Quantitative properties of oscillating-grid turbulence in a homogeneous fluid

Oscillating-grid turbulence in a homogeneous fluid is in equilibrium betwee n the diffusion of turbulent energy acid the dissipation rate of the energy . Such a field has been investigated experimentally and analyzed by using t he k-epsilon turbulence model. Vertical and horizontal components of fluctu ating velocity have been measured under the vertical oscillation of a squar e grid. Vertical profiles of five characteristic quantities, the turbulent energy k, the dissipation rate epsilon, the vertical energy flux F, the edd y viscosity v(t) and a lengthscale l(t), have been obtained from the measur ements. In the model analysis, the governing equations and the boundary con ditions have been non-dimensionalized by using the turbulent energy k(0) an d the dissipation rate Eo which are given virtually at the center of the gr id oscillation as boundary conditions. Dimensionless analytical solutions o f k, epsilon,F, nu(t) and l(t) have been derived. The experimental data sho w some relationships existing between the analytical solutions. This shows the application of the k-epsilon model to the oscillating-grid turbulence t o be valid. The analytical solutions include three model parameters. Their values have been determined from the experimental data. The values of k(0) and epsilon(0) have been evaluated by superposing the analytical solutions of k, epsilon and F on their experimental data, and have been related empir ically to the experimental parameters. Using the empirical relations for k( 0) and epsilon(0) and the analytical solutions, we can estimate k,epsilon,F , nu(t) and l(t) of the oscillating-grid turbulence. (C) 1999 The Japan Soc iety of Fluid Mechanics and Elsevier Science B.V. All rights reserved.