a Search for Strange Attractors in the Saturation of Middle Atmosphere Gravity Waves

In this study, we searched for evidence of a strange attractor associated with the saturation of middle atmosphere gravity waves in the echo data from a partial reflection radar located in Saskatoon, Canada. Theiler's extension of the Grassberger-Procaccia correlation integral algorithm was used to estimate the fractal dimension of the attractor. Chaotic regimes have been observed in experimental fluid studies of the transition from ordered to turbulent behavior. Breaking gravity waves are thought to decay to turbulence, transporting momentum from the lower to upper atmosphere. Extending the results from laboratory studies to middle atmosphere gravity waves, it seems reasonable to expect to find a strange attractor in gravity wave saturation. Echo data was analyzed because it offered a high sampling rate. The Grassberger-Procaccia algorithm places stringent requirements upon the amount of data necessary to obtain an accurate estimate of the system dimension; a large number of points is required. We did not detect a strange attractor with dimension <3 in the data from the Saskatoon partial reflection radar for the time scales (6 min 39 s) which were studied. Because of the small number of points which were examined, we can not assert that there was only noise in the data. However, the supporting evidence from the power spectra suggest that we mainly investigated time scales in the viscous and inertial regions. This study can not assert that a strange attractor is absent in gravity wave absorption. The data requirements to implement the Grassberger-Procaccia algorithm make it unlikely that such an attractor, if it exists, will be detected. Calculations of the amount of data necessary to estimate the dimension indicate that over 6 hours of data would be required to detect a strange attractor in gravity wave absorption.