Steady streaming in a turbulent oscillating boundary layer

• Published in: Journal of fluid mechanics Vol. 571; pp. 265 - 280
• Main Author: SCANDURA, PIETRO
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.01.2007
• Subjects: Boundary layer and shear turbulence; Boundary layers; Exact sciences and technology; Flow rates; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic waves; Mathematical models; Physics; Simulation; Theory; Turbulence; Turbulent flow; Turbulent flows, convection, and heat transfer; Reynolds stress; Oscillating flow; Turbulent flow; Digital simulation; Modelling; Velocity distribution; Incompressible fluid; Boundary layers; Turbulence structure; Navier-Stokes equations; Pressure gradients; Flat plate
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112006002965

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.