Methods of Calculating Turbulent Processes in the Atmosphere

Methods of Calculating Turbulent Processes in the Atmosphere

Copyright: © 2018 |Pages: 35
DOI: 10.4018/978-1-5225-2636-0.ch006
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The hydrodynamics laws describe well the laminar motion of a continuous medium where the particle trajectories and streamlines have fully defined regular character. However, random deviations, or “disturbances”, significantly change the nature of the initial motion, and cause a transition to a new or constant movement, or to some chaotic. This chapter studies forms of motion of a viscous fluid that is very common in the atmosphere and is called the turbulent motion.
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Brief Introduction

Experts in the field of hydrodynamics know that the system of equations (3.2.29) – (3.2.35) well describes the laminar motion of a continuous medium, i.e., those cases where the particle trajectories, streamlines, velocity and pressure fields in these movements have a fully defined “regular” character. The example is Poiseuille movement of viscous fluid in a circular tube. It clearly confirms the compliance of the theoretically calculated characteristics (parabolic profile of velocity, the values of flow rate and resistance) and the experimental data. Available in a variety of natural conditions, mostly small in size, random deviations, or “disturbances”, may either very little change the motion under consideration, indicating the constancy of motion with respect to small perturbations, or completely distort it, what is typical for the unsteady flow. In the latter case, small at first perturbations increase, significantly changing the nature of the initial motion, and cause a transition to a new or constant movement, or to some chaotic movement formed by liquid elemental masses (moles), irregularly moving and interacting with each other. This form of motion of a viscous fluid is very common in nature and is called the turbulent motion.

According to modern concepts, a turbulence arises from external disturbances and irregularities in the flow of a viscous fluid because of a chaotic variety of vortex tubes, thus appearing. These tubes are stretched in certain directions under the influence of deformations of the main flow and move in random directions in conjunction with each other. In the developed turbulent flow, vortex lines constantly change direction and intertwist. Vortex lines near the wall are the most confused, they can curl up in harnesses and overlap. Thus, despite the presence of the dominant direction, turbulence is essentially a three-dimensional process.

Dimensions in vortices developed turbulent flow vary widely. In order of magnitude, the size of the largest eddies is of the size of the flow region, and the size of the smallest eddies is of the size of the field, across which can be carried out the transfer of momentum, heat and mass under the action of molecular viscosity. The smaller vortices are exposed to strain created by larger vortices; in this way, there is a transfer of energy between vortices. In the process of these deformations, the vorticity of smaller vortices increases and thus increases their energy due to the energy of larger vortex. Energy can be exchanged only eddies of comparable dimensions. Thus, there is a cascade of energy transfer process between adjacent turbulent flow vortices in size, and the energy is transmitted to all of smaller vortices and ultimately converted into internal energy of the thermal motion by the action of viscous forces on the smallest eddies.

Chaotic velocity field produced by elementary eddy tubes leads to intensive mixing and the moving fluid, and, as a consequence, the exchange of momentum, heat and mass in the transverse direction. The turbulent velocity field, pressure, temperature, concentration, and other hydrodynamic quantities have a very complex structure. The complexity of the structure of these fields is due to the extremely irregular and random nature of their change in space and time. Fields of flow variables in a turbulent flow, unsteady as always, are very dependent on the initial conditions, which are generally known far from complete. At present, there is no general and universal theory of the study of these fields.

The search of acceptable for meteorological practice forms the mathematical description of turbulent processes in the atmosphere, i.e., the turbulence models, occupies the minds of many outstanding mathematicians and meteorologists for over 120 years (starting with the classic work of (Reynolds, 1895)). This is due to the exceptional complexity of the turbulence as a physical phenomenon and the fact that it is this form of turbulent air movement that is most often realized in nature.

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