gross motion may cancel the thermodynamic vorticity. We indicate the explicit condition for this cancellation (topological transition from vortex sheet to shear flow) for general complex fluids described by coarse-grained order parameters and extended forms of Ginzburg-Landau energies. As a prominent sample case we treat first Korteweg's fluid, used commonly as a model of capillary motion or phase transitions characterized by diffused interfaces. Then we discuss general complex fluids. We show also that, when the entropy and the total enthalpy are constant throughout the flow, vorticity may be generated by the inhomogeneous character of the distribution of material substructures, and indicate the explicit condition for such a generation. We discuss also some aspects of unsteady motion and show that in two-dimensional flows of incompressible perfect complex fluids the vorticity is in general not conserved, due to a mechanism of transfer of energy between different levels.Comment: 12 page

Balint Vaszonyi Collection

Balint Vazsonyi (March 7, 1936-January 2003) was a Hungarian-American pianist, perhaps best known for playing all thirty-two chronological cycles of Beethovens sonatas. Vazsonyi also was an author who wrote extensively on political science in the Washington Times and other media sources. The collection consists of concert programs, reviews, correspondence, newspaper and magazine articles, recordings, lectures, scrapbooks, brochures, manuscripts, books, and videos related to Vazsonyis performing and teaching careers, the ensembles he was involved in, events in his life, his political involvement, and his relationships with several people and organizations, especially his teacher, Ernst von Dohnanyi, and his management, Kazuko Hillyer International, Inc

Shock Layer Instability near the Newtonian Limit of Hypervelocity Flows

The curved bow shock in hypersonic flow over a blunt body generates a shear layer with smoothly distributed vorticity. The vorticity magnitude is approximately proportional to the density ratio across the shock, which may be very large in hypervelocity flow, making the shear layer unstable. A computational study of the instability reveals that two distinct nonlinear growth mechanisms occur in such flows: First, the vortical structures formed in the layer move supersonically with respect to the flow beneath them and form shock waves that reflect from the body and reinforce the structures. Second, the structures deform the bow shock, forming triple points from which shear layers issue that feed the main shear layer. Significant differences exist between plane and axisymmetric flow. Particularly rapid growth is observed for free-stream disturbances with the wavelength approximately equal to the nose radius. The computational study indicates that the critical normal shock density ratio for which disturbances grow to large amplitudes within a few nose radii is approximately 14. This served as a guide to the design of a physical experiment in which a spherical projectile moves at high speed through propane or carbon dioxide gas. The experiment confirms the approximate value of the critical density ratio, as well as the features of the computed flows. Comparisons of calculations of perfect gas flows over a sphere with shadowgraphs of the projectile show very good agreement. The Newtonian theory of hypersonic flow, which applies at high density ratio, makes the assumption that the flow remains smooth. The results show that high density ratio also causes this assumption to fail