Transition to turbulence in slowly divergent pipe flow

The results of a combined experimental and numerical study of the flow in slowly diverging pipes are presented. Interestingly, an axisymmetric conical recirculation cell has been observed. The conditions for its existence and the length of the cell are simulated for a range of diverging angles and expansion ratios. There is a critical velocity for the appearance of this state. When the flow rate increases further, a subcritical transition for localized turbulence arises. The transition and relaminarization experiments described here quantify the extent of turbulence. The findings suggest that the transition scenario in slowly diverging pipes is a combination of stages similar to those observed in sudden expansions and in straight circular pipe flow.Comment: 8 pages, 5 figure

Helicity cascades in rotating turbulence

The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the dynamics of the flow. In particular, at small Rossby number, the energy cascades to large scales, as expected, but helicity then can dominate the cascade to small scales. A phenomenological interpretation in terms of a direct cascade of helicity slowed down by wave-eddy interactions leads to the prediction of new inertial indices for the small-scale energy and helicity spectra.Comment: 7 pages, 8 figure

Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions

Viscous fluid dynamical calculations require no-slip boundary conditions. Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. However, such calculations have been limited to two-dimensional situations. Here we present a method that yields orthogonal decompositions of incompressible, three-dimensional flow fields and apply it to periodic cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure

The decay of Batchelor and Saffman rotating turbulence

The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two cannonical self-preserving solutions of the von K\'arm\'an-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\sim k^4$ (Batchelor turbulence) and $\sim k^2$ (Saffman turbulence) and show that, while a self-similar decay cannot be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two-dimensional and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von K\'arm\'an-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution

Laminar Craya-Curtet jets

This Brief Communication investigates laminar Craya-Curtet flows, formed when a jet with moderately large Reynolds number discharges into a coaxial ducted flow of much larger radius. It is seen that the Craya-Curtet number, C=(J/sub c//J/sub j/)/sup 1/2/, defined as the square root of the ratio of the momentum flux of the coflowing stream to that of the central jet, arises as the single governing parameter when the boundary-layer approximation is used to describe the resulting steady slender jet. The numerical integrations show that for C above a critical value C/sub c/ the resulting streamlines remain aligned with the axis, while for C<C/sub c/ the entrainment demands of the jet cannot be satisfied by the coflow, and a toroidal recirculation region forms. The critical Craya-Curtet number is determined for both uniform and parabolic coflow, yielding C/sub c/=0.65 and C/sub c/=0.77, respectively. The streamlines determined numerically are compared with those obtained experimentally by flow visualizations, yielding good agreement in the resulting flow structure and also in the value of C/sub c

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling

Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling allows for steady-state hump profiles at different flow rates and tube heights to be scaled onto a single similarity profile. I show that the scaling behavior is independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl

Variance anisotropy in compressible 3-D MHD

All Rights Reserved.We employ spectral method numerical simulations to examine the dynamical development of anisotropy of the variance, or polarization, of the magnetic and velocity field in compressible magnetohydrodynamic (MHD) turbulence. Both variance anisotropy and spectral anisotropy emerge under influence of a large-scale mean magnetic field B0; these are distinct effects, although sometimes related. Here we examine the appearance of variance parallel to B0, when starting from a highly anisotropic state. The discussion is based on a turbulence theoretic approach rather than a wave perspective. We find that parallel variance emerges over several characteristic nonlinear times, often attaining a quasi-steady level that depends on plasma beta. Consistency with solar wind observations seems to occur when the initial state is dominated by quasi-two-dimensional fluctuations