The Spectrum of the Final Decay of Localized Disturbances in a Viscous Fluid

摘要

Based on previous work of Batchelor and Phillips it is shown that in an unbounded viscous fluid any decaying localized disturbance with a negligible nonlinear inertial force consists of a spectrum of dissipating spherical vortices. All these vortices can be derived from decaying multipoles. Such disturbances are characterized by a vorticity field which originates from a point source of vorticity and vanishes exponentially far away from its center. The result has been obtained by a Taylor-series expansion of the vorticity about the origin in a wave-number space. Vorticity fields which are produced in an extended region and over a finite period of time can be described by superposition. An example is given for decaying axisymmetric spherical discontinuity surfaces. (Author)