Nonlinear dynamics of long-wave perturbations of the Kolmogorov flow for large Reynolds numbers

The nonlinear dynamics of long-wave perturbations of the inviscid Kolmogorov flow, which models periodically varying in the horizontal direction oceanic currents, is studied. To describe this dynamics, the Galerkin method with basis functions representing the first three terms in the expansion of spatially periodic perturbations in the trigonometric series is used. The orthogonality conditions for these functions formulate a nonlinear system of partial differential equations for the expansion coefficients. Based on the asymptotic solutions of this system, a linear, quasilinear, and nonlinear stage of perturbation dynamics is identified. It is shown that the time-dependent growth of perturbations during the first two stages is succeeded by the stage of stable nonlinear oscillations. The corresponding oscillations are described by the oscillator equation containing a cubic nonlinearity, which is integrated in terms of elliptic functions. An analytical formula for the period of oscillations is obtained, which determines its dependence on the amplitude of the initial perturbation. Structural features of the field of the stream function of the perturbed flow are described, associated with the formation of closed vortex cells and meandering flow between them. As a supplement, an asymptotic analysis of nonlinear dynamics of long-wave perturbations superimposed on a damped by small viscosity Kolmogorov flow (very large, but finite Reynolds numbers) is made. It is strictly shown that all velocity components of the perturbed flow remain bounded in this case.     

Dynamic Meteorology Research in Russia, 2015–2018

Izvestiya, Atmospheric and Oceanic Physics - This review outlines the most important results of research in dynamic meteorology performed by Russian scientists in 2015–2018. It is part of the...     

On the instability of internal gravity waves propagating at small but finite angles to the vertical

The question of the instability of internal gravity waves (IGWs) propagating at small angles to the vertical is re-visited. The case of an IGW of finite-amplitude propagating at a very small but finite angle to the vertical is considered. This angle serves as a small parameter in the problem, and the instability of such an IGW is investigated by using the Fourier method and the Sivashinsky integral relations. The analysis undertaken confirms the existence of short-wave instability for small IGW amplitudes and for an arbitrarily small value of their propagation angle to the vertical. For small viscosity and thermal conductivity of the fluid medium, the growth rate of the most unstable mode is proportional to the square of the amplitude of the IGW. The results obtained may be of interest for interpreting the results of observations and confirming the existence of turbulence in the middle atmosphere.     

Analysis of changes in tornadogenesis conditions over Northern Eurasia based on a simple index of atmospheric convective instability

Doklady Earth Sciences - A simple index of convective instability (3D-index) is used for analysis of weather and climate processes that favor to the occurrence of severe convective events including...     

Statistical Distribution of Atmospheric Dust Devils on Earth and Mars

Boundary-Layer Meteorology - Numerical weather prediction is often used to supply the mean wind and turbulence fields for atmospheric transport and dispersion plume models as they provide dense...     

Hydrodynamic Instability of the Periodic System of Updrafts and Downdrafts in the Atmosphere

The linear hydrodynamic instability of the spatially periodic system of updrafts and downdrafts in a stably stratified atmosphere is studied. Such formulation of the problem is used to simulate the cloud systems observed in the atmosphere, when the zones of updrafts correspond to clouds and those of downdrafts correspond to intercloud intervals. A rather unexpected conclusion was made that the consideration of turbulent viscosity and thermal conductivity of the atmosphere as well as of radiative cooling leads to the instability at the Richardson numbers exceeding the critical value of 1/8 for the nondissipative case.     

Research in dynamic meteorology in Russia in 2011–2014

This review outlines the most significant results of research in dynamic meteorology performed by Russian scientists in 2011–2014. It is part of the Russian National Report on Meteorology and Atmospheric Sciences submitted to the International Association of Meteorology and Atmospheric Sciences (IAMAS). The report was considered and approved at the 26th General Assembly of the International Union of Geodesy and Geophysics (IUGG).¹ The review is followed by a list of key publications on dynamic meteorology of Russian scientists in 2011–2014.     

On the Theory of Symmetric Instability of Time-Periodic Flows with a Complete Account for the Coriolis Force

Izvestiya, Atmospheric and Oceanic Physics - The symmetric (inertial) parametric instability of time-periodic flows with a linear velocity profile has been investigated, with a complete account for...     

Vertical Helicity Flux as an Index of General Atmospheric Circulation

As an index of the general atmospheric circulation over the hemisphere, it is proposed to calculate the hemisphere-area-averaged (poleward of the latitude 20°) product of the Coriolis parameter by the wind velocity squared at the upper boundary of the planetary boundary layer. In practical calculations, data on the wind velocity at an isobaric level of 850 hPa were used. Control calculations for the 900 hPa level gave similar results. It is shown that the index introduced adequately characterizes the seasonal and interannual variability of the general atmospheric circulation over both hemispheres.     

Genesis environments and characteristics of the severe tornado in the South Urals on August 29, 2014

Considered are the formation conditions of the severe tornado in the South Urals (in the Republic of Bashkortostan) on August 29, 2014. It is noted that the tornado was associated with the supercell, and the synoptic conditions of its formation corresponded to the type 1 according to the classification proposed by A.I. Snitkovskii in 1987. Estimated are the tornado basic characteristics: the vortex funnel width is 150-200 m, and the maximum wind speed is 65 m/s. It is revealed that the tornado was of EF3 category following the enhanced Fujita scale. Proposed is the simple index of convective instability based on the data of ground-based observations for diagnosing the tornado genesis environments.