scholarly journals Exact Solution of Navier-Stokes Equations

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Exact Solution ◽  
Potential Function ◽  
Laplace Equation ◽  
Stokes Equations ◽  
Time Function ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
3 Dimensional ◽  
Newton Potential

In Navier-Stokes equations (NASA’s Navier-Stokes Equations, 3-dimensional-unsteady), wed iscover the exact solution by Newton potential function and time-function. We think the solution likely Newton potential function that be able to solve Laplace equation

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

Particle dynamics and mixing in a viscously decaying shear layer

1991 ◽  
Vol 227 ◽  
pp. 211-244 ◽  
Author(s):  
E. Meiburg ◽  
P. K. Newton
Keyword(s):  
Exact Solution ◽  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Core Size ◽  
Mixing Processes ◽  
Navier Stokes Equations ◽  
Interface Generation ◽  
Self Similar ◽  
Detailed Picture

We study the mixing of fluid in a viscously decaying row of point vortices. To this end, we employ a simplified model based on Stuart's (1967) one-parameter family of solutions to the steady Euler equations. Our approach relates the free parameter to a vortex core size, which grows in time according to the exact solution of the Navier-Stokes equations for an isolated vortex. In this way, we approach an exact solution for small values of t/Re. We investigate how the growing core size leads to a shrinking of the cat's eye and hence to fluid leaking out of the trapped region into the free streams. In particular, we observe that particles initially located close to each other in neighbouring intervals along the streamwise direction escape from the cat's eye near opposite ends. The size of these intervals scales with the inverse square root of the Reynolds number. We furthermore examine the particle escape times and observe a self-similar blow-up for the particles near the border between two adjacent intervals. This can be explained on the basis of a simple stagnation-point flow. An investigation of interface generation shows that viscosity leads to an additional factor proportional to time in the growth rates. Numerical simulations confirm the above results and give a detailed picture of the underlying mixing processes.

Flow Due to Eccentric Rotating a Porous Disk and a Fluid at Infinity

1976 ◽  
Vol 43 (2) ◽  
pp. 203-204 ◽  
Author(s):  
M. Emin Erdogan
Keyword(s):  
Exact Solution ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Porous Disk ◽  
Navier Stokes Equations ◽  
Uniform Suction ◽  
Asymptotic Profile

An exact solution of the steady three-dimensional Navier-Stokes equations is obtained for the case of flow due to noncoaxially rotations of a porous disk and a fluid at infinity. It is shown that for uniform suction or uniform blowing at the disk an asymptotic profile exists for the velocity distribution.

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