Helicity turbulence model: Validations and application to stellar angular-momentum transport
Helicity, as an inviscid invariant of a system of fluid equations, may contribute in a crucial way to the dynamic behaviors and statistical properties of turbulence [1,2]. It is shown that the inhomogeneous turbulent helicity enters the Reynolds-stress expression as the coupling coefficient of the mean absolute vorticity (anti-symmetric part of velocity shear), and counter-balances the eddy-viscosity coupled with the mean velocity strain (symmetric part of velocity shear) [3,4]. A subgrid-scale (SGS) turbulence model with structural effects incorporated through the SGS helicity is constructed [5] and validated with the aid of a series of high-resolution numerical simulations [6]. The helicity turbulence model is applied to the stellar convection as one of the possible prescriptions of the effective angular-momentum transport problem in a star [7].
References
[1] Pouquet, A. and Yokoi, N. Phil. Trans. Roy. Soc. A 387, 2021-0087-1-18 (2022). https://doi.org/10.1098/rsta.2021.0087
[2] Yokoi, N. "Transport in helical fluid turbulence," in Helicities in Geophysics, Astrophysics, and Beyond (Eds.) Kuzanyan, Yokoi, Gregoulis, and Stepanov, pp. 25-50 (2024). https://doi.org/10.1002/9781119841715.ch3
[3] Yokoi, N. and Yoshizawa, A. "Statistical analysis of the effects of helicity in inhomogeneous turbulence," Phys. Fluids A 5, 464-477 (1993). https://doi.org/10.1063/1.858869
[4] Yokoi, N. and Brandenburg, A. "Large-scale flow generation by inhomogeneous helicity," Phys. Rev. E, 93, 033125-1-14 (2016). https://doi.org/10.1103/PhysRevE.93.033125
[5] Yokoi, N. and Yoshizawa, A. "Subgrid-scale model with structural effects incorporated through the helicity," Progress in Turbulence VII 115-121 (2017). https://doi.org/10.1007/978-3-319-57934-4_17
[6] Yokoi, N., Mininni, P., Pouquet, A., Rosenberg, D., and Marino, R. "Helicity subgrid-scale model and its numerical validation," Phys. Fluids 1-34 (to be submitted).
[7] Yokoi, N. and Miesch, M. S. "Kinetic helicity effects in stellar angular-momentum transport," Geophys. Astrophys. Fluid Dyn. 119, 1-32 (2025). https://doi.org/10.1080/03091929.2025.2502908
Nobu Yokoi is a physicist working on analytical theories and modeling of hydrodynamic and magnetohydrodynamic turbulence. He got his PhD in 1995 at Department of Physics, University of Tokyo with the work on helicities: "Relationship of pseudoscalar invariants with the sustainment of global structures in hydrodynamic and magnetohydrodynamic turbulence". With the aid of the multiple-scale direct-interaction approximation: a combination of renormalized perturbation expansion theory and multiple-scale analysis, Nobu has explored the turbulent fluxes in inhomogeneous, anisotropic, and non-equilibrium turbulence from the fundamental equations. His interests range over the formation of large-scale vortical structures, turbulent dynamos in geophysical and astrophysical bodies, magnetic reconnection in turbulent media, transport suppression in fusion and engineering devices, the electromotive force, mass and heat transports in strongly compressible MHD turbulence, angular-momentum and energy fluxes in stellar convection, shock-wave / turbulent-boundary-layer interaction. He has collaborated with lots of applied mathematicians, physicists, astrophysicists, space and fusion plasma scientists, engineers, as well as solar physicists.