GENERAL

Turbulence is a natural phenomenon in fluids that occurs when velocity gradients are high, resulting in disturbances in the flow domain as a function of space and time. Examples include smoke in the air, condensation of air on a wall, flows in a combustion chamber, ocean waves, stormy weather, atmospheres of planets, and interaction of the solar wind with magnetosphere, among others.

Although turbulence has been the subject of intensive study for the past century, it appears that many difficulties still remain unresolved, particularly in flows with high Mach numbers and high Reynolds numbers. Turbulent flows arise in contact with walls or in between two neighboring layers of different velocities. They result from unstable waves generated from laminar flows as the Reynolds number increases downstream. With velocity gradients increasing, the flow becomes rotational, leading to a vigorous stretching of vortex lines, which cannot be supported in two dimensions. Thus, turbulent flows are always physically three-dimensional, typical of random fluctuations. This makes 2-D simplifications unacceptable in most of the numerical simulation.

In turbulent flows, large and small scales of continuous energy spectrum, which are proportional to the size of eddy motions, are mixed. Here, eddies are overlapping in space, with large ones carrying small ones. In this process, the turbulent kinetic energy transfers from larger eddies to smaller ones, with the smallest eddies eventually dissipating into heat through molecular viscosity. In direct numerical simulation (DNS), a refined mesh is used so that all of these scales, large and small, are resolved. This is known as the deterministic method.