The voltage against current curves of cation exchange membranes have been studied. They have a characteristic shape with a region of slow current variation (the plateau) followed by a region of accelerated current growth as the voltage is increased (the inflexion).

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Dynamically relevant alignments are used in order to show that regions with weak vorticity are not structureless, non-Gaussian and dynamically not passive. For example, the structure of vorticity in quasi-homogeneous/isotropic turbulent flows is associated with strong alignment between vorticity to and the eigenvectors of the rate of strain tensor 2i (especially -but not only -between to and 22) rather than with intense vorticity only. Consequently, much larger regions of turbulent flow than just those with intense vorticity are spatially structured. The whole flow field -even with the weakest measurable enstrophy is strongly non-Gaussian, which among other things is manifested in strong alignment between vorticity and the vortex stretching vector Wi-tojsij. It is shown that the quasi-two-dimensional regions corresponding to large cos(to, 22) are qualitatively different from purely two-dimensional ones, e.g. in that they possess essentially nonvanishing enstrophy generation, which is larger than its mean for the whole field. * Corresponding author. 1A brief presentation of some results of this paper was published in Tsinober et al. (1995b).

A comparison is made between a number of properties of a quasi-homogeneous isotropic turbulent field obtained from a direct numerical simulation of the Navier–Stokes equation and its random counterpart with the same energy spectrum. It is demonstrated that some effects in a real flow have a considerable contribution of a kinematic nature (e.g. reduction of nonlinearity), while others are mostly dynamical (e.g. alignment between vorticity and eigenvectors of the rate of strain).

The dynamics of helical decaying homogeneous turbulence is investigated in direct numerical simulations at moderate Reynolds numbers. A new initialization procedure is presented that allows one to control both the energy and the helicity spectral density of the initial flow field. It is observed that large initial helicity impedes the transfer of energy toward smaller scales, inhibits the buildup of enstrophy, and reduces dissipation for several turnover times. Also, the skewness and flatness of the velocity derivatives reach values typical of turbulence much later than in comparable flows without helicity. However, these effects are significant only if the helicity of the flow is quite high. In simulations with small or vanishing initial helicity it is found that the fluctuations of the average helicity and the helicity spectral density lie within the range suggested by a quasi-Gaussian approximation. This suggests that at moderate Reynolds number spontaneous fluctuations of helicity are not large enough to directly influence the energy transfer.