In this paper we investigate the relationship between the stretching tensor 2 and the logarithmic (Hencky) strain Any, with V the left stretch tensor. We establish the simple formula (AnV)-sym (j3l), which holds for arbitrary three-dimensional motions. Here F is the deformation gradient, (1n)) 0 is the time derivative of Any measured in a coordinate system which rotates with the left principal strain axes, and Nr is the spin of the right principal strain axes. we use this formula to show that 2-(tnV), (or, equivalently, p-(Int)* , the Jaumann derivative of ln,V) , if and only if the characteristic spaces of the right stretch tensor are constant on any time interval in which the number of distinct principal stretches is constant. Finally, we show that the asymptotic approximation j-(.)* + O(e 3 holds whenever the displacement gradient ! satisfies ow.
The AEPI (Atmospheric Emissions Photometric Imager) experiment on the ATLAS‐1 shuttle mission (launched March 24, 1992) imaged the earth night airglow emission in the O2 Atmospheric (0,0) bands, at 762.0 nm. Earthward views of O2 A bands show structure from gravity waves which exhibit extended horizontal structure with horizontal wavelengths on the order of 50–100 km. These observations of the O2 A (0,0) bands are particularly interesting since in this wavelength the lower atmosphere absorbs all the earth‐reflected emissions and most of the spectrally diffuse backgrounds. Herein we present observations of gravity waves using a topside airglow imaging technique.
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