Quantitative properties of oscillating-grid turbulence in a homogeneous fluid

Oscillating-grid turbulence in a homogeneous fluid is in equilibrium between the diffusion of turbulent energy and the dissipation rate of the energy. Such a field has been investigated experimentally and analyzed by using the k-ε turbulence model. Vertical and horizontal components of fluctuating velocity have been measured under the vertical oscillation of a square grid. Vertical profiles of five characteristic quantities, the turbulent energy k, the dissipation rate ε, the vertical energy flux F, the eddy viscosity v(t) and a lengthscale l(t), have been obtained from the measurements. In the model analysis, the governing equations and the boundary conditions have been non-dimensionalized by using the turbulent energy k₀ and the dissipation rate ε₀ which are given virtually at the center of the grid oscillation as boundary conditions. Dimensionless analytical solutions of k, ε, F, v(t) and l(t) have been derived. The experimental data show some relationships existing between the analytical solutions. This shows the application of the k-ε model to the oscillating-grid turbulence to be valid. The analytical solutions include three model parameters. Their values have been determined from the experimental data. The values of k₀ and ε₀ have been evaluated by superposing the analytical solutions of k, ε and F on their experimental data, and have been related empirically to the experimental parameters. Using the empirical relations for k₀ and ε₀ and the analytical solutions, we can estimate k, ε, F, v(t) and l(t) of the oscillating-grid turbulence.