For turbulent channel flows with a uniform magnetic field perpendicular to insulated walls, the performance of the coherent structure Smagorinsky model (CSM) is investigated in comparison to the Smagorinsky model (SM) and the dynamic Smagorinsky model (DSM). The Lorentz force acts against a streamwise flow. The effect of the Hartmann flattening leads to an increase in the wall shear stress, so that the skin friction coefficient increases. In contrast, the turbulence suppression by the magnetic field results in a decrease of the Reynolds shear stress near the wall, so that the skin friction coefficient decreases. As the magnetic field increases, a turbulent magnetohydrodynamic (MHD) flow transits to a laminar MHD flow at a critical Hartmann number. The CSM predicts a higher transition Hartmann number than the DSM and SM, because the model parameter of the CSM is locally determined based on coherent structures and the fluctuations are reflected in the shear stress. On the other hand, the model parameter of the DSM is averaged in the homogeneous directions, so that the shear stress is somewhat underestimated for the subcritical Hartmann number. The SM with a model constant and a wall damping function of the Van Driest type reproduces the laminar MHD flow at the lowest transition Hartmann number, because the model parameter (which does not change in the magnetic field) provides significant energy dissipation. Moreover, the CSM and DSM can reproduce properly the laminar MHD flow at high Hartmann number, because the model parameters of the CSM and DSM are drastically damped near the wall and the Reynolds shear stresses are suppressed to zero. The skin friction coefficients predicted by the CSM and DSM agree with the “two-dimensional” laminar solution, whereas the SM gives higher values than the laminar solution. The coherent structures become large and align themselves along the magnetic field in the transition to the laminar MHD flow.

Turbulent duct flows in a uniform magnetic field are examined at low magnetic Reynolds number. Large-eddy simulation is conducted to reveal a sidewall effect on the skin friction. The duct has a square cross section and entirely insulated walls. The duct flow has two kinds of boundary layers: Hartmann layer and sidewall layer. The Hartmann layer is located on the wall perpendicular to the magnetic field, while the sidewall layer exists on the wall parallel to the magnetic field. As the magnetic field increases in the range of turbulent flows, the Hartmann layer becomes thin because of the “Hartmann flattening”—a flattening effect of the flow by the Lorentz force. The sidewall layer, however, becomes thick because of the turbulence suppression until the laminarization takes place. When the Reynolds number, Re, based on the hydraulic diameter, molecular viscosity, and bulk velocity is 5 300, the Hartmann and sidewall layers are laminarized at the same Hartmann number that is proportional to the magnetic field. When the Hartmann layer is laminarized at Re=29 000, the sidewall layer remains turbulence. This is due to a sidewall effect and is the condition that a local maximum takes place in the skin friction profile. When the sidewall layer is laminarized, the flow totally becomes laminar and the skin friction becomes minimum.

We investigate the thermal counterflow of the superfluid ${}^4\mathrm{He}$ by numerically simulating three-dimensional fully coupled dynamics of the two fluids, namely quantized vortices and a normal fluid. We analyze the velocity fluctuations of the laminar normal fluid arising from the mutual friction with the quantum turbulence of the superfluid component. The streamwise fluctuations exhibit higher intensity and longer-range autocorrelation, as compared to transverse ones. The anomalous fluctuations are consistent with visualization experiments [Mastracci et al., Phys. Rev. Fluids 4, 083305 (2019)], and our results confirm their analysis with simple models on the anisotropic fluctuations. This success validates the model of the fully coupled dynamics and paves the way for solving some outstanding problems in this two-fluid system.

The motion of quantized vortices is responsible for many intriguing phenomena in diverse quantum-fluid systems. Having a theoretical model to reliably predict the vortex motion therefore promises a broad significance. But a grand challenge in developing such a model is to evaluate the dissipative force caused by thermal quasiparticles in the quantum fluids scattering off the vortex cores. Various models have been proposed, but it remains unclear which model describes reality due to the lack of comparative experimental data. Here we report a visualization study of quantized vortex rings propagating in superfluid helium. By examining how the vortex rings spontaneously decay, we provide decisive data to identify the model that best reproduces observations. This study helps to eliminate ambiguities about the dissipative force acting on vortices, which could have implications for research in various quantum-fluid systems that also involve similar forces, such as superfluid neutron stars and gravity-mapped holographic superfluids.

Direct numerical simulation (DNS) and large eddy simulation (LES) were performed on the wall‐bounded flow at Re_τ = 180 using lattice Boltzmann method (LBM) and multiple GPUs (Graphic Processing Units). In the DNS, 8 K20M GPUs were adopted. The maximum number of meshes is 6.7 × 10⁷, which results in the nondimensional mesh size of Δ⁺ = 1.41 for the whole solution domain. It took 24 hours for GPU‐LBM solver to simulate 3 × 10⁶ LBM steps. The aspect ratio of resolution domain was tested to obtain accurate results for DNS. As a result, both the mean velocity and turbulent variables, such as Reynolds stress and velocity fluctuations, perfectly agree with the results of Kim et al. (1987) when the aspect ratios in streamwise and spanwise directions are 8 and 2, respectively. As for the LES, the local grid refinement technique was tested and then used. Using 1.76 × 10⁶ grids and Smagorinsky constant (C_s) = 0.13, good results were obtained. The ability and validity of LBM on simulating turbulent flow were verified.