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2. Reynolds-averaged Navier–Stokes equations - Wikipedia

   en.wikipedia.org/wiki/Reynolds-averaged_Navier...

   The basic tool required for the derivation of the RANS equations from the instantaneous Navier–Stokes equations is the Reynolds decomposition.Reynolds decomposition refers to separation of the flow variable (like velocity ) into the mean (time-averaged) component (¯) and the fluctuating component (′).

3. Reynolds equation - Wikipedia

   en.wikipedia.org/wiki/Reynolds_Equation

   The equation can either be used with consistent units or nondimensionalized. The Reynolds Equation assumes: The fluid is Newtonian. Fluid viscous forces dominate over fluid inertia forces. This is the principle of the Reynolds number. Fluid body forces are negligible.

4. Derivation of the Navier–Stokes equations - Wikipedia

   en.wikipedia.org/wiki/Derivation_of_the_Navier...

   The derivation of the Navier–Stokes equation involves the consideration of forces acting on fluid elements, so that a quantity called the stress tensor appears naturally in the Cauchy momentum equation. Since the divergence of this tensor is taken, it is customary to write out the equation fully simplified, so that the original appearance of ...

5. Reynolds stress - Wikipedia

   en.wikipedia.org/wiki/Reynolds_Stress

   In fluid dynamics, 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 for turbulent fluctuations in fluid momentum.

6. Reynolds decomposition - Wikipedia

   en.wikipedia.org/wiki/Reynolds_decomposition

   Reynolds decomposition allows the simplification of the Navier–Stokes equations by substituting in the sum of the steady component and perturbations to the velocity profile and taking the mean value. The resulting equation contains a nonlinear term known as the Reynolds stresses which gives rise to turbulence.

7. Dynamic similarity (Reynolds and Womersley numbers)

   en.wikipedia.org/wiki/Dynamic_similarity...

   From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length. [5] By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer ...