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In contrast to that the model with predominantly vertical fields show downward propagation. This crucial difference in the propagation direction is also revealed in the difference in energy transported by waves for heights below 0.8 Mm. see more Higher up, the propagation properties show a peculiar behaviour, which require further study. Our analysis suggests that IGWs may play a significant role in the heating of the chromospheric layers of the internetwork region where horizontal fields are thought to be prevalent. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.Internal gravity waves have been observed in the Earth's atmosphere and oceans, on Mars and Jupiter, and in the Sun's atmosphere. Despite ample evidence for the existence of propagating gravity waves in the Sun's atmosphere, we still do not have a full understanding of their characteristics and overall role for the dynamics and energetics of the solar atmosphere. Here, we present a new approach to study the propagation of gravity waves in the solar atmosphere. It is based on calculating the three-dimensional cross-correlation function between the vertical velocities measured at different heights. We apply this new method to a time series of co-spatial and co-temporal Doppler images obtained by SOHO/MDI and Hinode/SOT as well as to simulations of upward propagating gravity wave-packets. We show some preliminary results and outline future developments. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.The suitability of solar pores as magnetic wave guides has been a key topic of discussion in recent years. Here, we present observational evidence of propagating magnetohydrodynamic wave activity in a group of five photospheric solar pores. Employing data obtained by the Facility Infrared Spectropolarimeter at the Dunn Solar Telescope, oscillations with periods of the order of 5 min were detected at varying atmospheric heights by examining Si ɪ 10827 Å line bisector velocities. Spectropolarimetric inversions, coupled with the spatially resolved root mean square bisector velocities, allowed the wave energy fluxes to be estimated as a function of atmospheric height for each pore. We find propagating magnetoacoustic sausage mode waves with energy fluxes on the order of 30 kW m-2 at an atmospheric height of 100 km, dropping to approximately 2 kW m-2 at an atmospheric height of around 500 km. The cross-sectional structuring of the energy fluxes reveals the presence of both body- and surface-mode sausage waves. Examination of the energy flux decay with atmospheric height provides an estimate of the damping length, found to have an average value across all five pores of L d  ≈ 268 km, similar to the photospheric density scale height. We find the damping lengths are longer for body mode waves, suggesting that surface mode sausage oscillations are able to more readily dissipate their embedded wave energies. This work verifies the suitability of solar pores to act as efficient conduits when guiding magnetoacoustic wave energy upwards into the outer solar atmosphere. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.Sunspots have played a key role in aiding our understanding of magnetohydrodynamic (MHD) wave phenomena in the Sun's atmosphere, and it is well known they demonstrate a number of wave phenomena associated with slow MHD modes. Recent studies have shown that transverse wave modes are present throughout the majority of the chromosphere. Using high-resolution Ca II 8542 Å observations from the Swedish Solar Telescope, we provide the first demonstration that the chromospheric super-penumbral fibrils, which span out from the sunspot, also show ubiquitous transverse motions. We interpret these motions as transverse waves, in particular the MHD kink mode. We compile the statistical properties of over 2000 transverse motions to find distributions for periods and amplitudes, finding they are broadly consistent with previous observations of chromospheric transverse waves in quiet Sun fibrils. The very presence of the waves in super-penumbral fibrils raises important questions about how they are generated, and could have implications for our understanding of how MHD wave energy is transferred through the atmosphere of a sunspot. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.We report detection of oscillations in brightness temperature, size and horizontal velocity of three small bright features in the chromosphere of a plage/enhanced-network region. The observations, which were taken with high temporal resolution (i.e. 2 s cadence) with the Atacama large millimetre/ submillimetre array (ALMA) in Band 3 (centred at 3 mm; 100 GHz), exhibit three small-scale features with oscillatory behaviour with different, but overlapping, distributions of period on the order of, on average, 90 ± 22 s, 110 ± 12 s and 66 ± 23 s, respectively. We find anti-correlations between perturbations in brightness, temperature and size of the three features, which suggest the presence of fast sausage-mode waves in these small structures. In addition, the detection of transverse oscillations (although with a larger uncertainty) may also suggest the presence of Alfvénic oscillations which are likely representative of kink waves. This work demonstrates the diagnostic potential of high-cadence observations with ALMA for detecting high-frequency magnetohydrodynamic waves in the solar chromosphere. Such waves can potentially channel a vast amount of energy into the outer atmosphere of the Sun. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.By direct measurements of the gas temperature, the Atacama Large Millimeter/submillimeter Array (ALMA) has yielded a new diagnostic tool to study the solar chromosphere. Here, we present an overview of the brightness-temperature fluctuations from several high-quality and high-temporal-resolution (i.e. 1 and 2 s cadence) time series of images obtained during the first 2 years of solar observations with ALMA, in Band 3 and Band 6, centred at around 3 mm (100 GHz) and 1.25 mm (239 GHz), respectively. The various datasets represent solar regions with different levels of magnetic flux. We perform fast Fourier and Lomb-Scargle transforms to measure both the spatial structuring of dominant frequencies and the average global frequency distributions of the oscillations (i.e. averaged over the entire field of view). We find that the observed frequencies significantly vary from one dataset to another, which is discussed in terms of the solar regions captured by the observations (i.e. linked to their underlying magnetic topology).
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