A theory is presented which explains the universal nature of one‐dimensional vertical wave number, k, power spectral densities (PSDs) of horizontal winds as measured in the atmosphere and predicted by VanZandt. The theory is that the PSD amplitude at any given wave number (greater than a certain minimum, k*) is determined by its saturation value due either to shear instability (i.e., critical Richardson Number) or, more likely, to convective instability. This explains why the PSD amplitudes observed do not grow exponentially with increasing altitude. This saturation theory assumption plus other considerations leads to a PSD of the form N2/kn, where n is in the range of about 2.5 to 3 and N is the Brunt frequency. A simplified model involving superimposed narrow bands of gravity waves as well as a model based merely on dimensional arguments both lead to n = 3. The full model not only explains the observed spectral slopes but also predicts the PSD amplitude in the troposphere to be 3.5 times smaller than in the stratosphere. The derivation of the model is based on the saturation condition that ∫ k2PSD(k) dk = N2. The model may also apply to the ocean and explain the Garrett‐Munk vertical wave number spectrum.

Mersey, England, taken from the air. The front of the bore (which is moving upward in the figure and opposite the direction of normal river flow) is followed by a series of waves. There is a striking resemblance to the airglow images in Figure 1. This suggests the spectacular event was caused by an internal undular bore in the mesosphere. 6295

Wescott, E. M.; Picard, R. H.; Winick, J. R.; Stenbaek-Nielsen, H. C.; Dewan, E. M.; Moudry, D. R.; São Sabbas, F. T.; Heavner, M. J.; and Morrill, J., "Simultaneous observations of mesospheric gravity waves and sprites generated by a midwestern thunderstorm" (2003 AbstractThe present report investigates using simultaneous observations of coincident gravity waves and sprites to establish an upper limit on sprite-associated thermal energy deposition in the mesosphere. The University of Alaska operated a variety of optical imagers and photometers at two ground sites in support of the NASA Sprites99 balloon campaign. One site was atop a US Forest Service lookout tower on Bear Mt. in the Black Hills, in western South Dakota. On the night of 18 August 1999 we obtained from this site simultaneous images of sprites and OH airglow modulated by gravity waves emanating from a very active sprite producing thunderstorm over Nebraska, to the Southeast of Bear Mt. Using 25 s exposures with a bare CCD camera equipped with a red ÿlter, we were able to coincidentally record both short duration (¡10 ms) but bright (¿3 MR) N2 1PG red emissions from sprites and much weaker (∼1 kR), but persistent, OH Meinel nightglow emissions. A time lapse movie created from images revealed short period, complete 360• concentric wave structures emanating radially outward from a central excitation region directly above the storm. During the initial stages of the storm outwardly expanding waves possessed a period of ≈10 min and wavelength ≈50 km. Over a 1 h interval the waves gradually changed to longer period ≈11 min and shorter wavelength ≈40 km. Over the full 2 h observation time, about two dozen bright sprites generated by the underlying thunderstorm were recorded near the center of the outwardly radiating gravity wave pattern. No distinctive OH brightness signatures uniquely associated with the sprites were detected at the level of 2% of the ambient background brightness, establishing an associated upper limit of approximately T . 0:5 K for a neutral temperature perturbation over the volume of the sprites. The corresponding total thermal energy deposited by the sprite is bounded by these measurements to be less than ∼1 GJ. This value is well above the total energy deposited into the medium by the sprite, estimated by several independent methods to be on the order of ∼1-10 MJ.

Data from the Midcourse Space Experiment Tilere is evidence (R. H. Picard, J,'unes H. Brown (MSX) has provided the first observations of thunderstorm-personal communications, 1997) that gravity wave generated gravity waves imaged from space. Gravity wave structures are present in a number of MSX MWIR images. theory predicts that isolated, sufficiently convective This evidence is based on morphology, length scales, thunderstorms can launch waves mid create a unique power specUa and MWIR mdimive properties. The present intensity pattern of concentric circles on a radiating sinface paper shows that in particular cases the sources of these of constant altitude above such a storm. banong the MSX waves can be established as thunderstorms. This source constant-nadir-angle mid-wave hlfmred (MWIR) identification was prompted by the work of Taylor anti observations, two instances of such patterns have been Hapgood [1988] who showed that a pattern of concentric identified. It was conf'mned frown •neteorological satellite circles in ground-based observations of nightglow images that highly convective isolated thunderstorms emissions in the mesopause region was caused by va• occurred at the locations and ti•nes expected. isolated thunderstorm that occurred six hours prior to the nightglow observation.

Pollution effects on ozone raise the question of the significance of turbulence in vertical transport in the stratosphere. The aircraft in situ measurements of velocity fluctuations previously employed to estimate turbulence transport were, it is hypothesized, due to atmospheric waves, despite their classical turbulence spectrum. This new hypothesis implies that previous turbulence estimates are invalid. Experimental tests are suggested.