Explicit, but accurate formulas for the friction factor are given as a substitute for the more inconvenient implicit formulas which are at present considered to be the most accurate.

Abstract. We have used vector measurements of the electron drift velocity made by the Electron Drift Instrument (EDI) on Cluster between February 2001 and March 2006 to derive statistical maps of the high-latitude plasma convection. The EDI measurements, obtained at geocentric distances between ~4 and ~20 RE over both hemispheres, are mapped into the polar ionosphere, and sorted according to the clock-angle of the interplanetary magnetic field (IMF), measured at ACE and propagated to Earth, using best estimates of the orientation of the IMF variations. Only intervals of stable IMF are used, based on the magnitude of a "bias-vector" constructed from 30-min averages. The resulting data set consists of a total of 5862 h of EDI data. Contour maps of the electric potential in the polar ionosphere are subsequently derived from the mapped and averaged ionospheric drift vectors. Comparison with published statistical results based on Super Dual Auroral Radar Network (SuperDARN) radar and low-altitude satellite measurements shows excellent agreement between the average convection patterns, and in particular the lack of mirror-symmetry between the effects of positive and negative IMF By, the appearance of a duskward flow component for strongly southward IMF, and the general weakening of the average flows and potentials for northerly IMF directions. This agreement lends credence to the validity of the assumption underlying the mapping of the EDI data, namely that magnetic field lines are equipotentials. For strongly northward IMF the mapped EDI data show the clear emergence of two counter-rotating lobe cells with a channel of sunward flow between them. The total potential drops across the polar caps obtained from the mapped EDI data are intermediate between the radar and the low-altitude satellite results.

We used the Lyon‐Fedder‐Mobarry global magnetohydrodynamics model to study the effects of the interplanetary magnetic field (IMF) By component on the coupling between the solar wind and magnetosphere‐ionosphere system. When the IMF reconnects with the terrestrial magnetic field with IMF By≠0, flux transport is asymmetrically distributed between the two hemispheres. We describe how By is induced in the closed magnetosphere on both the dayside and nightside and present the governing equations. The magnetosphere imposes asymmetric forces on the ionosphere, and the effects on the ionospheric flow are characterized by distorted convection cell patterns, often referred to as “banana” and “orange” cell patterns. The flux asymmetrically added to the lobes results in a nonuniform induced By in the closed magnetosphere. By including the dynamics of the system, we introduce a mechanism that predicts asymmetric Birkeland currents at conjugate foot points. Asymmetric Birkeland currents are created as a consequence of y directed tension contained in the return flow. Associated with these currents, we expect fast localized ionospheric azimuthal flows present in one hemisphere but not necessarily in the other. We also present current density measurements from Active Magnetosphere and Planetary Electrodynamics Response Experiment that are consistent with this picture. We argue that the induced By produces asymmetrical Birkeland currents as a consequence of asymmetric stress balance between the hemispheres. Such an asymmetry will also lead to asymmetrical foot points and asymmetries in the azimuthal flow in the ionosphere. These phenomena should therefore be treated in a unified way.