Experiments on the radial propagation of axisymmetric free-surface solitary waves are reported and compared with theoretical and numerical solutions of the cylinderical Korteweg–de Vries (CKdV) equation. A new experimental technique to obtain a continuous amplitude signature on photographic paper is reported. These measurements show that an isolated disturbance evolves into a slowly varying solitary wave with amplitude decaying as $r^{-\frac{2}{3}}$, where r is the radius measured from the centre of the disturbance. A numerical study of the CKdV equation is made to interpret the transient development of these waves into the nonlinear asymptotic regime. It is further pointed out that the CKdV equation also describes weakly nonlinear axisymmetric internal waves, and a comparison of theory for this case with internal-wave trajectory measurements reported by Maxworthy (1980) exhibit good agreement.
An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag versus Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendriteStokes settling velocities are always less than that of a sphere of equal mass and voIume.In the Stokes limit, the settling speed ratio is found to correlate well with the primary dendrite arm aspect ratio and a second dimensionless shape parameter which serves as a measure of the fractal-like nature of the dendrite models.These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings.The drag measurements may be used in numerical codes to calculate the movement of grains in a eonvecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.
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