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m/s, ΔNt from the start of the model to its arrival at the probe was reduced to 0.05. For U=0.90 m/s, there was no noticeable upstream effect. Apparently, the nonlinear waves generated by the model are traveling at speeds larger than 0.46 m/s but not much larger than about 0.90 m/s. Figure 17 shows a comparison of the impulsively and non-impulsively started runs. It must be emphasized that experiments with impulsive starts have been repeated a number of times at different initial accelerations with different mechanisms and with or without a small uniform current in order to ascertain that the observed upstream effect was not due to some anomalous phenomenon. The addition of sail planes did not materially affect the results. The individual probe data differed very little from the ensemble averaged data and the upstream effect decreased at higher speeds. These are clear indications of the fact that the observed upstream effect is a genuine hydrodynamic phenomenon, at least, in model tests. As noted earlier, however, its prototypical significance remains unclear and should be the subject of a number of judiciously conducted large scale experiments.

Fig. 17 Comparison of the upstream effects of impulsively (o) and non-impulsively (x) started models (N=0.15 rad/s, U=0.46 m/s)


Variations of the relative conductivity in the wake of self-propelled, single-screw, submarine-shaped bodies in a linearly stratified fluid were measured. The model Froude number ranged from about 50 to 200 and the Reynolds number, from about 3×104 to 6×104.

The results have shown that the wake collapse (at a distance of about 400 diameters downstream) gives rise to large conductivity changes and to many modes of short internal waves [15]. The relative conductivity is sufficiently large to cause measurable changes in the geomagnetic field. The conductivity field ahead of the body anticipates the arrival of the body for relatively short distances and then only for impulsively-started or impulsively-stopped motions at relatively moderate speeds.

As in the case of many other studies in stratified fluids, the range of the governing parameters is dictated not by technological needs but by what is achievable under the laboratory conditions. Even though the Froude numbers encountered in this investigation are the largest we have ever seen, and certainly closest to the prototypical conditions, the scale effects (due to widely different model and prototype Reynolds numbers) cannot be assessed and must be evaluated through prototype tests. As noted earlier, trip wires were used to render the boundary layer turbulent and, furthermore, the size of the propeller was scaled with respect to the size of the wake, and not the size of the body, by scaling wake diameter on the basis of Reynolds number. The validity of such common practices in laboratory experiments needs to be assessed through sea tests, particularly when the Reynolds numbers of the model and prototype differ by several orders of magnitude.


Support for this investigation was provided by Naval Research Program Office. The authors would like to thank Mr. Thomas H.McCord and Mr. Charles E.Crow for their assistance with the construction and smooth operation of the test facilities.


1. Schetz, J.A., and Jakubowski, A.K., “Experimental Studies of the Turbulent Wake behind Self-Propelled Slender Bodies,” American Institute of Aeronautics and Astronautics Journal, Vol. 13, 1975, pp. 1568–1575.

2. Schlichting, H., Boundary-Layer Theory, 7th ed., McGraw-Hill, New York, 1987, pp. 729–755.

3. Stockhausen, P.J., Clark, C.B., and Kennedy, J.F., “Three-Dimensional Momentumless Wakes in Density Stratified Fluids, ” Massachusetts Institute of Technology Hydrodynamics Laboratory Report Number 93, 1966, Massachusetts Institute of Technology, Cambridge, Mass.

4. Torobin, L.B., and Gauvin, W.H., “Fundamental Aspects of Solids-Gas Flow. Part 1: Introductory Concepts and Idealized Sphere Motion in

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