scholarly journals Three-dimensional Navier–Stokes equations driven by space–time white noise

2015 ◽  
Vol 259 (9) ◽  
pp. 4443-4508 ◽  
Author(s):  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
White Noise ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Space Time ◽  
Navier Stokes ◽  
Navier Stokes Equations

Approximating 3D Navier–Stokes equations driven by space-time white noise

2017 ◽  
Vol 20 (04) ◽  
pp. 1750020 ◽  
Author(s):  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
White Noise ◽  
Stokes Equations ◽  
Space Time ◽  
Structure Theory ◽  
Navier Stokes ◽  
Solution Theory ◽  
Navier Stokes Equations ◽  
Drift Terms

In this paper we study approximations to 3D Navier–Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in Ref. 13. A solution theory for this equation has been developed recently in Ref. 27 based on regularity structure theory and paracontrolled distribution. In order to make the approximating equation converge to 3D NS equation driven by space-time white noise, we should subtract some drift terms in approximating equations. These drift terms, which come from renormalizations in the solution theory, converge to the solution multiplied by some constant depending on approximations.

scholarly journals Estimating intermittency in three-dimensional Navier–Stokes turbulence

2009 ◽  
Vol 625 ◽  
pp. 125-133 ◽  
Author(s):  
J. D. GIBBON
Keyword(s):  
Reynolds Number ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Space Time ◽  
Navier Stokes ◽  
Local Velocity ◽  
Vortex Sheets ◽  
Navier Stokes Equations ◽  
Local Number

The issue of why computational resolution in Navier–Stokes turbulence is hard to achieve is addressed. Under the assumption that the three-dimensional Navier–Stokes equations have a global attractor it is nevertheless shown that solutions can potentially behave differently in two distinct regions of space–time $\mathbb{S}$± where $\mathbb{S}$− is comprised of a union of disjoint space–time ‘anomalies’. If $\mathbb{S}$− is non-empty it is dominated by large values of |∇ω|, which is consistent with the formation of vortex sheets or tightly coiled filaments. The local number of degrees of freedom ± needed to resolve the regions in $\mathbb{S}$± satisfies $\mathcal{N}^{\pm}(\bx,\,t)\lessgtr 3\sqrt{2}\,\mathcal{R}_{u}^{3},$, where u = uL/ν is a Reynolds number dependent on the local velocity field u(x, t).

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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