Drag Spectra of Simple Structures in Turbulence

An approach to the problem of predicting the spectrum of the fluctuating component of the drag force on simple structures situated in turbulent flow is developed. Through an extensive use of Fourier analysis, expressions are derived which relate the drag spectrum to the general wave-number spectrum tensor of the oncoming turbulent velocity fluctuations. For the special case of isotropic turbulence considerable simplifications are achieved. The theory is applied to the study of uniplanar, uniform lattice structures and an analytic expression if found for the drag spectrum of a disk lattice in isotropic turbulence. In this case simple asymptotic results are also obtained for the high and low wavenumber regions. The drag spectrum of a square lattice in turbulent flow is evaluated by the same technique and is shown to collapse reasonably well with the disk drag spectrum, when scaled on an area basis. Comparisons are made between these theoretical results, previous theoretical work and experimental results for solid flat plates.