Quasi-periodic pulsations (or QPPs) are periodic intensity variations in the flare emission, across all wavelength bands. In this paper, we review the observational and modelling achievements since the previous review on this topic by Nakariakov and Melnikov (2009). In recent years, it has become clear that QPPs are an inherent feature of solar flares, because almost all flares exhibit QPPs. Moreover, it is now firmly established that QPPs often show multiple periods. We also review possible mechanisms for generating QPPs. Up to now, it has not been possible to conclusively identify the triggering mechanism or cause of QPPs. The lack of this identification currently hampers possible seismological inferences of flare plasma parameters. QPPs in stellar flares have been detected for a long time, and the high quality data of the Kepler mission allows to study the QPP more systematically. However, it has not been conclusively shown whether the time scales of stellar QPPs are different or the same as those in solar flares.

Space Sci. Rev. manuscript No.

Quasi-periodic pulsations (QPP) of microwave emission generated in single flaring loops observed with the Nobeyama Radioheliograph (NoRH) and Nobeyama Radio Polarimeters (NoRP) are studied. Specific features of the time profiles, i.e. the visible presence or absence of QPPs, are not accounted for in the selection. The time evolution of the periods of the QPPs is examined using wavelet and correlation analyses. In ten out of twelve considered events, at least one or more significant spectral components with periods from 5 -60 s have been found. The quality of the oscillations is rather low: Q = πN, where N is the number of cycles, mostly varies in the range 12 to 40, with an average of 25. We suggest that the detected QPPs can be classified into four types: i) those with stable mean periods (e.g. of 15 -20 s or 8 -9 s, the prevailing type); ii) those with spectral drift to shorter periods (mostly in the rise phase of the microwave emission); iii) those with drift to longer periods (mostly in the decay phase); iv) those with multiple periods showing an X-shaped drift (e.g. in the range from 20 -40 s in the rise phase).

Context. Fast magneto-acoustic waves are highly dispersive in waveguides, so they can generate quasi-periodic wave trains if a localised, impulsive driver is applied. Such wave trains have been observed in the solar corona and may be of use as a seismological tool since they depend upon the plasma structuring perpendicular to the direction of propagation. Aims. We extend existing models of magnetoacoustic waveguides to consider the effects of an expanding magnetic field. The funnel geometry employed includes a field-aligned density structure. Methods. We performed 2D numerical simulations of impulsively generated fast magneto-acoustic perturbations. The effects of the density contrast ratio, density stratification, and spectral profile of the driver upon the excited wave trains were investigated. Results. The density structure acts as a dispersive waveguide for fast magneto-acoustic waves and generates a quasi-periodic wave train similar to previous models. The funnel geometry leads to generating additional wave trains that propagate outside the density structure. These newly discovered wave trains are formed by the leakage of transverse perturbations, but they propagate upwards owing to the refraction caused by the magnetic funnel. Conclusions. The results of our funnel model may be applicable to wave trains observed propagating in the solar corona. They demonstrate similar properties to those found in our simulations.