Large eddy simulation of aircraft wake vortices within homogeneous turbulence: crow instability

Ambient atmospheric turbulence effects on aircraft wake vortices are studied using a validated large eddy simulation model. Our results confirm that the most amplified wavelength of the Crow instability and the lifetime of wake vortices are significantly influenced by ambient turbulence (Crow, S. C., 'Stability Theory for a Pair of Trailing Vortices,' AIAA Journal, Vol. 8, No. 12, 1970, pp. 2172-2179). The Crow instability becomes well developed in most atmospheric turbulence levels, but in strong turbulence the vortex pair deforms more irregularly due to turbulence advection. The most amplified wavelength of the instability decreases with increasing dimensionless turbulence intensity η, although it increases with increasing turbulence integral length scale. The vortex lifespan is controlled primarily by η and decreases with increasing η, whereas the effect of integral scale of turbulence on vortex lifespan is of minor importance. The lifespan is estimated to be about 40% larger than Crow and Bate's predicted value (Crow, S. C., and Bate, E. R., 'Lifespan of Trailing Vortices on a Turbulence Atmosphere,' Journal of Aircraft, Vol. 13, No. 7, 1976, pp. 476-482) but in agreement with Sarpkaya's recent modification (Sarpkaya, T., 'Decay of Wake Vortices of Large Aircraft,' AIAA Journal, Vol. 36, No. 9, 1998, pp. 1671-1679) to Crow and Bate's theory. This larger lifespan is also supported by data from water tank experiments and direct numerical simulations. There appears to be a possibility that the scatter in vortex lifespans due to ambient turbulence alone decreases with increasing Reynolds number, whereas larger scatter of lifespans in flight tests may result from other factors such as stratification, wind shear, and inhomogeneous ambient turbulence.