Том 54, № 5 (2018)

The problem of finding optimal perturbations, which are perturbations with a maximum ratio of the final energy to the initial energy, is considered in the Eady model of baroclinic instability. The solution to the problem uses explicit expressions for the energy functional, which are functions of parameters of an initial perturbation. For perturbations with zero potential vorticity, the basic parameters are the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and a phase shift between these distributions. Dependences of the optimal phase shift and maximum energy ratio on the wave number and time optimization are determined using an analysis for extremum. The parameters of the optimal perturbations are compared with those of the growing normal modes. It is found that only one exponentially growing mode is an optimal perturbation.

Latitudinal position and wind speed of the Southern Hemisphere subtropical jet stream have been investigated on the basis of ERA-Interim, JRA-55, and NCEP–NCAR reanalysis data for 1948–2013. The analysis covers different time intervals in summer and winter seasons, as well as different spatial domains. It has been shown that the variability of the southern jet stream parameters in both winter and summer seasons is predominantly characterized by wind-speed weakening on the jet-stream axis and its poleward shift. The winter seasons of 2000–2013 identified a shift in the jet-stream axis toward the equator in the Atlantic (60°–0° W) and African (0°–60° E) sectors; the wind-speed increase in the Atlantic sector was statistically significant. The wind speed on the jet-stream axis in both winter and summer is closely related to the temperature difference in the upper tropospheric layer of 200–400 hPa between the latitudinal zones of 0°–30° S and 30°–60° S. A significant negative correlation (r = −0.78) between wind speed and temperature difference has been revealed for the winter season in the upper tropospheric layer between the latitudinal zones of 30°–60° S and 60°–90° S, which can be explained by the Southern Annular Mode variability in this season. No such relationship has been found for the summer season.

In August 2014, measurements of the turbulent velocity rotor, turbulent temperature gradient, turbulent helicity, and turbulent potential vortex were performed at the Obukhov Institute of Atmospheric Physics testing ground in Tsimlyansk under different stratification conditions. The measurements were carried out using the technique first used in the Tsimlyansk expedition in 2012 [1]. The measuring facility consisted of four three-component acoustic Gill Windmaster anemometers–thermometers placed at the vertices of a rectangular tetrahedron with a base scale of 0.7 m (in contrast to the experiment in 2012, when the base scale was 5 m). The measuring facility was placed on top of a mast with an adjustable height of 3.5, 5, 13.5, and 25 m and was equipped with a rotator. The temperature profile in the 10–600 m layer was continuously recorded by the Kadygrov microwave profiler [2]. The series of density of instantaneous helicity He = u_i'ω'_i = u₁'ω₁' + u₂'ω'₂ + u₃'ω'₃ and average values of the total and its summands were calculated for 12 daytime and 10 daytime 2-hour intervals. The helicity value averaged over 12 day realizations is about 0.2 m/s², and the average cosine is close to 0.08 ± 0.03. At night, the helicity is estimated as 0.07 ± 0.03 m/s², and the cosine is close to 0.025 ± 0.03. For the abovementioned 12 daytime and 10 daytime 2-hour intervals, the covariance and correlation matrices of temperature components, velocity rotor, velocity, and temperature gradient are calculated. The off-diagonal terms of the covariance matrix exceed by absolute values the diagonal terms several times. Similar characteristics of a potential vortex were estimated in the incompressibility approximation. The systematic error due to spatial averaging of the measured quantities is discussed.

Micrometeorological measurements in the atmospheric boundary layer over a hilly forest terrain have been made on a meteorological tower at several levels from the forest canopy top to a height that exceeds the height of trees almost seven times. A semiempirical length scale depending on the local topography features and the underlying surface type has been proposed and calculated. This scale has been shown to allow the universal functions of the Monin–Obukhov similarity theory to be corrected for a stable atmospheric boundary layer over complex terrain without substantial modification when compared to the universal functions over a homogeneous surface with small roughness elements. This approach can be used to refine the methods for calculating turbulent momentum fluxes from profile measurements over spatially inhomogeneous landscapes.

The problem of the optimal control of aerosol emissions into the stratosphere to stabilize the Earth’s climate is considered based on the zero-dimensional energy balance model. The global surface-temperature deviation from the undisturbed value is the state variable, and the albedo of the artificial aerosol layer, whose time variations are functionally related to the change in the total mass of aerosol particles and, consequently, the rate of their emissions, is the control variable. The problem is solved with and without consideration for the system phase path and control variable constraints for the given performance measure (objective function). Unlike previous studies, the aerosol emission scenarios are not set a priori, but represent a rigorous solution of the optimal control problem, ensuring the minimization of the objective function. The method is illustrated using the RCP8.5 scenario of growing concentration of greenhouse gases in the atmosphere. The approach considered in this paper can be easily extended to the cases of applying other known methods of climate engineering to manipulate the climate.

The algorithm for splitting k–ω turbulence equations is used to parameterize viscosity and diffusion coefficients in the ocean general circulation model. The k–ω equations are split into stages describing the transport-diffusion and generation-dissipation of the turbulent kinetic energy and frequency function ω. At the generation-dissipation stage, the equations are solved analytically. Calculations of circulation in the North Atlantic–Arctic Ocean for 1948–2009 have been carried out. The experiments demonstrate an adequate reproduction of hydrophysical characteristics and high efficiency of the algorithm. It is shown that considering the climatic annual mean buoyancy frequency in the turbulence equations at the generation-dissipation stage is an important factor in improving the accuracy of simulated fields.