Reynolds stress equation model (RSM), also referred to as second moment closures are the most complete classical turbulence model. In these models, the...

To obtain equations containing only the mean velocity and pressure, we need to close the RANS equations by modelling the Reynolds stress term R i j {\displaystyle...

the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account...

Model: used when there are wall effects present within the case. Reynolds stress equation model: In case of complex turbulent flows, Reynolds stress models...

The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds...

fluid dynamics, the mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a Newtonian fluid boundary...

the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a...

independent of the Reynolds number (and thus the velocity) only in the case of rough pipes in a turbulent flow regime (Prandtl-von Kármán equation). In a cylindrical...

background models. In the frame work of single-point closures (Reynolds-stress transport models = RSTM) still provide the best representation of flow physics...

the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modelling provides a model of the effects of the turbulent...

"Two Equation" model because two transport equations (one for k {\displaystyle k} and one for ϵ {\displaystyle \epsilon } ) are solved. Reynolds stress model...

viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed...

turbulence stress tensor for the acoustic field. The Lighthill equation is an inhomogenous wave equation. Using Einstein notation, Lighthill’s equation can be...

same time. Reynolds number Reynolds analogy Reynolds equation Reynolds transport theorem Reynolds decomposition Reynolds stress Reynolds-averaged Navier–Stokes...

particle Reynolds number called the boundary Reynolds number. The mathematical solution of the equation was given by Dey. In general, a particle Reynolds number...

where σ is the Cauchy stress tensor, and f accounts for body forces present. This equation is called the Cauchy momentum equation and describes the non-relativistic...

the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model. The...

more complex models, such as the Darcy–Weisbach equation. The ratio of length to radius of a pipe should be greater than 1/48 of the Reynolds number for...

continuity equation holds), (unit: k g / m 3 {\displaystyle \mathrm {kg/m^{3}} } ) σ {\displaystyle {\boldsymbol {\sigma }}} is the stress tensor, (unit:...

full Navier-Stokes equations with k-epsilon, SST, k-omega and Reynolds stress, and large eddy simulation (LES) turbulence models, by numerically solving...

Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl, Theodore von Kármán), while various scientists such as Osborne Reynolds, Andrey...

crystalline solid). On the other hand, a crack introduces a stress concentration modeled by Inglis's equation σ e l l i p t i c a l   c r a c k = σ a p p l i e...

object.[citation needed] At low Reynolds number the same equation reduces to a diffusion equation, named Stokes equation − ∇ ∗ p ∗ + ∇ ∗ 2 u ∗ = 0 . {\displaystyle...

are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier–Stokes equations, are modelled by a linear constitutive...

is modeled by nonlinear partial differential equations and the stability of known steady and unsteady solutions are examined. The governing equations for...

the properties of a Reynolds operator. The governing equations of LES are obtained by filtering the partial differential equations governing the flow field...

stress) general Cauchy momentum equation becomes an inhomogeneous Burgers equation (here we make explicit the material derivative): Burgers equation (nondimensional...

equations is known as the Reynolds shear stress and is unknown a priori. The solution of the turbulent boundary layer equations therefore necessitates the...

using bulk atmospheric formulae, the equation above is the semi-empirical bulk formula for the surface wind stress. The height at which the wind speed...

Navier-Stokes equation the requirement is that terms of order ε2 and ε2Re are negligible, where ε ≪ 1 is the aspect ratio and Re is the Reynolds number. This...