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Vortex line representation for flows of ideal and viscous fluids
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid
coincides with the equations of motion of a charged {\it compressible} fluid
moving due to a self-consistent electromagnetic field. Transition to the
Lagrangian description in a new hydrodynamics is equivalent for the original
Euler equations to the mixed Lagrangian-Eulerian description - the vortex line
representation (VLR). Due to compressibility of a "new" fluid the collapse of
vortex lines can happen as the result of breaking (or overturning) of vortex
lines. It is found that the Navier-Stokes equation in the vortex line
representation can be reduced to the equation of the diffusive type for the
Cauchy invariant with the diffusion tensor given by the metric of the VLR
LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts
Solar radio emission features a large number of fine structures demonstrating
great variability in frequency and time. We present spatially resolved spectral
radio observations of type IIIb bursts in the MHz range made by the Low
Frequency Array (LOFAR). The bursts show well-defined fine frequency
structuring called "stria" bursts. The spatial characteristics of the stria
sources are determined by the propagation effects of radio waves; their
movement and expansion speeds are in the range of 0.1-0.6c. Analysis of the
dynamic spectra reveals that both the spectral bandwidth and the frequency
drift rate of the striae increase with an increase of their central frequency;
the striae bandwidths are in the range of ~20-100 kHz and the striae drift
rates vary from zero to ~0.3 MHz s^-1. The observed spectral characteristics of
the stria bursts are consistent with the model involving modulation of the type
III burst emission mechanism by small-amplitude fluctuations of the plasma
density along the electron beam path. We estimate that the relative amplitude
of the density fluctuations is of dn/n~10^-3, their characteristic length scale
is less than 1000 km, and the characteristic propagation speed is in the range
of 400-800 km/s. These parameters indicate that the observed fine spectral
structures could be produced by propagating magnetohydrodynamic waves
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