Vertical oscillations of a curved coronal slab in an inhomogeneous plasma

The influence of a few different Alfvén speed profiles V_A(z) on the development of vertical oscillations of a curved coronal slab is investigated. Three particular cases are discussed: (a) dV_A/dz < 0, (b) dV_A/dz = 0, (c) dV_A/dz > 0. These cases correspond respectively to the presence of wave tunnelling into the ambient medium above the slab (a), lack of any tunnelling (b), and tunnelling into the ambient medium below the slab (c). Two-dimensional ideal magnetohydrodynamic equations are solved by numerical means and the slab oscillations are triggered impulsively by an initial pulse in the vertical component of the momentum. We find that vertical oscillations exhibit time-signatures with characteristic wave period P and attenuation time τ. These parameters vary with V_A(z). A smallest value of P is associated with the case of (c). A strongest attenuation (smallest τ) of vertical oscillations takes place in the case of (a). A simple model of coronal loop oscillations leads to numerical results which are akin to the observational data of Wang and Solanki (2004).