Laminar flow at large distances from an infinite twodimensional grid
Abstract
The twodimensional, steady, incompressible flow at large distances from an infinite grid in a uniform stream perpendicular to its plane is investigated. The NavierStokes 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 NavierStokes 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;
 NavierStokes Equation;
 Oseen Approximation;
 Steady Flow;
 Two Dimensional Flow;
 Flow Velocity;
 Integral Equations;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer