{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T13:11:24Z","timestamp":1707225084572},"reference-count":60,"publisher":"AIP Publishing","issue":"6","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2003,6,1]]},"abstract":"<jats:p>The application to the solar wind motivates the consideration of Alfv\u00e9n waves in a radial background magnetic field and radial mean flow, in two cases, viz., with velocity and magnetic field perturbations along parallels, or also with perturbations along meridians, combined in the radial components of vorticity and electric current. In both cases the same second-order Alfv\u00e9n wave equation is obtained; it has, in general, two singularities. If the mean flow velocity is taken to be a power of radial distance, with exponent other than zero or unity, there is a transition layer. In general there is a second singularity, viz., a critical layer, where the Alfv\u00e9n speed equals the mean flow velocity. There is one exceptional case in which the critical layer does not exist, namely a homogeneous medium, for which the mean flow velocity decays on the inverse square of the radial distance, and then Alfv\u00e9n speed also decays in the same way, so that their ratio is a constant, leading to two possibilities: (i) the ratio is not unity, and the wave equation remains of the second-order; (ii) the wave equation becomes of first-order in the case the mean flow velocity and Alfv\u00e9n speed are equal everywhere, because then the waves can propagate only in one direction. Case (i) corresponds to Alfv\u00e9n waves in the solar breeze. Exact solutions of the wave equations are obtained for all values of the radius, as a single expression for the first-order wave equation, whereas for the second-order wave equation it is possible to obtain solutions for small and large radius; the transition level limits the radius of convergence of one of these solutions, but the two solutions together cover the full range of radial distances. The choices of boundary conditions are discussed and the wavefields plotted vs dimensionless distance for several values of the two dimensionless parameters of the problem, viz., the Alfv\u00e9n number and dimensionless frequency, which appear in one combination only. The analytical results of the present paper are compared with the mostly numerical results in the literature. It is shown that the Alfv\u00e9n waves exhibit some properties observed in the solar wind, like the nonequipartition of kinetic and magnetic energies.<\/jats:p>","DOI":"10.1063\/1.1565336","type":"journal-article","created":{"date-parts":[[2003,5,22]],"date-time":"2003-05-22T22:01:44Z","timestamp":1053640904000},"page":"2486-2500","update-policy":"http:\/\/dx.doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["On Alfv\u00e9n waves in the solar breeze"],"prefix":"10.1063","volume":"10","author":[{"given":"L. M. B. C.","family":"Campos","sequence":"first","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Sec\u00e7\u00e3o de Mec\u00e2nica Aeroespacial, ISR, Av. Rovisco Pais\u20141049-001 Lisboa Codex, Portugal"}]},{"given":"N. L.","family":"Isaeva","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Sec\u00e7\u00e3o de Mec\u00e2nica Aeroespacial, ISR, Av. Rovisco Pais\u20141049-001 Lisboa Codex, Portugal"}]}],"member":"317","reference":[{"key":"2024020611595480700_r1","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1086\/168384","volume":"350","year":"1990","journal-title":"Astrophys. J."},{"key":"2024020611595480700_r2","doi-asserted-by":"crossref","first-page":"14873","DOI":"10.1029\/JA095iA09p14873","volume":"95","year":"1990","journal-title":"J. Geophys. Res."},{"key":"2024020611595480700_r3","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/BF00146703","volume":"135","year":"1991","journal-title":"Sol. Phys."},{"key":"2024020611595480700_r4","first-page":"304","volume":"270","year":"1993","journal-title":"Astron. Astrophys."},{"key":"2024020611595480700_r5","doi-asserted-by":"crossref","first-page":"23489","DOI":"10.1029\/94JA02209","volume":"99","year":"1994","journal-title":"J. Geophys. 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