A Comparison of Length Scales and Decay Times of Turbulence in Stably Stratified Flows

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  • 1 Institute of Ocean Sciences, Sidney, B.C, Canada V8L 4B2
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Abstract

An examination of average values of a buoyancy length scale, LR = (ε/N3)½, and a Thorpe scale, LT, computed from vertical profiles of oceanic turbulence at 150°W in the tropical Pacific Ocean, shows reasonable agreement with the relation LR = 0.8LT found by Dillon. The present study uses direct measurements of velocity micro-structure to compute LR. It is also shown that if LR = 0.8LT, and the Brunt-Väisälä period 2π/N is constant, the decay-time constant of kinetic energy of turbulence in a stably stratified fluid is one-third to one-half of the Brunt-Väisälä period. Further investigation, using an exact formula for the energy, reveals that the assumption of constant N leads to an overestimate of the energy by a factor of 3. Correction for this factor reduces the decay time to between one-sixth and one-tenth of the Brunt-Väisälä period.

These results are compared with previous observations. Only one previous study investigates the covariation of N and ε within a patch of turbulence, finding a decay time of about one-tenth of 2π/N. Other studies, such as vertical profiles in decaying grid turbulence in a water tunnel and horizontal profiles in the ocean and the atmospheric stratosphere, assume N to be constant. Decay times in these studies are between 0.2 and 0.6 of 2π/N and are most likely high by a factor of 3 owing to the assumption of constant N. Therefore, these experiments show the decay time to be a small fraction of the Brunt-Väisälä period, with no evidence of a dependence of this time upon features of the turbulence or the large-scale flow.

Abstract

An examination of average values of a buoyancy length scale, LR = (ε/N3)½, and a Thorpe scale, LT, computed from vertical profiles of oceanic turbulence at 150°W in the tropical Pacific Ocean, shows reasonable agreement with the relation LR = 0.8LT found by Dillon. The present study uses direct measurements of velocity micro-structure to compute LR. It is also shown that if LR = 0.8LT, and the Brunt-Väisälä period 2π/N is constant, the decay-time constant of kinetic energy of turbulence in a stably stratified fluid is one-third to one-half of the Brunt-Väisälä period. Further investigation, using an exact formula for the energy, reveals that the assumption of constant N leads to an overestimate of the energy by a factor of 3. Correction for this factor reduces the decay time to between one-sixth and one-tenth of the Brunt-Väisälä period.

These results are compared with previous observations. Only one previous study investigates the covariation of N and ε within a patch of turbulence, finding a decay time of about one-tenth of 2π/N. Other studies, such as vertical profiles in decaying grid turbulence in a water tunnel and horizontal profiles in the ocean and the atmospheric stratosphere, assume N to be constant. Decay times in these studies are between 0.2 and 0.6 of 2π/N and are most likely high by a factor of 3 owing to the assumption of constant N. Therefore, these experiments show the decay time to be a small fraction of the Brunt-Väisälä period, with no evidence of a dependence of this time upon features of the turbulence or the large-scale flow.

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