We analyze the Navier Stokes equation, and show that all non-viscous, irrotational flows are barotropic. As far as we know, this has never been stated in the literature before, and indirectly suggests that vorticity is required to make these flows non-barotropic. Both the pressure, temperature, speed, entropy, enthalpy, and a Bernoulli function are derived to be only functions of the density (which is a function of space and time). When we also require steady flow, the Bernoulli function is a constant in all space, not just on streamlines.

Density measurements in the legs of coronal streamers, where there might be outflow, are reproduced here using a magnetohydrodynamic model of the flow inside the brightness boundary of streamers. The model returns values for the flow speed and stream tube geometry (spreading) between the base and a few solar radii. The flow speed is consistent with there being no measurable outflow below 2.5 R⊙ and an outflow of ∼100 km/s at 5 R⊙. We briefly describe the model, observations, and physical interpretation.

Slow solar wind is believed to arise inside the brightness boundary of streamers. In two recent studies, we describe analytic models of flow in this layer that are designed to analyze the effect of the magnetic field on the geometry of the flow (Suess & Nerney, 2002; Nerney & Suess, 2005). The first study described conditions that lead to a decrease of the flow speed with increasing height near the top of the closed magnetic helmet. The second study generalized the model to permit outflow in an arbitrarily thin layer inside the brightness boundary and the flow geometry to be constrictive or divergent above the helmet. A diverging streamer or ray above 2-3 solar radii occurs if the plasma beta is greater than unity inside the streamer and less than unity outside. The same argument can be used to discover the height above which the plasma beta in plumes, inside coronal holes, is greater than unity. The utility of this result is further examined here.

Streamers can extend to many solar radii but the closed field regions, or helmets, reach no higher than 2–4 solar radii. The brightness boundary defining streamers is therefore, a boundary between different flow regimes rather than between static plasma and expanding solar wind. It is reasonable to assume that, this boundary divides fast coronal hole wind from slow wind. Flow inside this boundary can be studied using MHD models and is a type of stagnation flow. We describe such a model that is essentially analytic and show examples of flow solutions within the context and assumptions of the model. The flow affects the stability of the underlying helmet, which can be subject to a leakage out of the cusp that is similar to the small mass releases observed with the SOHO/LASCO coronagraph. It can also cause the helmet to be susceptible to being carried away in a coronal mass ejection. The model therefore, also offers a way to study streamer stability.

Flow tubes adjacent to closed magnetic field lines on the boundaries of streamers can have spreading factors which change rapidly with height. Numerical models in this thin layer are subject to uncertainties. Here we use an analytic model of magnetically closed and adjacent open regions to analyze the spreading factor close to the closed field lines. The model is based on the one-temperature, isothermal flow model of Pneuman (1968), extended to calculate spreading factors and plasma beta, and to better explain streamer evolution with increasing temperature.

Streamers are generally described as regions of the corona in which the density is higher than in coronal holes because the plasma is trapped by closed loops of magnetic flux. In contrast, MHD models of the global corona show the plasma beta in streamers above siml.2R_S (heliocentric). There are three recent contributions to this topic. The first is that heating near the cusp further drives beta up and results in release of new slow solar wind plasma from the top of the streamer. The second is SOHO/UVCS observations, in combination with a potential field/source surface model of the magnetic field, that show beta above 1.2R_S in a streamer observed near solar sunspot minimum. The third is a magnetic field reconstruction technique that uses field deforming algorithms and is more versatile for local fields than potential field models . The field reconstruction algorithm was applied to an isolated active region (AR 7999) and to the Pneuman Kopp global MHD model (beta has never been published for their model). In the active region, beta becomes larger than unity at siml.2 R_S. In the Pneuman & Kopp model, beta at the base of the streamer and rises with increasing height, becoming 15-20 at 1.6R_S and 35- 50 at 1.7R_S. Global simulations go on to show that the reason streamers do not simply explode under such high beta conditions is that they are held down by pressure from the sides due to the magnetic fields (and low beta) in adjacent coronal holes. The main role of the closed magnetic loop near the cusp is to keep the steamer from continuously leaking plasma, as otherwise happens in a magnetic pinch which is similar but has no closed loops. Awareness of MHD physical conditions in streamers is causing us to focus more attention on the details of the heating. On obvious suggestion is that heating is at much lower heights in streamers than in coronal holes. Also, energy which is directly delivered as momentum in coronal holes might all be deposited as heat in streamers.

Flow tubes adjacent to closed magnetic field lines on the boundaries of streamers can have spreading factors which change rapidly with height. Numerical models in this thin layer are subject to uncertainties. Here we use an analytic model of magnetically closed and adjacent open regions to analyze the spreading factor close to the closed field lines. The model is based on the one-temperature, isothermal flow model of Pneuman (1968), extended to calculate spreading factors and plasma beta, and to better explain streamer evolution with increasing temperature.

The solar wind in the inner heliosphere, inside ~ 5 AU, has been almost fully characterized by the addition of the high heliographic latitude Ulysses mission to the many low latitude inner heliosphere missions that preceded it. The two major omissions are the high latitude solar wind at solar maximum, which will be measured during the second Ulysses polar passages, and the solar wind near the Sun, which could be analyzed by a Solar Probe mission. Here, existing knowledge of the global solar wind in the inner heliosphere is summarized in the context of the new results from Ulysses.

Measurements by Ulysses have confirmed that there is no significant gradient with respect to heliomagnetic latitude in the radial component, Br, of the interplanetary magnetic field. In the corona, the plasma β is ≪ 1, except directly above streamers, so longitudinal and latitudinal gradients in field strength will relax due to the transverse magnetic pressure gradient force as the solar wind carries magnetic flux away from the Sun. This happens quickly enough so that the field is essentially uniform by 5–10 R⊙, apparently remaining so as it is carried to beyond 1 AU. Here, we illustrate the coronal relaxation with a qualitative physical argument and by reference to a detailed MHD simulation.

The vector Burgers equation is extended to include pressure gradients and gravity. It is shown that within the framework of the Cole-Hopf transformation there are no physical solutions to this problem. This result is important because it clearly demonstrates that any extension of Burgers equation to more interesting physical situations is strongly limited.

The well-known analytical solution of Burgers’ equation is extended to curvilinear coordinate systems in three dimensions by a method that is much simpler and more suitable to practical applications than that previously used [22], The results obtained are applied to incompressible flow with cylindrical symmetry, and also to the decay of an initially linearly increasing wind.

The topology of the magnetic field in the heliosheath is illustrated using plots of the field lines. It is shown that the Archimedean spiral inside the terminal shock is rotated back in the heliosheath into nested spirals that are advected in the direction of the interstellar wind. The 22‐year solar magnetic cycle is imprinted onto these field lines in the form of unipolar magnetic envelopes surrounded by volumes of strongly mixed polarity. Each envelope is defined by the changing tilt of the heliospheric current sheet, which is in turn defined by the boundary of unipolar high‐latitude regions on the Sun that shrink to the pole at solar maximum and expand to the equator at solar minimum. The detailed shape of the envelopes is regulated by the solar wind velocity structure in the heliosheath.

We have solved for the potential flow downstream of the terminal shock of the solar wind in the limit of small departures from a spherical shock due to a latitudinal ram pressure variation in the supersonic solar wind. The solution connects anisotropic streamlines at the shock to uniform streamlines down the heliotail because we use a non-slip boundary condition on the heliopause at large radii. The rotational velocity about the heliotail in the near-field solution decays as the fourth power of distance from the shock. The polar divergence of the streamlines will have consequences for the previously discussed magnetic pressure ridge that may build-up just inside the heliopause.