Michael D. Greenberg

Line momentum source in shallow inviscid fluid

An array of closely spaced, aligned, turbulent, incompressible jets is effectively simulated by a line momentum source. In a shallow inviscid fluid, such a source induces a predominantly two-dimensional non-diffusive flow which is irrotational except along lines of velocity discontinuity downstream of the source. The flow can be generated by a distribution of line vortices of unknown strength along the unknown slipstreamlines. Based upon this vortex model, kinematic and dynamic conditions along the slipstreamlines are formulated, and the two resulting nonlinear singular integral equations are solved numerically using a Newton-Raphson-type iterative collocation method. The flow field shows a marked resemblance to that induced by a nonlinear actuator disk. For the case of no ambient current, experimental results indicate that the slipstreamlines emanate from points which are close to, but not at the ends of, the source. As the ambient current strength increases, a dividing streamline appears in the induced sink flow upstream of the source, and the points from which the slipstreamlines emanate move closer to the ends of the source. Further increases in the current strength result in the smooth blending of this dividing streamline with the slipstreamline. Laboratory experiments performed in a shallow water basin confirm all of the features predicted by the theory.

On the formulation of the zero creep method for small diameter wires

Abstract A mechanically consistent variational derivation of the zero creep relationship between surface energy and critical load is put forward for polycrystalline wires of small diameter. This entails the inclusion of necking, and it is found that for grain length/diameter ratios greater than unity there exist two possible equilibrium configurations, one moderately necked and one heavily necked. All equilibrium configurations are shown to be stable in the sense that the second variation of the energy is positive. It is found that the correct equilibrium expression for critical load differs from the formula currently in use by an amount which is negligible for grain length/diameter ratios below 0.5, but which increases with increasing length/diameter ratios.

The time-dependent free surface flow induced by a submerged line source or sink

The unsteady nonlinear potential flow induced by a submerged line source or sink is studied by a vortex sheet method, both to trace the free surface evolution and to explore the possible existence of steady-state solutions. Only steady-state flows have been considered by other investigators, and these flows have been insensitive to whether they are generated by a source or sink, except with respect to the flow direction along the streamlines. The time-dependent solution permits an assessment of the stability of previously found steady solutions, and also reveals differences between source and sink flows: for the infinite-depth case, steady stagnation-point-type solutions are found for source flows, even above the critical value of source/sink strength reported by other investigators; for the finite-depth case, steady stagnation-point-type solutions are found both for source flows and sink flows, above the critical value reported by other investigators; finally, it is shown that streamline patterns of steady stagnation-point flows are identical for source and sink flows only in the limiting case of infinite depth

Dynamic Stability of Wave-Convection Transport

A flexible inextensible horizontal belt is assumed to be formed, by closely spaced vertical push rods, into a traveling sine wave. A spherical object resting at the bottom of a trough will tend to be convected with the trough as the wave travels. The dynamic stability of such wave-convection transport is considered. Assuming the wave to be shallow, the governing nonlinear equations are expanded (through second order) in the ‘shallowness parameter’, and thus reduced to a single equation, essentially of forced Duffing type, which is integrated numerically, over the parameter space of practical interest, to yield a stability criterion.

Approximate Evaluation of Certain Functions Arising in Unsteady Airfoil Theory

appears in the kernel of an integral equation shown by Lawrence and Gerber [1] to govern the aerodynamics of low-aspect-ratio airfoils in unsteady motion. The Cicala function [2], F(p) = M*(oo, 3)/3, plays a similar role in Reissners unsteady lifting line theory [3]. Although M*(a, () has been partially tabulated [1], a simple approximate expression valid over the entire domain of interest (0 ? a oo. On the other hand, the bracketed portion of the integrand in (1) is a well-behaved function of the single parameter t x/l. We therefore seek an approximation of