Steady and unsteady Görtler boundary-layer instability on concave wall - Boiko, A.V.; Ivanov, A.V.; Kachanov, Y.S.; Mischenko, D.A. (European journal of mechanics, B, Fluids, 2010)
The subject of the present combined experimental and theoretical investigation is the steady and unsteady linear Görtler instability. The majority of previous experiments were devoted to the steady Görtler vortices, despite the unsteady ones are also observed in real transitional flows. Moreover, even for the steady Görtler vortices no quantitative agreement between the experimental and theoretical linear-stability characteristics was obtained, especially for disturbance amplification rates. The experimental difficulties were connected, in particular, with a rather poor accuracy of measurements at zero disturbance frequency, a possible influence of nonlinearity, and an admixture of non-modal (transient) growth mechanism. All these difficulties have been overcome in the experimental part of the present study by means of: ( i) tuning-out of the exact zero frequency of Görtler vortices and working, instead, with quasi-steady perturbations of very low frequencies, ( ii) performing measurements at low disturbance amplitudes, and ( iii) minimization and careful estimation of the disturbance-source near-field by means of utilizing a special controlled disturbance source and performing special numerical computations for exact experimental conditions. A detailed study of all linear-stability characteristics for essentially unsteady Görtler vortices was performed in this paper as well. The results are obtained in a range of Görtler numbers 13 ≲ Gö ≲ 17.3, frequency parameters F = 0.56–22.70, and spanwise wavelength parameters Λ = 149–775 (close to the most amplified Görtler modes). Appropriate calculations based on locally-parallel and non-local non-parallel linear-stability theories were performed and compared quantitatively with experimentally obtained linear-stability characteristics. For the first time all stability characteristics measured for steady Görtler vortices (in quasi-steady regimes) are found to agree very well with those calculated for the most amplified first discrete-spectrum mode of the linear Görtler-instability problem. Similar good agreement is obtained for essentially unsteady Görtler vortices. The roles of effects of the base-flow non-parallelism and the disturbance-source near-field are examined.