Three-dimensional stability of a vortex pair

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

Short-wave vortex instability in stratified flow

“…5 (b),(g) and (c),(h) respectively, we can see similar structure in the vorticity fields. Additionally, the anti-symmetric structure of the perturbation can be observed in the dominant eigenmodes in all cases, as found by [22,17]. Fig.…”

“…Continuing to even smaller vertical scales, viscous effects increase and may damp out the instability, and hence the growth rate decays with increasing k z F h in the limit of large k z F h . Oscillatory growth rates are observed for the smallest k z F h as observed in [22]. The imaginary part of the growth rate σ i remains zero everywhere else except in a small region surrounding the local minimum between the zigzag and short-wave peaks.…”

“…To evaluate σ, we compute the average value of the growth rate beginning at t = 20, after the initial transient behaviour has died out and the leading mode dominants, from the time series of σ produced by (13) until the end time t = 100. In the case of an oscillatory growth rate, as considered in [22], we drop the assumption that σ is real and instead compute the growth rate from…”

“…The LambChaplygin dipole, an exact 2D solution to the Euler equations, is a good approximation to columnar counter-rotating dipole generated in lab experiments [16]. Additionaly, the instabilities of the Lamb-Chaplyin dipole have been studied in both the unstratified [22,23] and the stratified case [17], so it provides a popular model to investigate vortex instabilities.…”

Stochastic forcing of the Lamb–Oseen vortex

“…In the context of aeronautics, the will to reduce the aircraft wake and the associated hazards to forthcoming planes has motivated the study of the stability of columnar vortices. Since the early works of Crow (1970), Moore & Saffman (1975) and Tsai & Widnall (1976), many studies have shown the sensitivity of the wing-tip vortex pair to both long-and short-wave cooperative instabilities, see Leweke & Williamson (1998) or Billant et al (1999) amongst others. Conversely, a single vortex is asymptotically stable but it supports various families of oscillating and damped modes amongst which are the so-called Kelvin waves (Fabre et al 2006).…”