Nonlinear analysis of laminar boundary layer flow over a periodic wavy surface

Abstract

The problem of laminar, incompressible flow over a periodic wavy surface is treated as a first-order perturbation to the boundary layer flow on a flat surface. The analysis demonstrates that some nonlinear terms in the disturbance boundary-layer equations are first order if the wave amplitude and disturbance sublayer thickness are comparable in magnitude. Further, the theory predicts that the nonlinear effects are confined to the thin sublayer adjacent to the wavy surface. Computer-generated, nonlinear solutions are presented for sinusoidal waves with a range of wave amplitudes, including cases with local separated flow regions.

The effective slip length and vortex formation in laminar flow over a rough surface

“…4 for different corrugation amplitudes. The maximum value of the shear stress is located at the peak of the surface corrugation (x/λ = 0.25) and it increases with increasing amplitude, which is consistent with the results of previous analytical studies of a laminar flow over a wavy wall [37,49]. The fluid tangential velocity near the boundary is proportional to the wall shear stress shown in Fig.…”

“…The laminar flow separation at the corrugated surface with the local no-slip boundary conditions depends on the depth of the grooves and the Reynolds number [36,37,38,39,40,41,42,43]. In a creeping flow over a sinusoidal surface, the flow circulation appears in sufficiently deep grooves and, as the corrugation amplitude increases, the vortex grows and remains symmetric [41,44,45].…”

Sand Ripples and Dunes

“…A promising direction is weakly nonlinear analysis, following studies in the laminar regime (Bordner 1978, Caponi et al 1982, Valance 2011) and turbulent regime (Andreotti et al 2009, Colombini & Stocchino 2008) (the coupling with the neutral mode k = 0, arising from Equation 11, has not been included in the analysis yet). Another possible direction is the development of the triple-deck theory for turbulent flow.…”

Kinneyia: A Flow-Induced Anisotropic Fossil Pattern from Ancient Microbial Mats

“…Calculating the pressure distribution above the perturbation exactly requires the full boundary layer theory to be considered. A treatment of this problem was carried out by Bordner (1978). He found that the pressure scales as ε/δ, where δ is the thickness of the disturbance sublayer in the fluid flowing above the mat, which itself scales as δ ∝ q 2/3 .…”