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

xviĤ Time-averaged Ĥ˜H Time-averaged ˜HH rec Reconstruction of H after mask filter<strong>in</strong>g <strong>in</strong> the FK doma<strong>in</strong>H slope Difference <strong>in</strong> height btw <strong>in</strong>ner <strong>and</strong> outer cyl<strong>in</strong>ders <strong>in</strong> QG modelh Poloidal scalar for the perturbation magnetic fieldh m lS<strong>in</strong>e Gauss coefficientsI Incl<strong>in</strong>ation: angle between the magnetic field <strong>and</strong> the horizontal planeI 0 Zeroth-order spherical Bessel function√i −1, used with imag<strong>in</strong>ary numbersJ Electrical current densityJ H Internal heat<strong>in</strong>g rate per unit volumej Axial component of the perturbation electrical currentk Wavevector <strong>in</strong> direction of wave propagationk x Component of wavevector <strong>in</strong> the cartesian x directionk y Component of wavevector <strong>in</strong> the cartesian y directionk z Component of wavevector <strong>in</strong> the cartesian z directionk Wavenumber (Fourier transform partner with x)Also wavenumber of disturbance ( 2πL λ)L Number of spherical harmonic degrees used <strong>in</strong> representation of variablesL MC Typical length scale of MC wave disturbance <strong>in</strong> the field <strong>and</strong> flowL SV Maximium spherical harmonic degree of secular variationL U Maximium spherical harmonic degree used <strong>in</strong> expansiosn of flow scalarsL λ Wavelength of a general disturbanceL 1 L<strong>in</strong>ear operator premultiply<strong>in</strong>g (ẑ × u) <strong>in</strong> Malkus model of hydromagnetic <strong>waves</strong>L 2 L<strong>in</strong>ear operator premultiply<strong>in</strong>g u <strong>in</strong> Malkus model of hydromagnetic <strong>waves</strong>L 2 Angular momentum operator (angular part of Laplacian)l Spherical harmonic degreeM n Fourth order B-spl<strong>in</strong>e basis functionsm Field model obta<strong>in</strong>ed by <strong>in</strong>vert<strong>in</strong>g observationsm Azimuthal wavenumber (Fourier transform partner with φ)Also <strong>in</strong>dex for discrete po<strong>in</strong>ts on z axis <strong>in</strong> Radon transformAlso order of associated Legendre function Plmm c Azimuthal wavenumber of wave at the onset of <strong>in</strong>stabilityN Number of Chebyshev modes used <strong>in</strong> representation of variablesN t Number of discete time sample po<strong>in</strong>ts <strong>in</strong> a time series under studyN φ Number of discete spatial sample po<strong>in</strong>ts <strong>in</strong> a region under studyn In context of Radon transform, is an <strong>in</strong>dex for discrete angles of qO Order of magnitudeP Comb<strong>in</strong>ed mechanical <strong>and</strong> centrifugal pressuresP 0 Background pressureP ′ Perturbation pressure fieldP v Percentage ratio of R v to G v , each summed over all locationsP r Pr<strong>and</strong>tl number (see non-dimensional control parameters)P r m Magnetic Pr<strong>and</strong>tl number (see non-dimensional control parameters)Plm Associated Legendre function of degree l <strong>and</strong> order mQ Operator aris<strong>in</strong>g from double curl of momentum <strong>and</strong> <strong>in</strong>duction eqns