Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

Abstract: We investigate similarity solutions for the outer part of a zero-pressure-gradient turbulent boundary layer in the limit of infinite Reynolds number. Previous work by George (Phil. Trans. R. Soc. vol. 365, 2007 p. 789) has suggested that the only appropriate velocity scale for the outer region is U 1 , the free-stream velocity. This is based on the fact that scaling with U 1 leads to a mathematically valid similarity solution of the momentum equation for the outer region in the asymptotic limit of infinite Reynolds number. Here we show that the classical scaling using the friction velocity also leads to a valid similarity solution for the outer flow in this limit. Therefore on this basis it is not possible to dismiss the friction velocity as a possible scaling as has been suggested by George (2007) and others. We show that both the free-stream velocity and the friction velocity are potentially valid scalings according to this theoretical criterion.

Vortex generation and wave-vortex interaction over a concave plate with roughness and suction

Abstract: The generation and amplification of vortices by surface inhomogeneities, both in the form of surface waviness and of wall-normal velocity, is investigated using the nonlinear PSE equations. Transients and issues of algebraic growth are avoided through the use of a similarity solution as initial condition for the vortex. In the absence of curvature, the vortex decays as $ when flowing over streamwise aligned riblets of constant height, and grows as $ when flowing over a corresponding streamwise aligned variation of blowing/suction transpiration velocity. However, in the presence of wall inhomogeneities having both streamwise and spanswise periodicity, the growth of the vortex can be much larger. In the presence of curvature, the vortex develops into a "rtler vortex. The ``direct'''' and ``indirect'''' interaction mechanisms possible in wave-vortex interaction are presented. The ``direct'''' interaction does not lead to strong resonance with the flow conditions investigated. The ``indirect'''' interaction leads to K-type transition.

Viscous spreading of an inertial wave beam in a rotating fluid

Abstract: We report experimental measurements of inertial waves generated by an oscillating cylinder in a rotating fluid. The two-dimensional wave takes place in a stationary cross-shaped wavepacket. Velocity and vorticity fields in a vertical plane normal to the wavemaker are measured by a corotating particle image velocimetry system. The viscous spreading of the wave beam and the associated decay of the velocity and vorticity envelopes are characterized. They are found in good agreement with the similarity solution of a linear viscous theory, derived under a quasiparallel assumption similar to the classical analysis of Thomas and Stevenson [“A similarity solution for viscous internal waves,” J. Fluid Mech. 54, 495 (1972)] for internal waves.