A pulsar wind is expected to be inhomogeneous and intermixed with disturbances originating from the central pulsar in terms of dynamic, electromagnetic and thermal properties. We examine, in this paper, basic properties of two-dimensional compressible perturbations in a magnetized equatorial pulsar wind. Asymptotic solutions at large radii for both fast and slow disturbances in a relativistic magnetohydrodynamic (RMHD) wind are derived analytically. We describe the process of forming RMHD shocks in a pulsar wind with inhomogeneous wind streams emanating from the spinning pulsar and with interlaced, alternately reversed, spiral magnetic field stripes resulting from a pulsar whose rotation and magnetic axes misalign. Spiral bands of forward-reverse shock pairs are expected to appear frequently in a magnetically striped pulsar wind within a certain latitude range about the rotation equator. In highly compressed regions between forward and reverse shocks, magnetized pulsar wind flow could become turbulent so that extremely relativistic particles can be produced in profusion and be injected into the surrounding nebula. Based on our analysis and physical considerations, we propose a scenario for the appearance of wisps in the inner Crab nebula, in which the pattern of inward propagating RMHD fast waves and/or shocks (relative to the pulsar wind) gives rise to the quasi-stationary structure of wisps in the inner Crab nebula, while outward propagating RMHD fast and slow disturbances appear as transients in the sidereal reference frame. The fine wisp region ( ~ 1016 cm) across a strong RMHD reverse shock can squeeze ~ 106_107 magnetic stripes with opposite polarities; magnetic reconnections proceed turbulently therein and lead to dramatic enhancement of relativistic particle acceleration at the expense of flow and magnetic energies continuously supplied from upstream. These processes could also contribute to the production of high-energy cosmic rays.
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