Three-dimensional instability of strained vortices in a stably stratified fluid

Miyazaki, Takeshi; Fukumoto, Yasuhide

doi:10.1063/1.858438

Cited by 58 publications

(91 citation statements)

References 13 publications

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“…Irregular zigzags are then also observed to grow. The threshold for the inhibition of the elliptic instability F h0 =0.2 ± 0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for F h0 < 0.13 is probably due to viscous effects since the associated Reynolds number is low, Re 0 < 260.…”

supporting

confidence: 71%

“…As seen in figure 9, the experimental critical Froude number values are close to this theoretical threshold (indicated by a solid line) despite the fact that it is based on a crude extrapolation of the Miyazaki & Fukumoto (1992) criterion.…”

Section: 2mentioning

confidence: 75%

“…This indicates that the inhibition of the elliptic instability is controlled by buoyancy effects and not by viscous effects. This value can be accounted for from the study of Miyazaki & Fukumoto (1992). They have shown theoretically that the elliptic instability is suppressed by the stratification when…”

Section: 2mentioning

confidence: 99%

“…(4.2) In the limiting case of weak strain ǫ/γ → 0, Miyazaki & Fukumoto (1992) have provided a clear understanding for this threshold based on the physical mechanism of the elliptic instability in homogeneous fluid (Waleffe 1990). The essence of the elliptic instability is a resonant interaction between the strain and inertial waves.…”

Section: 2mentioning

confidence: 99%

“…Stratification effects on the elliptic instability are described in § 4.1. In § 4.2, the threshold at which the elliptic instability is suppressed is compared to the theoretical study of Miyazaki & Fukumoto (1992). In § 4.3, the zigzag instability is characterized by means of flow visualizations.…”

Section: Introductionmentioning

confidence: 99%

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Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid

2000

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This paper shows that a long vertical columnar vortex pair created by a double flap apparatus in a strongly stratified fluid is subjected to an instability distinct from the Crow and short-wavelength instabilities known to occur in homogeneous fluid. This new instability, which we name zigzag instability, is antisymmetric with respect to the plane separating the vortices. It is characterized by a vertically modulated twisting and bending of the whole vortex pair with almost no change of the dipole's crosssectional structure. No saturation is observed and, ultimately, the vortex pair is sliced into thin horizontal layers of independent pancake dipoles. For the largest BruntVäisälä frequency N =1.75 rad s −1 that may be achieved in the experiments, the zigzag instability is observed only in the range of Froude numbers: 0.13 0.21, the elliptic instability develops resulting in three-dimensional motions which eventually collapse into a relaminarized vortex pair. Irregular zigzags are then also observed to grow. The threshold for the inhibition of the elliptic instability F h0 =0.2 ± 0.01 is independent of N and in good agreement with the theoretical study of Miyazaki & Fukumoto (1992). Complete stabilization for F h0 < 0.13 is probably due to viscous effects since the associated Reynolds number is low, Re 0 < 260. In geophysical flows characterized by low Froude numbers and large Reynolds numbers, we conjecture that this viscous stabilization will occur at much lower Froude number.It is tentatively argued that this new type of instability may explain the layering widely observed in stratified turbulent flows. IntroductionFluid motions in the atmosphere and oceans are often strongly affected by stable density stratification. In these flows, large vertical motions are inhibited by the buoyancy force, leaving only two possible modes of motion: internal gravity waves and vortices with vertical axis (Riley, Metcalfe & Weissman 1981). Laboratory experiments (Lin & Pao 1979;Hopfinger 1987;Chomaz et al. 1993;Fincham, Maxworthy & Spedding 1996;Spedding, Browand & Fincham 1996;Spedding 1997;Bonnier, Eiff & Bonneton 2000), numerical simulations (Riley et al. 1981;Kimura & Herring 1996) and oceanic measurements (Gregg 1987) have revealed that these vortices never have a large vertical extent, but are † Present address:

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supporting

confidence: 71%

Section: 2mentioning

confidence: 75%

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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