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The two-dimensional mode of the variable-density Kelvin-Helmholtz billow

Joly, Laurent and Fontane, Jérôme and Reinaud, Jean The two-dimensional mode of the variable-density Kelvin-Helmholtz billow. (2007) In: 60th Annual Meeting of the Divison of Fluid Dynamics, 18 November 2007 - 20 November 2007 (Salt Lake City, United States).

(Document in English)

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We perform a three-dimensional stability analysis of the Kelvin-Helmholtz billow, formed upon a shear-layer between two fluids with a density ratio of 3. We begin with two- dimensional simulations of the temporally evolving mixing- layer yielding the unsteady base flow fields. The Reynolds number is 3000 while the Schmidt and Froude numbers are infinite. Then exponentially unstable modes are extracted from a linear stability analysis validated against previous results in the homogeneous case. Among the least stable modes, we retain those growing faster than the primary wave thus ensuring the validity of the quasi-steady approach. The spectrum of rapidly growing modes is analyzed and shown to exhibit a typical two-dimensional mode, in addition to core-centered and braid-centered ones. These modes are developing on the braid lying on the light side. There the flow evolves toward a sharp vorticity ridge due to a baroclinic vorticity source concentrated on a steep density-gradient. For the present density contrast, the wave-length of the two-dimensional instability is ten times shorter than the one of the primary wave. Its amplification rate competes well against the one of the braid-centered least-stable three-dimensional mode. The numerical continuation of the non-linear development of this particular mode is carried out from two starting points along the roll-up of the primary wave. We describe secondary small-scale roll-ups due to a Kelvin-Helmholtz mechanism favored by the strain field. This mode is demonstrated consistent with finite Reynolds number mixing-layers. We are also able to discuss its precedence against transverse modes thus contributing to the complex picture of the transition of the variable-density shear-layer.

Item Type:Conference or Workshop Item (Other)
Audience (conference):International conference without published proceedings
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > University of St Andrews (UNITED KINGDOM)
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Deposited On:28 Nov 2008 12:59

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