We perform a numerical simulation of quantum turbulence produced by thermal counterflow in superfluid 4 He by using the vortex filament model with the full Biot-Savart law. The pioneering work of Schwarz has two shortcomings: it neglects the non-local terms of the Biot-Savart integral (known as the localized induction approximation, LIA) and it employs an unphysical mixing procedure to sustain the statistically steady state of turbulence. For the first time we have succeeded in generating the statistically steady state under periodic boundary conditions without using the LIA or the mixing procedure. This state exhibits the characteristic relation L = γ 2 v 2 ns between the line-length density L and the counterflow relative velocity vns and there is quantitative agreement between the coefficient γ and some measured values. The parameter γ and some anisotropy parameters are calculated as functions of temperature and the counterflow relative velocity. The numerical results obtained using the full Biot-Savart law are compared with those obtained using the LIA. The LIA calculation constructs a layered structure of vortices and does not proceed to a turbulent state but rather to another anisotropic vortex state; thus, the LIA is not suitable for simulations of turbulence.PACS numbers:

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A zero-temperature superfluid is arguably the simplest system in which to study complex fluid dynamics, such as turbulence. We describe computer simulations of such turbulence and compare the results directly with recent experiments in superfluid 3 He-B. We are able to follow the entire process of the production, evolution, and decay of quantum turbulence. We find striking agreement between simulation and experiment and gain insights into the mechanisms involved.

This paper reports results of the computation of the drag force exerted on an oscillating object in quantum turbulence in superfluid 4 He. The drag force is calculated on the basis of numerical simulations of quantum turbulent flow about the object. The drag force is proportional to the square of the magnitude of the oscillation velocity, which is similar to that in classical turbulence at high Reynolds number. The drag coefficient is also calculated, and its value is found to be of the same order as that observed in previous experiments. The correspondence between quantum and classical turbulences is further clarified by examining the turbulence created by oscillating objects.

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