Triad interactions investigated by dual wave component injection

Abstract

The study of the exchange of momentum and energy between wave components of the turbulent velocity field, the so-called triad interactions, offers a unique way of visualizing and describing turbulence. Most often, this study has been carried out by direct numerical simulations or by power spectral measurements. Due to the complexity of the problem and the great range of velocity scales in high Reynolds number developed turbulence, direct measurements of the interaction between the individual wave components have been rare. In the present work, we present measurements and related computations of triad interactions between controlled wave components injected into an approximately laminar and uniform flow from an open wind tunnel by vortex shedding from two rods suspended into the flow. This results in two-dimensional interactions of three-dimensional turbulence, which makes the analysis of the triadic interactions considerably less complex to analyze than in a fully developed three-dimensional flow. With the information obtained from the computations, we are able to isolate the individual triad interactions contributing to the generated frequency components as the flow develops downstream as well as understanding, mapping out and predicting the strengths of these interactions. The analysis also provides the time constants governing the development of higher order frequency components. We are thus able to see the pattern of frequency combinations, the strengths of the individual mode combinations and the time sequence in which they occur. Any of the higher order combinations is not just the result of a single term in the Navier–Stokes Equation, but a combination of various previous combinations occurring with different strengths and in a varied pattern of generation. The combination of these experiments and computations thus provide unique insight into the inner workings of turbulence and shows how the nonlinear term in the Navier–Stokes equation on average forces the energy towards higher frequencies, which is the reason for the so-called energy cascade.