Vol 60, No 1 (2024)

A comparative analysis of the properties of two-dimensional infinitesimal periodic perturbations propagating over the incompressible fluid surface in various representations of the medium density profiles is carried out. Stratified and homogeneous in density viscous or ideal liquids are considered. Calculations are carried out by methods of the theory of singular perturbations. Dispersion relations and dependences of phase and group velocities for surface waves in physically observed variables are given. The change in the meaning of dispersion relations during the transition from ideal liquids to viscous and from homogeneous to stratified is shown. Taking into account the influence of electric charge does not qualitatively change the nature of two-dimensional dispersion relations. An increase in the surface density of the electric charge leads to a decrease in the wavelength at a fixed frequency and has no noticeable effect on the fine structure of the periodic flow.

The main multifractal properties of time series of mean, maximum and minimum daily temperatures are analyzed using the method of multifractal fluctuation analysis. As initial data, we used the results of instrumental temperature observations made at the Zugspitze meteorological station in the period from August 1, 1900 to January 31, 2023. In general, variations in the mean, maximum and minimum daily temperatures demonstrate multifractal behavior, especially for small time scales, up to about 90 days An analysis of the generalized Hurst exponent found that the considered time series have a long-term positive correlation and that the multifractality is weaker with large fluctuations. The singularity spectrum for all time series is truncated to the left, which means that the time series have a multifractal structure that is insensitive to local fluctuations of large values.

The approximation of the turbulent moments of the atmospheric convective layer is based on a variant of the local similarity theory using the concepts of the semi-empirical theory of Prandtl turbulence. In the proposed variant of the local similarity theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used as basic parameters. This approach allows us to extend Prandtl’s theory to turbulent moments of vertical velocity and buoyancy and additionally offer more than ten new approximations. The comparison of the proposed approximation with other variants of the theory of local similarity is considered. It is shown that the selected basic parameters significantly improve the agreement between the local similarity approximations and experimental data. The approximations are consistent with observations in the turbulent convective layer of the atmosphere, the upper boundary of which nearly corresponds to the lower boundary of the temperature inversion. Analytical approximations of local similarity can find applications in the construction of high-order moment closures in the vortex of resolving numerical turbulence models, as well as in the construction of “mass-flux” parametrization.

Some possibilities of using microwave radiometric measurements from the EOS Aqua and GCOM-W1 satellites to study the influence of tropical waves in the Atlantic on cyclogenesis processes in the Gulf of Mexico by monitoring the spatial and temporal variability of water vapor fields in the Gulf are illustrated. Examples of the use of satellite images of atmospheric humidity fields obtained from DMSP and EOS Aqua satellites are given to demonstrate the processes of transformation of tropical waves into Atlantic hurricanes Bonnie (1998), Frances (2004), Ivan (2004).

An adequate description of the interaction between the atmosphere and ocean remains one of the most important problems of modern oceanology and climatology. An extremely wide variety of physical processes occurring in the coupled layers, a large range of scales, a moving boundary, all this factors significantly complicates the creation of models that would allow calculating the physical characteristics in both media with the necessary accuracy. In this paper the temporal variability of dynamic parameters in the driving layer of the atmosphere and in the near-surface layer of the sea on small and sub-mesoscales from one to several tens of hours is considered. The collected experimental data show a very high correlation between the dynamic wind speed and turbulence intensity in the upper sea layer on all scales recorded. An important distinguishing feature of all measured physical quantities in both media is the presence of quasi-periodic oscillations with different periods. For a more accurate description of momentum and energy fluxes from the atmosphere a non-stationary model of turbulent exchange in the near-surface layer of the sea is proposed. The model takes into account quasi-periodicity in the intensity of dynamic interaction between the atmosphere and the sea at these scales. In the model we use the equations of momentum and turbulent energy balance, the system of equations is solved numerically, the calculation results are compared with other models and with experimental data. It is shown that taking into account the non-stationarity of the wind strain improves the correspondence between the calculations and the experimental data. It is noted that in the nonstationary case, the energy and momentum flux from the atmosphere and the turbulence intensity increases compared to the action of a constant average wind of the same duration. Therefore, the strong averaging often used in global models may markedly underestimate the intensity of the dynamic interaction between the atmosphere and ocean.