Linearized Non-Stokesian Drag in Turbulent Flow

An analytical technique has been developed which enables the nonlinear viscous drag force to be linearized. The linearized analysis was applied to the determination of a modified particle response function. It was found that nonlinear viscous drag tends to increase the particle response in a definite frequency band which tends to shift toward lower frequencies as particle size and weight are increased. It was found that in many cased of practical interest the nonlinear addition occurred at frequencies much higher than those at which the fluid's energy was contained. However, in the interpretation of the laboratory research data, inclusion of the nonlinear effects can become important because the frequency range of the fluid turbulence field is often much higher than it is under field conditions. As a result there can be significant common frequency range. The application used to illustrate the technique is but one of the uses of this theory. It is hoped that it may prove useful in others where non-Stokesian viscous drag effects must be considered. The ease with which this linearization technique can be applied to accommodate non-Stokesian drag conditions is a distinct advantage to extending the range of analytical treatment of problems of importance.