scholarly journals A Low-Frequency Assumption for Optimal Time-Decay Estimates to the Compressible Navier–Stokes Equations

2019 ◽  
Vol 371 (2) ◽  
pp. 525-560 ◽  
Author(s):  
Jiang Xu
Keyword(s):  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Optimal Time ◽  
Decay Estimates ◽  
Time Decay ◽  
Navier Stokes Equations

scholarly journals Time-Decay Estimates for Linearized Two-Phase Navier–Stokes Equations with Surface Tension and Gravity

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 761
Author(s):  
Hirokazu Saito
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensional Euclidean Space ◽  
Decay Estimates ◽  
Time Decay ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Linearized Equations ◽  
Estimates Of Solutions

The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible viscous flow with a sharp interface that is close to the hyperplane xN=0 in the N-dimensional Euclidean space, N≥2. It is well-known that the Rayleigh–Taylor instability occurs when the upper fluid is heavier than the lower one, while this paper assumes that the lower fluid is heavier than the upper one and proves time-decay estimates of Lp-Lq type for the linearized equations. Our approach is based on solution formulas for a resolvent problem associated with the linearized equations.

Optimal time decay of the compressible Navier–Stokes equations for a reacting mixture

Nonlinearity ◽  
2021 ◽  
Vol 34 (9) ◽  
pp. 5955-5978
Author(s):  
Zefu Feng ◽  
Guangyi Hong ◽  
Changjiang Zhu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Time ◽  
Time Decay ◽  
Navier Stokes Equations

Low-Frequency Fluctuations In The Flow Over Confined Cylinder In A Narrow Rectangular Duct At Re = 3 750

2017 ◽  
Vol 12 (1) ◽  
pp. 43-49
Author(s):  
Egor Palkin ◽  
Rustam Mullyadzhanov
Keyword(s):  
Stokes Equations ◽  
Low Frequency ◽  
Horseshoe Vortex ◽  
Navier Stokes ◽  
Infinite Cylinder ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Frequency Modulations ◽  
Bounding Surfaces

Flows between two closely spaced bounding surfaces are frequently appear in engineering applications and natural flows. In current paper the flow over a cylinder in a narrow rectangular duct was investigated by numerical computations of Navier-Stokes equations using Large eddy simulations (LES) at ReD = 3 750 based on cylinder diameter and the bulk velocity at inflow boundary. The influence of the bounding walls was demonstrated by comparing mean flow streamlines with the flow over an infinite cylinder at close Reynolds numbers. A comparison between the time-averaged velocity field in front and past the cylinder with experimental from the literature data showed good agreement although the characteristic horseshoe vortex structures are highly sensitive to Reynolds number and turbulence level at inflow boundary. Most energetic modes in recirculating region were revealed by spectral analysis. These low-frequency modulations were characterized by the pair of dominating vortices which are expected to have high influence on the heat transfer in near wake of the cylinder.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

Wave propagation for the compressible Navier–Stokes equations

2015 ◽  
Vol 12 (02) ◽  
pp. 385-445 ◽  
Author(s):  
Tai-Ping Liu ◽  
Se Eun Noh
Keyword(s):  
Green Function ◽  
Stokes Equations ◽  
Low Frequency ◽  
Explicit Construction ◽  
Large Time Behavior ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
The Green Function

We establish the pointwise description of solutions to the isentropic Navier–Stokes equations for compressible fluids in three spatial dimensions. First, we give an explicit construction of the Green function for the linearized system. The Green function consists of singular waves, which dominate the short-time behavior, while the low frequency waves, the dissipative Huygens, diffusion and Riesz waves representing the large-time behavior. The nonlinear terms are treated by a suitable combination of energy estimates and pointwise estimates using the Duhamel's principle for the Green function.

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