Fundamental Aspects Of Incompressible And Compressible Turbulent Flows

Turbulence generally can be characterized by a number of length scales: at least one for the energy containing range, and one from the dissipative range; there may be others, but they can be expressed in terms of these. Whether a turbulence is simple or not depends on how many scales are necessary to describe the energy containing range. Certainly, if a turbulence involves more than one production mechanism (such as shear and buoyancy, for example, or shear and density differences in a centripetal field) there will be more than one length scale. Even if there is only one physical mechanism, say shear, a turbulence which was produced under one set of circumstances may be subjected to another set of circumstances. For example, a turbulence may be produced in a boundary layer, which is then subjected to a strain rate. For a while, such turbulence will have two length scales, one corresponding to the initial boundary layer turbulence, and the other associated with the strain rate to which the flow is subjected. Or, a turbulence may have different length scales in different directions. Ordinary turbulence modeling is restricted to situations that can be approximated as having a single scale of length and velocity. Turbulence with multiple scales is much more complicated to predict. Some progress can be made by applying rapid distortion theory, or one or another kind of stability theory, to the initial turbulence, and predicting the kinds of structures that are induced by the applied distortion. We will talk more about this later. For now, we will restrict ourselves to a turbulence that has a single scale of length in the energy containing range.