Spatial Decay of Time-Dependent Incompressible Navier--Stokes Flows with Nonzero Velocity at Infinity

2013 ◽  
Vol 45 (3) ◽  
pp. 1388-1421 ◽  
Author(s):  
Paul Deuring
Keyword(s):  
Time Dependent ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Stokes Flows

On the spatial decay of 3-D steady-state navier-stokes flows

2000 ◽  
Vol 25 (11-12) ◽  
pp. 2107-2117 ◽  
Author(s):  
Vladimír Šver´k ◽  
Tai-Peng Tsai
Keyword(s):  
Steady State ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Stokes Flows

Weighted spatial decay rates for the Navier–Stokes flows in a half-space

2014 ◽  
Vol 144 (3) ◽  
pp. 491-510 ◽  
Author(s):  
Pigong Han
Keyword(s):  
Half Space ◽  
Stokes Flow ◽  
Projection Operator ◽  
Decay Rates ◽  
Navier Stokes ◽  
Convection Term ◽  
Spatial Decay ◽  
Stokes Flows ◽  
Spatial Derivatives ◽  
Derivatives Of

The weighted Lq − Lr-estimates for the Stokes flow are given in half-spaces. Furthermore, the weighted decays for the first and second spatial derivatives of the Navier-Stokes flows are also established, where the unboundedness of the projection operator is overcome by employing a decomposition for the convection term. The main results in this paper are inspired by the works of Bae and Jin.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

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