On the scaling of vertical temperature gradient spectra

Abstract

A physical interpretation is proposed for the temperature gradient wave number scaling of Caldwell et al. [1980]. It is shown that kc/kB = (5.5 AT)1/2, where AT is the turbulence activity parameter of Gibson [1980] used to classify fossil turbulence. AT = 1 corresponds to active turbulence in a stratified fluid where the largest eddies are slightly affected by buoyancy, and AT = 1.4 (Pr/C)1/2 corresponds to fossil turbulence in a fluid with nearly saturated internal waves but no active turbulence. The Caldwell et al. [1980] scaling, with kc/kB = 1, is equivalent to AT = 0.18. According to the Gibson [1980] fossil turbulence model, this indicates completely fossil temperature turbulence for Cox number C < 600 and a mixture of active and fossil turbulence for C > 600. The tendency for kc/kB to decrease with increasing C noted by Caldwell et al. [1980] may reflect both the wider range of possible AT values, 1 to 1.4(Pr/C)1/2, for partially fossilized temperature turbulence microstructure with large C, as well as the relatively long persistence times of such remnants of strong mixing events which makes it more likely that such large C microstructure will be encountered in an advanced stage of decay of its fossil phase. Because all the microstructure encountered was fossil to some degree, the turbulent mixing process has apparently been undersampled.