Hydromagnetic waves in Earth's core and their influence on ...

xviiiu yu zVv nXx̂xxYŷyZẑzFlow magntitude <strong>in</strong> cartesian y directionFlow magntitude <strong>in</strong> cartesian z directionMagnetic potentialArray of azimuthal speeds derived us<strong>in</strong>g the Radon transform methodAmplitude of magnetic field <strong>in</strong> the northwards directionVector of unknown expansion coefficients <strong>in</strong> magnetoconvection problemUnit vector <strong>in</strong> the direction of the cartesian x-axisSpatial displacement (distance) along cartesian x-axisAlso displacement <strong>in</strong> the eastward direction <strong>in</strong> β-plane modelsAmplitude of magnetic field <strong>in</strong> the eastwards directionAlso represents spherical harmonic functionsUnit vector <strong>in</strong> the direction of the cartesian y-axisSpatial displacement (distance) along cartesian y-axisAmplitude of magnetic field <strong>in</strong> the radially <strong>in</strong>wards directionUnit vector <strong>in</strong> the direction of the cartesian z-axisSpatial displacement along the cartesian y-axisAlso x axis rotated by angle q when referr<strong>in</strong>g to the Radon transformNon-dimensional control parametersE =ν2Ωd 2 0Ekman numberP r = ν κPr<strong>and</strong>tl NumberP r m = ν ηMagnetic Pr<strong>and</strong>tl numberRa = |g| α |∇T 0| d 4 0κνRayleigh numberRa m = ERaP rModified Rayleigh numberR m = Urmsd 0ηMagnetic Reynolds numberR m = U kηMagnetic Reynolds number of Clark (1965)Λ = B2 02Ωµρ 0 ηβ ∗ = tan H slopeDElsasser numberAngle of slop<strong>in</strong>g upper boundary <strong>in</strong> QG modelValues adopted for physical constants, relevant to Earth’s <strong>core</strong>α=1.3 × 10 −5 K −1η=1.6 m 2 s −1κ=8.6×10 −6 m 2 s −1ν=10 −6 m 2 s −1ρ 0 =1×10 4 kg m −3µ 0 =4π × 10 −7 H m −1Ω=7.29 × 10 −5 s −1B 0 ∼ 1× 10 −3 Td 0 = r cmb − r i =3485 km - 1215 km=2260 kmγ=9.8 s −2|∇T 0 | ∼ 0.1 K km −1 (superadiabatic)(values taken from Gubb<strong>in</strong>s (2000))