Laminar flow at large distances from an infinite two-dimensional grid
Abstract
The two-dimensional, steady, incompressible flow at large distances from an infinite grid in a uniform stream perpendicular to its plane is investigated. The Navier-Stokes equations are linearized in the Oseen fashion and each grid element is represented by a force concentrated at a point. The solution is obtained in two different ways, as a superposition of infinitely many elementary solutions of the Oseen equations, and by separation of variables. It is found that both velocity and pressure decay exponentially to their values at upstream and downstream infinity. Our solution differs essentially from an exact solution of the Navier-Stokes equations found by Kovasznay who considers it as representing the flow behind a grid. Several arguments are given to show that Kovasznay's physical interpretation of his solution is incorrect, even at large distances.
- Publication:
-
Journal de Mecanique
- Pub Date:
- 1976
- Bibcode:
- 1976JMec...15..209P
- Keywords:
-
- Incompressible Flow;
- Laminar Flow;
- Navier-Stokes Equation;
- Oseen Approximation;
- Steady Flow;
- Two Dimensional Flow;
- Flow Velocity;
- Integral Equations;
- Reynolds Number;
- Fluid Mechanics and Heat Transfer