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drops in temperature as it expands. If the temperature in the surrounding air at the new height is higher than the lifted par- cel’s temperature, then the parcel, denser than its surround- ings, will sink back down. This is the condition for vertical sta- bility. Instability for vertical displacement creates some of the most interesting and violent weather; however, most regions of the atmosphere are stable most of the time (at least for dis- placement of dry air). When there is vertical stability, there is a natural frequency for buoyant oscillation. This frequency—the Brunt-Väisälä frequency—depends on the vertical temperature gradient; however, the corresponding oscillation period is fre- quently in the range from 5 to 10 minutes. Since the dominant frequencies at long range for the pressure pulse from Krakatoa are well below the Brunt-Väisälä frequency, buoyancy would have played a significant role with respect to vertical particle displacements.
In addition to records of the pressure wave, the Krakatoa Committee compiled reports of audible sound from the explo- sion (Fig. 5). Only reports from at least 30 km distant are includ- ed in the tabulation: 84 reports from land observers and 15 reports from ships’ logs. There were 53 reports from greater than 1500 km and 16 reports from greater than 3000 km. The farthest credible report4 came from Rodrigues Island in the Indian Ocean (600 km east of Mauritius), a distance of more than 4800 km. In most cases, observers reported sounds like those of artillery or cannon fire. While many locations reported hearing sounds intermittently for hours, “...it is very remarkable that at many places in the more immediate neighborhood of the volcano they ceased to be heard soon after [the main eruption] ...although it is known that the explosions continued with great intensity for some time longer.” The Committee speculates that the ejected ash may have acted to block the sound at nearby locations; however, not enough is known of the local atmos- pheric conditions to rule out formation of acoustic shadows by refraction.
While the linear theory and the roots of nonlinear theory were published within a decade of the Krakatoa explosion, inter- est in the propagation of very-low-frequency waves in the atmosphere continues to the present. A more complete under- standing of the atmosphere and recognition that waves can propagate at least as high as the lower thermosphere (100 km altitude) have improved model calculations. The roles of absorp- tion and nonlinearity especially at high altitudes are areas of current research interest. Rayleigh (among others) set the stage for the importance of nonlinearity by pointing out that, if ener- gy is conserved in the wave front, then as the ambient density decreases, the wave particle velocity must increase (as the square-root of density). With a drop in density by a three orders of magnitude from the surface to 100 km, the acoustic Mach number will be significantly greater at extreme altitudes; conse- quently, nonlinearity will likely be of more importance than at low altitudes. Whatever the fate of theoretical investigations, global observation will be as important in the future as it was for understanding the Krakatoa explosion.AT
ENDNOTES
Note: The more common spelling—Krakatoa—is used in this article. When searching for further information, consider the alternate form: Krakatau.
1 See http://www.ndbc.noaa.gov/. Historical data is archived
for several years. For example, select Buoy 43412 and set the start and end dates to 27 February 2010 to see the tsunami passage on the water-column height plot. The buoys with the DART II (Deep-ocean Assessment and Reporting of Tsunamis) instrumentation payload record water-column height. Buoy 51406 also shows a clear signature.
2 I have assembled those contours into an animation of the wave front evolution. That animation is available in the side- bar of this article.
3 Variations in apparent speed from measurements at differ- ent stations were considerably higher than could be accounted for by measurement uncertainty. From the text of the Krakatoa Committee report, “The probable limits of error in the estimation of the times are, in almost all cases, well within thirty minutes...”
4 The Committee cites an account in Comptes Rendus (March, 1885, Vol. c, pg. 755) of sounds heard in the Cayman Islands, 1600 km from the antipodal point: “The evidence, however, is of so indefinite a nature that it has not been inserted in the tabular statement annexed.”
REFERENCES
Airy, G. B. (1845). “Tides and waves,” Encyclopaedia Metropolitana, London, 1845. See discussions in Lamb, Hydrodynamics, and Lighthill, Waves in Fluids. Beyond the linear equations, Airy’s work coupled with observations by Scott Russell of what would later be called solitons inspired development of nonlin- ear theories.
Lamb, H. (1911). “On atmospheric oscillations,” Proc. Royal Soc. A 84, No. 574 (Feb. 15, 1911), pp. 551–572.
LeConte, John (1884). “Atmospheric waves from Krakatoa,” Science 3 (71), 701–702.
Pekeris, C. L. (1939).“The propagation of a pulse in the atmos- phere,” Proc. Royal Soc. A 171 (947) 434–449.
Rayleigh (1890).“On the vibrations of an atmosphere,” Phil. Mag. 29, 173–180.
Scott, R. H. (1883) “Note on a series of barometrical disturbances which passed over Europe between the 27th and the 31st of August, 1883,” Proc. Royal Soc. 36, 139–143, 1883-1884.
Strachey, R. (1884).“Note on the foregoing paper,” Proc. Royal Soc. 36, 143–151, 1883-1884.
Symons, G. J. (ed.) (1888).“The eruption of Krakatoa and subse- quent phenomena,” Report of the Krakatoa Committee of the Royal Society (Trübner and Co., London), 1888. Only a small part of this large volume concerns the pressure wave and sounds from Krakatoa.
Taylor, G. I. (1929).“Waves and tides in the atmosphere,” Proc. Royal Soc. A 126 (800), 169–183.
18 Acoustics Today, April 2010