Papers by nishant pratap singh
Arxiv preprint arXiv:0910.2141, 2009
We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear ... more We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow, in the low conductivity limit. Our treatment is non perturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rm) but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Rm. Our principal results are as follows: (i) The magnetic fluctuations are determined to lowest order in Rm by explicit calculation of the resistive Green's function for the linear shear flow; (ii) The mean electromotive force is then calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the "C" and "D" terms, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals; (iii) The contribution of the "D" terms is such that their contribution to the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. Therefore, to lowest order in Rm but to all orders in the shear strength, the "D" terms cannot give rise to a shear-current assisted dynamo effect; (iv) Casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) The integral kernels are expressed in terms of the velocity spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) The "C" terms couple different components of the mean magnetic field, so they can, in principle, give rise to a shear-current type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non helical velocity dynamics at low fluid Reynolds number does not result in a shear-current assisted dynamo effect.
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Papers by nishant pratap singh