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

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. 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 localized turbulent spots, is carefully studied. Subcritical routes disconnected from secondary laminar flows have also been identified.

Figure 1

(Color online) Spiral turbulence between counterrotating concentric cylinders (outer cylinder rotating clockwise). (a) Three dimensional view of angular momentum distribution. (b) Annular cross section of axial vorticity distribution. The structure rotates clockwise (see film in [22]).

Figure 2

Time series analysis of SPT for $\left(R_{\text{o}},R_{\text{i}}\right)=\left(-3000,650\right)$. (a) Radial velocity measured at $\left(r,\theta ,z\right)=\left(8.1,0,0\right)$: time scale in $T_{\text{o}}=2\pi /R_{\text{o}}\left(1-\eta \right)$ outer cylinder rotation period units. (b) Power spectra: frequency scale in ${\Omega }_{\text{o}}=R_{\text{o}}\left(1-\eta \right)$ outer cylinder angular speed units.

Figure 3

Explored regions in $\left(R_{\text{o}},R_{\text{i}}\right)$-parameter space. Black triangles, gray triangles, gray squares and white triangles correspond to SPT, INT, ISP, and CCF flows, respectively. See text for explanation.

Figure 4

Averaged norm ${⟨E⟩}^{1/2}$ of the perturbation as a function of $R_{\text{o}}$ and $R_{\text{i}}$. The vertical dotted line of the top curve $R_{\text{o}}=-3000$ is located at the relaminarization value

Figure 5

Radial vorticity ${\left(\mathbf{\nabla }\times \mathbf{u}\right)}_r$ at intermediate radial surface $r_m=8.21$. (a) and (b) showing large and small turbulent spots for $\left(R_{\text{o}},R_{\text{i}}\right)=\left(-3000,550\right)$. From (c) to (d), same quantity for $R_{\text{o}}=-1200$. (c) ISP, $R_{\text{i}}=480$; (d) INT, $R_{\text{i}}=520$; (e) INT, $R_{\text{i}}=530$; and (f) SPT, $R_{\text{i}}=600$ (see films in [22]).