ИСТИНА

Цель выполняемого проекта состоит в исследовании стохастической параметризации на примере трехмерных течений вязкой несжимаемой жидкости во вращающихся сферических слоях.

Studies of turbulence properties in large-scale atmospheric flows are important for modeling climate change and weather forecasting. The complex nature of atmospheric phenomena and the lack of a complete theory lead to a continuous updating of the ideas explaining the type of spectrum and the direction of the cascade of turbulence energy transfer in the upper atmosphere. The formation of circulation and turbulence in the atmosphere occurs at the Earth rotation, but one cannot ignore the influence of external influences with a wide range of time scales - from millisecond changes in the day length, the spectrum of which is close to the noise spectrum, to periodic seasonal fluctuations of the heat inflow. A number of phenomena, such as stratospheric warming and changes in the atmospheric circulation regime, are usually explained by the influence of noise. Consideration of a limited number of factors does not allow us to consider all processes occurring in the atmosphere, but allows modeling of three-dimensional turbulent flows on limited scales. The aim of the proposed project is to investigate the susceptibility of turbulence formed in three-dimensional flows of viscous incompressible fluid in rotating spherical layers to external noise in the form of random fluctuations in rotational velocity. The project involves a combination of laboratory experiment and direct calculation of three-dimensional turbulent flows using the Navier-Stokes equations for viscous incompressible fluid. The second method is an internationally accepted way to study turbulent flows, which needs neither additional averaging procedures nor additional parameters. Limitations on the size of the time integration step and the size of the computational grid cell, allowing for the resolution of Kolmogorov scales, prevent the use of the method at high Reynolds numbers. The results obtained by direct calculation can serve both as input data for climate models and determine directions for their improvement. The project participants were the first in the world to reproduce qualitatively both in a laboratory experiment and in direct calculation the type of turbulence spectra obtained earlier during in-situ measurements in the atmosphere. The project participants also obtained by direct calculation of the influence of external noise on stationary flows of viscous incompressible fluid the power dependences between the relative change in the kinetic energy of the flows and the noise amplitude, which retain their shape when the Reynolds number and the relative distance between spherical boundaries are changed. In existing weather forecast models based on ideal fluid hydrodynamics, various types of subgrid-scale parameterization are usually applied. One of them is stochastic parameterization of subgrid scales. The validity of such a subgrid parameterization is usually verified by comparing the results of climate models. The scientific novelty of the proposed project consists in the study of stochastic parameterization on the example of three-dimensional flows of viscous incompressible fluid in rotating spherical layers. It is known that far from bifurcation points, in direct calculation, when reducing the size of the computational grid cell and time integration step, convergence to a solution is observed, which we will call correct, which can be evaluated by the convergence of flow parameters to the same values. On the contrary, when the size of the computational grid cell increases, the solution moves away from the correct one; we will call it distorted. It is supposed to study the possibilities of approximation of the "distorted" solution to the "correct" one, on a "crude" grid without changing its size. The convergence of solutions will be carried out only by adding "internal" noise, the sources of which are located in all or part of the nodes of the "crude" computational grid. Thus, the results of the proposed project can be used in improving the methods of numerical weather forecasting in models with subgrid parameterization.

Полученные прямым расчетом результаты могут послужить как исходными данными для климатических моделей, так и определить направления их совершенствования.

Участниками проекта впервые в мире качественно был воспроизведен и в лабораторном эксперименте, и в прямом расчете вид спектров турбулентности, полученных ранее при натурных измерениях в атмосфере. Также участниками проекта путем прямого расчета влияния внешнего шума на стационарные течения вязкой несжимаемой жидкости получены степенные зависимости между относительным изменением кинетической энергии течений и амплитудой шума, сохраняющие свой вид при изменении чисел Рейнольдса и относительного расстояния между сферическими границами.