Self-similar solution of the Navier-Stokes equations governing gas flows in rotary logarithmically spiral two-dimensional channels

1995 ◽  
Vol 30 (6) ◽  
pp. 838-844
Author(s):  
S. N. Aristov ◽  
V. I. Grabovskii
Keyword(s):  
Stokes Equations ◽  
Similar Solution ◽  
Navier Stokes ◽  
Gas Flows ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Existence of Leray's Self-Similar Solutions of the Navier-Stokes Equations In 𝒟 ⊂ ℝ3

2004 ◽  
Vol 47 (1) ◽  
pp. 30-37
Author(s):  
Xinyu He
Keyword(s):  
Boundary Condition ◽  
Stokes Equations ◽  
Local Existence ◽  
Similar Solution ◽  
Navier Stokes ◽  
Smooth Bounded Domain ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar ◽  
Similar Solutions

AbstractLeray's self-similar solution of the Navier-Stokes equations is defined bywhere . Consider the equation for U(y) in a smooth bounded domain D of with non-zero boundary condition:We prove an existence theorem for the Dirichlet problem in Sobolev space W1,2(D). This implies the local existence of a self-similar solution of the Navier-Stokes equations which blows up at t = t* with t* < +∞, provided the function is permissible.

scholarly journals Far Field of a Three-Dimensional Laminar Wall Jet

2021 ◽  
Vol 56 (6) ◽  
pp. 812-823
Author(s):  
I. I. But ◽  
A. M. Gailfullin ◽  
V. V. Zhvick
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Plane Surface ◽  
Three Dimensional ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar

Abstract We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

The self-similar solutions to full compressible Navier–Stokes equations without heat conductivity

2019 ◽  
Vol 29 (12) ◽  
pp. 2271-2320
Author(s):  
Xin Liu ◽  
Yuan Yuan
Keyword(s):  
Small Perturbation ◽  
Heat Conductivity ◽  
Stokes Equations ◽  
The Self ◽  
Similar Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Self Similar Solution ◽  
Self Similar ◽  
Similar Solutions

In this work, we establish a class of globally defined large solutions to the free boundary problem of compressible full Navier–Stokes equations with constant shear viscosity, vanishing bulk viscosity and heat conductivity. We establish such solutions with initial data perturbed around the self-similar solutions when [Formula: see text]. In the case when [Formula: see text], solutions with bounded entropy can be constructed. It should be pointed out that the solutions we obtain in this fashion do not in general keep being a small perturbation of the self-similar solution due to the second law of thermodynamics, i.e. the growth of entropy. If, in addition, in the case when [Formula: see text], we can construct a solution as a global-in-time small perturbation of the self-similar solution and the entropy is uniformly bounded in time. Our result extends the one of Hadžić and Jang [Expanding large global solutions of the equations of compressible fluid mechanics, J. Invent. Math. 214 (2018) 1205.] from the isentropic inviscid case to the non-isentropic viscous case.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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