The study of solar rotation has a 150-year history. Early studies were restricted to looking at the movement of sunspots; much later came studies using other tracers such as supergranules, and spectroscopic measurements using Doppler shifts of spectral lines. These studies also found evidence of other large-scale flows, such as the meridional flows in the north-south direction and the zonal flows, or torsional oscillations, parallel to the equator. However, until the 1980s, the study of solar rotation and large-scale flows was restricted to what could be observed on the solar surface. The advent of good helioseismic data changed that and gave us the means to study flows in the solar interior. Instruments like GONG, MDI and HMI have now collected helioseismic data for two solar cycles and these also allow us to study the large scale flows and their variations with time and solar activity. We review what the long data sets tell us about the these flows and discuss some of the differences between solar cycles 23 and 24.

We studied the fast kink modes of a cylindrical model of coronal loops, in coronal conditions, stratified density and low-β plasma. The mode frequencies and profiles are calculated.

We have studied spicules observed at the northern solar limb by using simultaneous high resolution image sequences. The images were obtained by Hinode/SOT (in the Ca II H passband) and TRACE (in the 1600 Å passband) during a coordinated campaign. Both data sets were reduced and then carefully co-aligned in order to compare the observed patterns in this highly dynamic region of the Sun. The identification of individual structures in both spectral bands allows us to trace their spatial and temporal behaviour. Persistent intensity variations at certain locations, indicate that at least some spicules have a recurrent behavior. Using wavelet analysis we investigate oscillatory phenomena along the axis of off-limb spicules and we construct 2-D maps of the solar limb with the observed oscillations.

We review the theoretical studies of the Alfvén wave model of spicules and coronal heating, mainly based on the papers by Kudoh & Shibata (1999), Saito et al. (2001) and Moriyasu et al. (2004) which performed MHD numerical simulations of nonlinear Alfvén waves propagating along a magnetic flux tube in the solar atmosphere. Kudoh & Shibata (1999) and Saito et al. (2001) found that, if the root mean square of the perturbation is greater than ~ 1 km s−1 in the photosphere, (1) the transition region is lifted up to more than ~ 5000 km (i.e., the spicule is produced), (2) the energy flux sufficient for heating the quiet corona (~ 3.0 × 105 ergs s−1 cm−2) is transported into the corona by Alfvén waves. Moriyasu et al. (2004) demonstrated that a hot corona is created in an initially cool loop as a result of the nonlinear Alfvén waves produced near the photosphere. We conclude that the nonlinear Alfvén wave model is the promising model of spicules and coronal heating.

Excitation of f- and p- modes by Reynolds stresses and entropy fluctuations is reviewed. Approximations made to allow semi-analytic analysis are discussed. The spectrum of solar convection is presented and shown to NOT be separable into independent spatial and temporal factors. An appropriate fitting formula is presented.

Time-distance local helioseismology has been analyzed using numerical simulations. One approach is simulation of solar surface convection on supergranule scales (48 Mm wide by 20 Mm deep). A surface shear layer develops. There is a continuous increase in the horizontal scale of the convective motions with increasing depth. Some small granular scale downflows at the surface are swept sideways by diverging larger scale upflows from below to merge into stronger downdrafts in these larger downflow boundaries. Elsewhere, some granular downflows have to beat their way against the upflows from below are halted. These simulations have a rich spectrum of f- and p- modes that turn within the computational domain. Cross-correlations between each surface location and each location below the surface reveals the wave propagation pattern from the surface. Waves at the surface that propagate into the interior, spread horizontally and are refracted back toward the surface. Time-distance diagrams have been constructed and inverted to determine the subsurface flows, which can then be compared with the average flows in the simulation.

A second approach calculates the propagation of linearized waves through a fixed, but non-uniform, background state. Some examples of such analysis are presented.

Evidence of coronal oscillations over the interior of supergranular cells was found through SUMER observations. The observations are rasters of quiet Sun regions and the oscillations were detected, in the Ne ${\sc viii}\, 770 \AA$ Doppler maps, as a characteristic pattern. It should be noted that the Ne ${\sc viii}\,$ ion has coronal formation temperature (650 000 K) and that reports of oscillations in the quiet Sun corona are scarce. Magnetic extrapolation from MDI magnetogram showed that at the location where the oscillation was detected, the gas and magnetic pressures get equalized ($\beta$=1) higher in the atmosphere, compared to the surrounding, non oscillating quiet Sun. This could indicate a non-compressible wave propagating inside the gas dominated medium of the cell causing the detected oscillation.