Models of quasi-discontinuous solar-wind streams. Steady-state and time-dependent numerical solutions

The modeling of the solar-wind outflow patterns is addressed in terms of local transient distortions of the flow, temperature, and density profiles due to the presence of local energy sources. A recently introduced related new class of analytically derived quasi-discontinuous solar-wind solutions is numerically approached. The analytical discontinuous solutions can asymptotically obtained from steady-state and time-dependent models in the limit of very localized external heating. The aim of the current study is to develop a numerical confirmation for the presence of quasi-discontinuous distortions of the wind profiles by mimicking the local energy sources with additional source terms in the governing equations of the numerical models. Corresponding systems of ordinary and partial differential equations, respectively, are formulated employing prescribed heating functions. After a comparison of sequences of numerically obtained steady-state solutions with the analytical one, the stability of the former is tested with a time-dependent simulation. The analytical discontinuous solutions are asymptotically reproduced with the quasi-discontinuous steady-state and time-dependent numerical solutions in the limit of vanishingly small width (compared to the other characteristic length scales of the system) of the heating function. The interpretation that such solutions result from strongly localized heating has been confirmed both qualitatively and quantitatively. The applied numerical approach enables the building of more complex, multidimensional counterpart models and local profiles of typical local energy sources that are presumably responsible for the dynamical properties of the solar-wind patterns found.