Pressure fluctuations at the edge of a uniform turbulent stream

Abstract

Information on the pressure at the edge of a turbulent stream is necessary for many dynamic calculations of waterworks and for the design of structures which move at high speed in water or air.

The integral theorems of hydrodynamics are used with success for estimating the time-averaged (“static”) value of the pressure. Several investigators have also applied this approach to the dynamic problems, using the connection between velocity and pressure in the form of the Bernoulli equation written for a local fluid volume or fluid filament [1]. This approach is not adequately effective, since the pressure fluctuations (in contrast with the velocity fluctuations) are determined not only by the local flow properties near the point in question, but also to a considerable degree by the kinematic conditions through the entire flow region.

The problem of pressure fluctuations at the edge of a stream was first considered in a sufficiently rigorous formulation by Corcos [2], who calculated the autocorrelation function and other characteristics of the pressure fluctuation on a thin plate. Corcos started from a linearized equation of the type (2), whose solution was represented in the form of the convolution integral of the crosscorrelation function of the pressure fluctuation and the velocity derivative δv/δx.

The Corcos method still cannot be considered perfect, since in the calculation it is necessary to start from an indirect measurement of the function being sought.

A similar problem is solved differently in the present paper. The objective of the solution, carried out in some detail at the level of the usual engineering methods, is to find an explicit connection between the kinematic characteristics of the uniform turbulent stream and the statistical parameters of the pressure fluctuation at its rigid boundary.