Instability mechanisms and transition scenarios of spiral turbulence in Taylor-Couette flow

Abstract

Alternating laminar and turbulent helical bands appearing in shear flows between counterrotating cylinders are accurately computed and the near-wall instability phenomena responsible for their generation identified for the first time. The computations show that this intermittent regime can only exist within large domains and that its spiral coherence is not dictated by endwall boundary conditions. A supercritical transition route, consisting of a progressive helical alignment of localised turbulent spots, is carefully studied. Subcritical routes disconnected from secondary laminar flows have also been identified. 47.20.Lz, 47.27.Cn A comprehensive understanding of turbulent phenomena necessarily requires a previous explanation of the mechanisms that mediate between laminar and fully disordered fluid motion. One of the most challenging shear flow problems is the understanding of laminar-turbulent coexistence phenomena or intermittency, i.e., spatio-temporal coexistence between laminar and turbulent regions in a fluid flow. Canonical shear flows such as plane Couette flow between inertially countersliding parallel plates or pipe flow in a very long straight pipe of circular cross section exhibit localised turbulence as a prelude to fully developed turbulent flow [1][2][3][4][5][6]. Open shear flows share many common drawbacks when studying the long term behaviour of turbulent or intermittent regimes, since localised turbulent spots are often advected downstream and leave the domain. Computation of these flows usually assumes streamwise periodicity, overlooking the real boundary conditions at the entrance and exit of the domains and potentially leading to artificial interaction of the leading and trailing edges of localised turbulent spots. A naturally streamwise-periodic problem such as the Taylor-Couette system between independently rotating concentric cylinders solves these difficulties. Furthermore, while transition in open shear flows is typically subcritical, i.e., bypassing linear stability, Taylor-Couette flow exhibits a huge variety of secondary supercritical steady, time periodic, or almost periodic laminar flows before an eventual transition to chaotic regimes [7]. This enables to study transition in a supercritical setting, along with degeneration into subcriticality. We refer the reader to standard monographs and references therein [8,9].Laminar-turbulent coexistence in Taylor-Couette flow was originally reported by Coles and Van Atta in the 1960s [10,11]. They observed interlaced laminar-turbulent helical patterns (see Fig. 1a) so called spiral turbulence or barber pole turbulence, according to Feynman [12]. This pattern has been studied experimentally by many authors later in the 1980s [7,13] and during the current decade [1,14]. Spiral turbulence, henceforth termed as SPT, may exhibit hysteretic subcritical behaviour, being sustained even in situations where linear theory predicts stability of the base laminar flow. Linear non-modal analysis has shown a strong correlation between the hysteretic ...

Instability of plumes driven by localized heating

“…Two well-known examples are found in the Taylor-Couette flows. When the outer cylinder is at rest, the axisymmetric Taylor vortices can be observed in fully turbulent flow, and when the cylinders counter-rotate, the turbulent spiral flow shows bands of laminar and turbulent flow that have a beautiful helical symmetry on average (Coles 1965;Andereck, Liu & Swinney 1986;Dong 2007;Meseguer et al 2009;Dong & Zheng 2011). Therefore, the analysis of the symmetries of invariant sets can play an important role in the description of the turbulence.…”

Turbulent-laminar patterns in plane Poiseuille flow

“…Transitional regimes in wall-bounded shear flows display regular patterns of turbulent and laminar bands which are wide and oblique with respect to the streamwise direction. These patterns have been studied in counter-rotating Taylor-Couette flow [1][2][3][4][5][6][7] and in plane Couette flow. [6][7][8][9][10][11][12][13][14] Turbulent-laminar banded patterns have also been observed numerically and experimentally in plane Poiseuille (channel) flow.…”

Subcritical transition and spiral turbulence in circular Couette flow

“…Featuring alternating oblique bands of laminar and turbulent flow, this state was first documented by Coles (1965) and van Atta (1966) and is a rich example of the complexity encapsulated within the Navier-Stokes equations. Later observations of spiral turbulence by others (such as Andereck, Liu & Swinney 1986;Hegseth et al 1989;Prigent et al 2002) in counter-rotating flows have added experimental details on this regime, and recent simulation efforts seem to be closing in on its fine-scale structure and mechanisms (Dong 2009;Meseguer et al 2009;Dong & Zheng 2011). Recent simulations of the turbulent banding phenomenon in planar Couette flows are also making significant progress (e.g.…”