MHD EQUILIBRIA WITH FLOWS IN UNIFORM GRAVITY .2. A CLASS OF EXACT 2-DLOOP-LIKE SOLUTIONS

We present a novel class of two-dimensional MHD equilibria which emerg e as exact solutions of the coupled transfield and Bernoulli nonlinear equations governing the dynamics of steady flows along magnetic lines in an atmosphere that is horizontally compressible and vertically str atified in the presence of a uniform gravitational field. The topology of the solutions is analysed in detail and is found to be controlled by a classical sonic and a novel X-type critical point corresponding t o a new characteristic speed for MHD wave propagation in an inhomogene ous medium. A subclass of low Alfven numbers loop-like solutions is fo und for a mildly stratified atmosphere; for very strong stratification no solutions exist while for moderate stratification only periodic so lutions are allowed. The results of the study are compared with those of models without flows and models with low Alfven number flows while the approach followed here extends that of treating the flux tube as r igid, or slender. Among our conclusions is that an increase of the mag nitude of the flow speed increases the height of the loops, while for stronger flows there are no equilibrium solutions and it is conjecture d that the loop is disrupted. Thus, the general trends emerging from t his analysis may be contrasted with solar observations wherein, for ex ample, some solar loops extend over heights much higher than those pre dicted by models without flows. Then, in the quiet Sun and in chromosp heric or coronal loops with plasma-beta and Alfven number not much sma ller than unity, the above nonlinear effects of the flows should be ta ken into account.