![]() Acquaintance with group analysis is important for constructing and investigating nonlinear mathematical models of natural and engineering problems. The solution of interest was obtained by means of Lie symmetries first reported in. In this research, we shall analyze one particular class of the exact invariant solution associated with the nonlinear shallow water equations representing planetary equatorial waves corresponding to the free boundary problem describing the non-stationary motion of an incompressible perfect fluid propagating around a solid circle. It has been discussed in, one method of visualizing the atmospheric waves is to measure water vapor affected by Coriolis effects detected by satellites, and in order to investigate atmospheric perturbations in a form propagating wave, a novel, robust algorithm to extract ring-shape patterns from satellite and model data has been developed in. ![]() To improve seasonal weather forecasting it is important to understand and improve the predictions of the dynamics of the atmospheric waves (see also ). It was discussed earlier in that the observed breakdowns in the polar vortex are an instability caused by atmospheric waves. Also, it was pointed out in, that El Nino is directly related with the effects of atmospheric waves on the polar vortex. Moreover, the effects of atmospheric waves on variations of the ozone layer are also essential to the control of the stratospheric temperature via atmospheric radiative heating, as those effects make El Nino to be related with the observed rapid decelerations of the stratospheric polar vortex ( ). The ozone layer, and in turn stratospheric ozone, plays a crucial role in protecting our life on Earth by absorbing harmful solar ultraviolet radiation ( ). The interest in planetary waves increased dramatically increase in the 1980s when the Antarctic ozone hole was discovered ( ). It is also believed that planetary waves are responsible for widespread changes in the climate system, especially in the ozone variation (see e.g. However, the exact role of equatorial planetary waves in tropical upwelling has not been resolved so far. Additionally, planetary waves are considered as an important component of the long-term mean upwelling at the tropical tropopause and the planetary wave breaking in the extratropical stratosphere ( ). Is a continuous gradient of wind speed across the NEB, as shown in Figure 2. Data Source: Hubble Space Telescope 2007. Hi-res image of the planet showing typical comparable large-scale wave structure in the southern equatorial zone called the South Equatorial Disturbance (SED) and the North Equatorial Belt (NEB), as well as small superfast spots on the SEBn jet, and rifts in both NEB and SEB. Bounded by the retrograde jet at 17˚N on its northern edge, and the very fast prograde jet at 7˚N on its southern edge, the visibly dark belt does not always respect these limits. It is almost always a scene of notable weather formations and activity, as shown in Figure 2. For example, Jupiter’s North Equatorial Belt (NEB) is one of the broadest and darkest belts on the planet. Usually such waves are associated with large-scale perturbations of the atmospheric motion extending coherently around a full longitude circle. ![]() Equatorial waves are a key part of the tropical climate system and play a vital role in the planet’s weather and climate by transferring heat towards the poles, and cold air towards the equator. In this paper, we would like to investigate if there is some correlation between atmospheric equatorial waves and the Fibonacci spiral. These waves are wrapped into spirals by the tangential wind of the cyclone and are described as spiral gravity waves. ![]() For example, as has been discussed in, recent observational studies confirm the existence of spiral gravity waves radiating horizontally outward from tropical cyclones. Spiral like gravity waves can also exist in the atmosphere. While the aesthetics and symmetry of Fibonacci spiral patterns has often attracted scientists, a mathematical or physical explanation for their common occurrence in nature is yet to be discovered ( ). The appearance and complexity of segmented spirals are suggestive of phenomena in living systems. The segmented spirals are complex dynamical structures with several levels of organization, characterized, for example by the wavelength between successive spiral turns and the turning wavelength between segments. Ĭhemical activity, segmented spiral waves were also found in reaction-diffusion systems ( ). ![]() These images were posted in Art/Science, Paul’s Journal, Workshops. ![]()
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