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Decaying homogeneous, isotropic turbulence is investigated using a phenomenological model based on the three-dimensional turbulent energy spectra. We generalize the approach first used by Comte-Bellot and Corrsin [J. Fluid Mech. 25, 657 (1966)] and revised by Saffman [J. Fluid Mech. 27, 581 (1967); Phys. Fluids 10, 1349 (1967)]. At small wave numbers we assume the spectral energy is proportional to the wave number to an arbitrary power. The specific case of power 2, which follows from the Saffman invariant, is discussed in detail and is later shown to best describe experimental data. For the spectral energy density in the inertial range we apply both the Kolmogorov −5/3 law, E(k)=Cε2/3k−5/3, and the refined Kolmogorov law by taking into account intermittency. We show that intermittency affects the energy decay mainly by shifting the position of the virtual origin rather than altering the power law of the energy decay. Additionally, the spectrum is naturally truncated due to the size of the wind tunnel test section, as eddies larger than the physical size of the system cannot exist. We discuss effects associated with the energy-containing length scale saturating at the size of the test section and predict a change in the power law decay of both energy and vorticity. To incorporate viscous corrections to the model, we truncate the spectrum at an effective Kolmogorov wave number kη=γ(ε/v3)1/4, where γ is a dimensionless parameter of order unity. We show that as the turbulence decays, viscous corrections gradually become more important and a simple power law can no longer describe the decay. We discuss the final period of decay within the framework of our model, and show that care must be taken to distinguish between the final period of decay and the change of the character of decay due to the saturation of the energy containing length scale. The model is applied to a number of experiments on decaying turbulence. These include the downstream decay of turbulence in wind tunnels and a water channel, the temporal decay of turbulence created by an oscillating grid in water and the decay of energy and vorticity created by a towed grid in a stationary sample of water. We also analyze decaying vorticity data we obtained in superfluid helium and show that decaying superfluid turbulence can be described classically. This paper offers a unified investigation of decaying isotropic, homogeneous turbulence that is based on accepted forms of the three-dimensional turbulent spectra and a variety of experimental decay data obtained in air, water, and superfluid helium.

The results of a number of recent experiments on high Reynolds number grid turbulence in helium II suggest that its flow on large length scales resembles that of a classical fluid. It has been known for some time that the effective kinematic viscosity of this turbulent fluid, describing energy flow in the inertial range of wave numbers, is of the order of η/ρ where η is the normal fluid viscosity and ρ is the total density of the liquid. However, dissipation must be strongly influenced by quantum processes, and it cannot be associated simply with the normal-fluid viscosity. The importance of quantum processes arises because the dissipation occurs at small length scales, comparable with the spacing of the quantized vortex lines that allow turbulent motion in the superfluid component. We report an analysis of experimental data that allows us to deduce experimental values of the effective kinematic viscosity, which we call ν′(≠η/ρ), to which theories of the quantum dissipative processes can be compared.

We have studied oscillatory flow through a 180° curved tube with the ratio of tube radius to radius of curvature equal to 1/7. The flow rate is constrained to vary sinusoidally about a non-zero mean at a specified period T, and mean flow rate Q. At a certain parameter range of interest Hamakiotes & Berger (1990) predict that fully developed flow undergoes a period-tripling bifurcation. Our measurements using laser-Doppler velocimetry found no bifurcation. An additional experiment was done to ensure that the flow was fully developed.

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