Recent advances in aero-optics

Further consideration of compressibility effects on shear layer optical distortion

An index-of-refraction model has been shown to produce a reasonable estimate of the aerooptical aberrations measured in a weakly compressible shear layer. This numerical model is a valuable tool both for its insight into the cause of the aberrations and as a source of the parametric data needed to explore and evaluate scaling laws. Scaling relations are developed that describe how the expected aerooptical distortion due to propagation through a free shear layer changes with altitude, that is, static pressure, and/or static temperature. Scaling laws for two cases are developed. In the e rst case, the Mach numbers of the shear layer’ s constituent e ows are held constant. For the second case, the shear layer’ s constituent e ow velocities are instead held constant. The parametric data are also used to evaluate a scaling law suggested by the literature.

Scaling Aerooptic Aberrations Produced by High-Subsonic-Mach Shear Layers

Several examples are described where the invariants of the velocity gradient tensor are used to describe the structure of a fluid flow. This approach provides a rational basis for understanding various dynamical processes which can occur in the flow. Two types of motions responsible for most of the Reynolds stress generation in turbulent wall flows are identified.

Discriminant-based analysis of the dynamics of turbulent flow

This paper is concerned with the geometry of flow patterns inthe classical problem of an impulsely-started, incompressible,axisymmetric, laminar jet generated by a point force. The second andthird invariants of the velocity gradient tensor, evaluated at criticalpoints in the jet, describe the fundamental dependence of the flow onthe jet Reynolds number. As the Reynolds number is increased from zeroto infinity, the critical points follow elliptic curves in the space ofinvariants and rational roots occur at bifurcation points in this space.The corresponding invariants of the acceleration gradient tensor traceout a trajectory with infinitely many, densely spaced rational roots.The results provide new insight into the viscous and pressure forceswhich act in the jet and the balance between strain and rotation whichleads to the onset of a starting vortex.

Elliptic Curves and Three-Dimensional Flow Patterns

Study of turbulence structure using the invariants of the velocity gradient tensor

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Study of turbulence structure using the invariants of the velocity gradient tensor