The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the 'formation number'. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the 'formation number' lies in the range of 3.6-4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin-Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin-Benjamin principle correctly predicts the range of observed formation numbers.

We outline a scenario which traces a direct path from freely-floating nebula particles to the first 10-100km-sized bodies in the terrestrial planet region, producing planetesimals which have properties matching those of primitive meteorite parent bodies. We call this primary accretion. The scenario draws on elements of previous work, and introduces a new critical threshold for planetesimal formation. We presume the nebula to be weakly turbulent, which leads to dense concentrations of aerodynamically size-sorted particles having properties like those observed in chondrites. The fractional volume of the nebula occupied by these dense zones or clumps obeys a probability distribution as a function of their density, and the densest concentrations have particle mass density 100 times that of the gas. However, even these densest clumps are prevented by gas pressure from undergoing gravitational instability in the traditional sense (on a dynamical timescale). While in this state of arrested development, they are susceptible to disruption by the ram pressure of the differentially orbiting nebula gas. However, self-gravity can preserve sufficiently large and dense clumps from ram pressure disruption, allowing their entrained particles to sediment gently but inexorably towards their centers, producing 10-100 km "sandpile" planetesimals. Localized radial pressure fluctuations in the nebula, and interactions between differentially moving dense clumps, will also play a role that must be allowed for in future studies. The scenario is readily extended from meteorite parent bodies to primary accretion throughout the solar system.

No abstract

No abstract

A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible flow. In this technique, it is assumed that the boundary layer grows so slowly in the streamwise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordinate transformation and a multiple-scale analysis. The result is a modified system of equations, in which the flow is homogeneous in both the streamwise and spanwise directions, and which represents the state of the boundary layer at a given streamwise location. The equations are solved using a mixed Fourier and B-spline Galerkin method.Results are presented for a case having an adiabatic wall, a Mach number of M = 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of Reθ′ = 849. The Reynolds number based on momentum integral thickness and free-stream viscosity is Reθ = 1577. The results indicate that the Van Driest transformed velocity satisfies the incompressible scalings and a small logarithmic region is obtained. Both turbulence intensities and the Reynolds shear stress compare well with the incompressible simulations of Spalart when scaled by mean density. Pressure fluctuations are higher than in incompressible flow. Morkovin's prediction that streamwise velocity and temperature fluctuations should be anti-correlated, which happens to be supported by compressible experiments, does not hold in the simulation. Instead, a relationship is found between the rates of turbulent heat and momentum transfer. The turbulent kinetic energy budget is computed and compared with the budgets from Spalart's incompressible simulations.