This paper gives localization and nonexistence conditions of periodic orbits in some subsets of the state space. Mainly, our approach is based on high-order extremum conditions, on high-order tangency conditions of a nonsingular solution of a polynomial system with an algebraic surface, and on some ideas related to algebraically-dependent polynomials. Examples of the localization analysis of pe...

In the context of linear stability analysis, considering unsteady base flows is notoriously difficult. A generalisation modal allowing for arbitrarily over a finite time, therefore required. The recently developed optimally time-dependent (OTD) modes form projection basis tangent space. They capture leading amplification directions in state space under constraint that they an orthonormal at all...

An experimental study was performed to analyze the stability of localized streaky structure in a Blasius boundary layer. An artificial streaky structure was created by using suction or blowing through a thin spanwise slot at the wall. The velocity gradient generated by the suction or blowing was controlled by a damper. The Reynolds number based on the displacement thickness d1 was Red1 =280 at ...

Here we have demonstrated that small amplitude vibration can artificially excite both two dimensional (2D) and three (3D) instability modes. The 2D modes were typical of Tollmien–Schlichting (TS) waves provided the frequency excitation lies within unstable region neutral stability predicted by modal linear theory. However, even if mechanically forced mode was stable bounds curve harmonics gener...

Turbulence enhances the wall shear stress in boundary layers, significantly increasing drag on streamlined bodies. Other flow features such as free stream pressure gradients and streamwise layer growth also strongly influence local skin friction. In this paper, an angular momentum integral (AMI) equation is introduced to quantify these effects by representing them torques that alter shape of me...

We consider free convection near a semi-innnite vertical at plate. This problem is singularly perturbed with perturbation parameter Gr, the Grashof number. Our aim is to nd numerical approximations of the solution in a bounded domain, which does not include the leading edge of the plate, for arbitrary values of Gr 1. Thus, we need to determine values of the velocity components and temperature w...