Starting from the Navier-Stokes equation, we rigorously prove that a modi ed third order structure function ~ S 3 (r) asymptotically equals 4 r=3 ( is the dissipation rate) in the large Reynolds number limit of Navier-Stokes equation in an inertial regime. From this result, we rigorously con rm the Kolmogorov fourfth law, without the Kolmogorov assumption on isotropy. Our de nition of the struc...

A composite model for area-average Nusselt number for forced, laminar  ow parallel to a Ž nite, isothermal rectangular plate for a wide range of Reynolds numbers is proposed. The correlation equation is based on the superposition of the dimensionless shape factor and a modiŽ ed laminar  ow boundary-layer asymptote with an empirically determined interpolation parameter. The Nusselt and Reynold...

The Reynolds equation, which describes the lubrication effect arising through the interaction of two physical surfaces that are separated by a thin fluid film, is formulated with respect to a continuously evolving third surface that is described by a time-dependent curvilinear coordinate system. The proposed formulation essentially addresses lubrication mechanics at interfaces undergoing large ...

Usually the Stokes equations that govern a flow in a smooth thin domain (with thickness of order ε) are related to the Reynolds equation for the pressure psmooth. In this paper, we show that for a rough thin domain (with rugosities of order ε) the flow is governed by a modified Reynolds equation for a pressure prough. Moreover we find the relation prough = K psmooth where K is an explicit coeff...

This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial interactions and the molecule Brownian diffusivities is found to be the bi-fractal mechanism behind multifractal scaling in the inertial range of scales of moderate Rey...

This paper introduces an improved friction model accounting for elastoplastic behavior of interacting asperities along contiguous rough surfaces for a line contact solution. It is based on Greenwood and Tripp’s original boundary friction model and specifically tailored for a boundary regime of lubrication. The numerical solution of Reynolds’ equation is achieved by implementing Elrod’s cavitati...

A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cϵ=Cϵ,∞+C/R-+O(1/R-(2)), where R- is a generalized Reynolds number. The constant Cϵ,∞ describes the total energy transfer flux. This flux ...