Non-linear aspects of Görtler instability in boundary layers with pressure gradient

Abstract

The laminar flow over a concave surface may undergo transition to a turbulent state driven by secondary instabilities initiated by the longitudinal vortices known as Görtler vortices. These vortices distort the boundary layer structure by modifying the streamwise velocity component in both spanwise and wall-normal directions. Numerical simulations have been conducted to identify the role of the external pressure gradients in the development and saturation of the vortices. The results show that flows with adverse pressure gradients reach saturation upstream from the saturation location for neutral and favorable pressure gradients. In the transition region, the mean spanwise shear stress is about three times larger than in the flow without the vortices.

Görtler vortices and streaks in boundary layer subject to pressure gradient: excitation by free stream vortical disturbances, nonlinear evolution and secondary instability

“…This conclusion was confirmed by the marching method calculations with the upstream condition being taken to be an eigenmode or a more or less arbitrary disturbance velocity distribution (Goulpié et al 1996; Matsson 2008). Rogenski, de Souza & Floryan (2016) performed simulations using the linearised Navier–Stokes (N–S) equations, which require an artificial ‘buffer region’. Spanwise periodic suction/blowing was introduced to excite Görtler vortices, and different forms of pressure gradient were considered.…”

Effect of Pressure Gradient on the Development of Görtler Vortices

“…The results for the nonlinear development and saturation of Görtler vortices obtained by Matsson (2008) can be compared with the results obtained by Souza and his group (Rogenski et al 2013;2016a;2016b), who have been using direct numerical simulation (DNS) to study the development of Görtler vortices in boundary layers with pressure gradient. In a first paper Rogenski et al (2013) studied the effect of curvature variation on the nonlinear development of Görtler vortices as a way to control their growth and consequent transition to turbulence.…”

“…The non-linear regime was further explored by Rogenski et al (2016b). They studied the development of Görtler vortices up to the nonlinear breakdown stage in boundary layers with pressure gradient.…”

“…The energy at the saturation point is also higher for adverse pressure gradient. Three different spanwise wavenumbers were tested by Rogenski et al (2016b), Λ = 160, 305 and 450. They show that the saturation point depends also on the wavenumber.…”

Investigation of the concave curvature effect for an impinging jet flow

“…It has been shown recently that pressure gradients affect the Görtler instability for boundary layer flows [75]. Indeed, Rogenski et al [75] have reported an alteration of the nonlinear development of Görtler vortices caused by an earlier saturation in the presence of an adverse pressure gradient (APG) compared to the zero pressure gradient case. On the other hand, a favorable pressure gradient (FPG) delays the saturation.…”