MOHIST APPROACH TO THE RULE-FOLLOWING PROBLEM

The Mohist conceives the dao-following issue as how we can put dao in words and speeches into practice. The dao-following issue is the Mohist counterpart of Wittgenstein\u27s rule-following problem. This paper aims to shed light on the rule-following issue in terms of the Mohist answer to the dao-following problem. The early Mohist takes fa(法, standard)and the later Mohist takes lei(類, analogy)as the key to the dao-following issue. I argue that the way of fa is not viable. Fa comes in various forms, but all of them are regarded as being cut off from everyday life and therefore subject to various interpretations and, hence, incapable of action-guiding. On the other hand, the Mohist lei represents a kind of life world action drama. A lei situates various elements of action in the context of an everyday life scene. I argue that lei is more qualified than fa in answering to the dao-following issue. I also show that lei substantializes what McDowell calls the course between a Scylla and a Charybdis hinted in terms of Wittgenstein\u27s idea of custom, practice, and institution in regard to the rule-following problem

Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence

We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but statistically stationary flow. We also develop a new method to solve the governing equations, based on the Helmholtz–Hodge decomposition, that guarantees discrete mass conservation regardless of iteration errors. Whilst some statistics were found to be sensitive to the computational box size, we show, from inner-scaled planar spectra, that the small scales exhibit similarity independent of Reynolds number, density ratio and aspect ratio. We also perform LES of the present flow using the stretched-vortex subgridscale (SGS) model. The utility of an SGS scalar flux closure for passive scalars is demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale character of the stretched-vortex SGS model is shown to enable extension of some second-order statistics to subgrid scales. Comparisons with DNS velocity spectra and velocity-density cospectra show that both the resolved-scale and SGS-extended components of the LES spectra accurately capture important features of the DNS spectra, including small-scale anisotropy and the shape of the viscous roll-off

Large-eddy simulation and wall modelling of turbulent channel flow

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Kármán-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Re_τ based on the friction velocity u_τ and the channel half-width δ in the range 2 × 10^3 to 2 × 10^7. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jiménez (2006) at Re_τ = 2003 and maintain an O(1) grid dependence on Re_τ