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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