next up previous
Next: Solution of the diffusion Up: Examples Previous: Gravity waves on water

Energy in a nuclear explosion

We next turn to a famous example worked out by the eminent British fluid dynamicist G. I. Taylor.gif1 In a nuclear explosion there is an essentially instantaneous release of energy E in a small region of space. This produces a spherical shock wave, with the pressure inside the shock wave thousands of times greater that the initial air pressure, which may be neglected. How does the radius R of this shock wave grow with time t? The relevant governing variables are E, t, and the initial air density tex2html_wrap_inline1226 , with dimensions tex2html_wrap_inline1228 , [t]=T, and tex2html_wrap_inline1232 . This set of variables has independent dimensions, so n=3, k=3. We next determine the exponents:


so that


with the solution a=1/5, b=-1/5, c=2/5. Therefore


with C an undetermined constant. If we plot the radius R of the shock as a function of time t on a log-log plot, the slope of the line should be 2/5. The intercept of the graph would provide information about the energy E released in the explosion, if the constant C could be determined. By solving a model shock-wave problem Taylor estimated C to be about 1; he was able to take de-classified movies of nuclear tests, and using his model, infer the yield of the bombs [6]. This data, of course, was strictly classified; it came as a surprise to the American intelligence community that this data was essentially publicly available to those well versed in dimensional analysis.


gif1 Taylor's name is associated with many phenomena in fluid mechanics: the Rayleigh-Taylor instability, Saffman-Taylor fingering, Taylor cells, Taylor columns, etc.

V. Celli
Thu Jul 10 16:27:59 EDT 1997