Abstract

In the past, a few investigators have examined theoretically and experimentally the optical properties of laminar compressible vortices. However, there is no theoretical study found in the scientific or technical literature for the turbulent kind. This thesis deals with the refracted shadows produced by turbulent compressible vortices. The construction of the theory is accomplished extending the previous laminar approach to include the effects of turbulence.
The pressure, temperature and density are calculated solving numerically the conservation of mass, momentum and energy equations along with the equation of state for the case of a turbulent vortex evolving in a compressible, viscous, heat conducting and calorically perfect gas in an unconfined domain. The radial distribution of light intensity is then deduced using the past general mathematical relation that links the density to luminosity of the shadowgraphs casted on an image plane by light ray refraction.
The differences in luminosity of laminar and turbulent vortices with Mach numbers ranging from 0.4 to 0.8 are compared. The darkness of the central disc and luminosity of the bright ring are found to be a function of the vortex Mach number: the higher the Mach number, the darker the disks and the brighter are the halos. Vortices of the turbulent kind are found to produce different shadow signatures than the laminar. Alike to the laminar case and depending on the focal length, turbulent vortices can also generate the previously disputed two caustics. The last effect is shown to generate the combination of dark circular area near the vortex center, followed by a thin halo that is succeeded by a dim ring, which is subsequently followed by a thicker corona.
In the future, the present methodology can potentially be developed to recover the thermo-fluid properties optically.