Dynamics of
Atmospheres and Oceans **23** (1996) pp. 183-192

### Some similarity states of stably-stratified homogeneous turbulence

- J. R.
Chasnov
*The Hong Kong University of Science and Technology, Hong
Kong*

The decay of statistically homogeneous velocity and density fluctuations in a
stably-stratified fluid is considered. Over decay times long compared to the
turbulence timescale but short compared to the period of internal gravity waves,
three distinct high Reynolds number similarity states may
develop. These similarity states are a consequence of the invariance of the
low wavenumber coefficients of the three-dimensional kinetic or potential energy
spectrum; and their preferential development depends on the relative magnitudes
of the initial kinetic and potential energy per unit mass of the fluid. When the
turbulence has decayed over a time comparable to the period of the gravity
waves, the three similarity states mentioned above are disrupted. Evidence will be
presented of a new similarity state which then develops asymptotically. In this similarity
state, the time decay exponent of the total energy per unit mass of the turbulence is reduced
by a factor of two from its value for decaying isotropic turbulence, and the associated vertical
integral scale approaches a constant independent of time.

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