On photospheric and chromospheric penumbral waves

The full magnetoatmospheric wave equation is numerically solved for the particular penumbral model of Nye and Thomas (1974). For chromospheric running penumbral waves it is found that the maximum vertical velocity occurs at the base of the Hα region (z ≈ 300 km) much lower than previous WKB estimates have suggested. The maximum ‘vertical’ kinetic energy occurs at z ≈ - 130 km. Very significant horizontal velocities are also found for these waves, and, in the absence of shear flow it appears that previous estimates of photospheric vertical velocities of order 10^?1 km s^?1 could be substantial underestimates. For the photospheric events of Musman et al. (1976), a high vertical velocity maximum is found in the corona, and the modes appear highly dispersive for periods ≥ 220 s. The effects of a sinusoidal shear flow profile on running penumbral waves are examined, and it is found that the eigenvalues (horizontal wavenumber k) are changed little, but the eigenmodes become significantly distorted; the position of the vertical velocity peak rises compared to the zero flow case, and the velocity below that peak drops significantly. This effect may well cancel the increased estimates based on zero flow.