Nonlinear waves in rotating magnetohydrodynamics

References

• Acheson , DJ . 1972 . On the asymptotic stability of a rotating annulus . J. Fluid Mech. , 52 : 539 – 541 .
   Google Scholar
• Acheson , DJ . 1973 . Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid . J. Fluid Mech. , 61 : 609 – 624 .
   Web of Science ®Google Scholar
• Acheson , DJ . 1980 . Stable density stratification as a catalyst for instability . J. Fluid Mech. , 96 : 723 – 733 .
   Web of Science ®Google Scholar
• Acheson , DJ . 1983 . Local analysis of thermal and magnetic instabilities in a rapidly rotating fluid . Geophys. Astrophys. Fluid Dynam. , 27 : 123 – 136 .
   Web of Science ®Google Scholar
• Bloxham , J , Zatman , S and Dumberry , M . 2002 . The origin of geomagnetic jerks . Nature , 420 : 65 – 68 .
   PubMedGoogle Scholar
• Braginsky , SI . 1967 . Magnetic waves in the earth's core . Geomagnetism and Aeronomy , 7 : 851 – 859 .
   Google Scholar
• Choquet-Bruhat , Y . 1969 . Ondes asymptotiques et approchees pour des systemes d'equations aux derivees partielles nonlineaires . J. Maths. Pures et App. , 48 : 117 – 158 .
   Google Scholar
• Chu , VH and Mei , CC . 1970 . On slowly varying Stokes waves . J. Fluid Mechanics , 41 : 873 – 877 .
   Google Scholar
• El Sawi , M and Eltayeb , I . 1981 . Wave action and critical surfaces for hydromagnetic-inertial-gravity waves . J. Mech. Appl. Math. , 34 : 187 – 202 .
   Google Scholar
• Ewen , S and Soward , A . 1994a . Phase mixed rotating magnetoconvection and Taylor's condition I: amplitude equations . Geophys. Astrophys. Fluid Dynam. , 77 : 209 – 230 .
   Web of Science ®Google Scholar
• Ewen , S and Soward , A . 1994b . Phase mixed rotating magnetoconvection and Taylor's condition II: travelling pulses . Geophys. Astrophys. Fluid Dynam. , 77 : 231 – 262 .
   Web of Science ®Google Scholar
• Ewen , S and Soward , A . 1994c . Phase mixed rotating magnetoconvection and Taylor's condition III: wave trains . Geophys. Astrophys. Fluid Dynam. , 77 : 263 – 283 .
   Web of Science ®Google Scholar
• Fearn , DR . 1983 . Hydromagnetic waves in a differentially rotating annulus I. A test of local stability analysis . Geophys. Astrophys. Fluid Dynam. , 27 : 137 – 162 .
   Web of Science ®Google Scholar
• Fearn , DR . 1984 . Hydromagnetic waves in a differentially rotating annulus II. Resistive instabilities . Geophys. Astrophys. Fluid Dynam. , 30 : 227 – 239 .
   Web of Science ®Google Scholar
• Fearn , DR . 1985 . Hydromagnetic waves in a differentially rotating annulus III. The effect of an axial field . Geophys. Astrophys. Fluid Dynam. , 33 : 185 – 197 .
   Web of Science ®Google Scholar
• Fearn , DR . 1988 . Hydromagnetic waves in a differentially rotating annulus IV. Insulating boundaries . Geophys. Astrophys. Fluid Dynam. , 44 : 227 – 239 .
   Google Scholar
• Fearn , DR and Proctor , MRE . 1983a . Hydromagnetic waves in a differentially rotating sphere . J. Fluid Mechanics , 128 : 1 – 20 .
   Web of Science ®Google Scholar
• Fearn , DR and Proctor , MRE . 1983b . The stabilizing role of differential rotation on hydromagnetic waves . J. Fluid Mechanics , 128 : 21 – 36 .
   Web of Science ®Google Scholar
• Fearn , DR and Weiglhofer , WS . 1991 . Magnetic instabilities in rapidly rotating spherical geometries I. From cylinders to spheres . Geophys. Astrophys. Fluid Dynam. , 56 : 159 – 181 .
   Web of Science ®Google Scholar
• Fearn , DR and Weiglhofer , WS . 1992 . Resistive instability and the magnetostrophic approximation . Geophys. Astrophys. Fluid Dynam. , 63 : 111 – 138 .
   Web of Science ®Google Scholar
• Finlay , CC and Jackson , A . 2003 . Equatorially dominated magnetic field change at the surface of the Earth's core . Science , 300 : 2084 – 2086 .
   PubMed Web of Science ®Google Scholar
• Glatzmaier , GA . 2002 . Geodynamo simulations–how realistic are they? . Ann. Rev. Earth Planet Sci. , 30 : 237 – 257 .
   Web of Science ®Google Scholar
• Gubbins , D and Roberts , PH . 1987 . “ Magnetohydrodynamics of the earth's core ” . In Geomagnetism, Vol. 2 , Edited by: Jacobs , JA . 1 – 183 . London : Academic Press .
   Google Scholar
• Hide , R . 1966 . Free hydromagnetic oscillations of the earth's core and the theory of the geomagnetic secular variation . Phil. Trans. Roy. Soc. London , A259 : 615 – 647 .
   Web of Science ®Google Scholar
• Hoogstraten , HN and van der Heide , R . 1972 . A perturbation method for nonlinear dispersive waves with an application to water waves . J. Eng. Maths. , 6 : 341 – 353 .
   Google Scholar
• Hutcheson , KA and Fearn , DR . 1996 . The stability of toroidal magnetic fields with equatorial symmetry: implications for the Earth's magnetic field . Phys. Earth Planet. Int. , 97 : 43 – 54 .
   Web of Science ®Google Scholar
• London , SD . 1984 . Slow hydromagnetic oscillations in a rotating spheroidal shell . Geophys. Astrophys. Fluid Dynam. , 28 : 205 – 222 .
   Web of Science ®Google Scholar
• London , SD . 1987 . Weakly nonlinear Rossby waves in a rotating fluid of spheroidal configuration . Dynamics of Oceans and Atmospheres , 11 : 39 – 58 .
   Google Scholar
• London , SD . 1992a . Hydromagnetic waves in a rotating sphere . Geophys. Astrophys. Fluid Dynam. , 63 : 91 – 109 .
   Web of Science ®Google Scholar
• London , SD . 1992b . A uniform asymptotic approximation for unstable hydromagnetic waves in a rotating sphere . Geophys. Astrophys. Fluid Dynam. , 67 : 185 – 198 .
   Web of Science ®Google Scholar
• London , SD . 1993 . Stability and trapping of slow hydromagnetic waves in rotating cylindrical geometry . J. Geomag. Geoelectr. , 45 : 153 – 1561 .
   Google Scholar
• London , SD . 1995 . An asymptotic analysis of the stability of slow hydromagnetic waves . Phys. Earth. Planet. Int. , 91 : 47 – 52 .
   Google Scholar
• London , SD . 1999 . An asymptotic model for resistive instability in the earth's outer core . Geophys. Astrophys. Fluid Dynam. , 91 : 251 – 268 .
   Web of Science ®Google Scholar
• London , SD . 2005 . Resistive wave breaking in the earth's outer core . Geophys. Astrophys. Fluid Dynam. , 99 : 397 – 411 .
   Web of Science ®Google Scholar
• Roberts , PH and Glatzmaier , GA . 2000 . Geodymamo theory and simulations . Rev. Mod. Phys. , 72 : 1081 – 1123 .
   Web of Science ®Google Scholar
• Shen , MC and Keller , JB . 1973 . Ray method for nonlinear wave propagation in a rotating fluid of variable depth . Phys. Fluids , 16 : 1565 – 1572 .
   Google Scholar
• Zhang , K and Fearn , DR . 1994 . Hydromagnetic waves in rapidly rotating spherical shells, generatied by toroidal decay modes . Geophys. Astrophys. Fluid Dynam. , 77 : 133 – 157 .
   Web of Science ®Google Scholar
• Zhang , K , Liao , XH and Schubert , G . 2003 . Nonaxisymmetric instabilities of a toroidal magnetic field in a rotating sphere . Astrophys. J. , 585 : 1124 – 1137 .
   Web of Science ®Google Scholar