1), F.

And, D.

Criminale, W.O.

Scarsoglio, Stefania

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[Proceeding] Role of the obliquity angle on the perturbed cross-flow
boundary layer
Original Citation:
1)F. De Santi, S. Scarsoglio, W.O. Criminale, And D. Tordella (2013). Role of the obliquity angle on
the perturbed cross-flow boundary layer. In: XXI Congresso AIMETA, Torino, 17-20 Sept 2013. p.
33
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 1 
Role of the obliquity angle on the perturbed cross-flow boundary layer 
 
Francesca De Santi
1
, Stefania Scarsoglio
1
, William O. Criminale
2
, D. Tordella
1
 
1
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy 
francesca.desanti@polito.it, stefania.scarsoglio@polito.it, daniela.tordella@polito.it 
2
Department of Applied Mathematics, University of Washington, Washington, USA 
wocriminale@gmail.com 
Keywords:  Hydrodynamic stability, Cross-flow boundary layer, Perturbative transient dynamics. 
 
We propose a linear investigation on the transient dynamics of arbitrary 3D perturbations acting on the 
Falkner-Skan-Cooke cross-flow boundary layer. The stability of this kind of flow has been recently 
analyzed using modal theory [1], in the context of receptivity and transient optimal perturbations [2, 
3], and experimentally. Works on optimal perturbations [3] usually consider obliquity angles in the 
neighborhood of a fixed value, while Breuer and Kuraishi [2] investigated the direction of the waves, 
but varying simultaneously  and k. Here, we consider the 3D perturbative problem, expressed through 
the initial-value problem formulation [4, 5], by paying particular attention to the role of the obliquity 
of the perturbation with respect to the base flow direction. Evidence is found of counterintuitive 
dependency of the transient and asymptotic behavior on the travelling waves obliquity with respect to 
the base flow. Examples of this non-trivial behavior are reported in Fig. 1, where the evolution of the 
normalized energy, G(t), is displayed for three different obliquity angles (=0, /4, /2). Panel (a) 
shows there can be instability even at very low Reynolds numbers (Re=100) if the pressure gradient is 
sufficiently large (=-0.1988). Panels (b) and (c) present, at a higher Reynolds number (Re=5000), 
configurations with a favorable (=1) and an adverse (=-0.1988) pressure gradient, respectively. In 
the favorable situation (panel b),  the instability is damped by decreasing the obliquity angle, . In the 
adverse condition (panel c), instead, the longitudinal and orthogonal waves are amplified, while the 
oblique perturbation (=/4) is damped. This result is unexpected because if the longitudinal wave is 
unstable, there is usually a progressive tendency to stability toward the orthogonal direction, or 
viceversa. Here, the intermediate wave only is stable, while the two extreme values of the obliquity 
angle lead to instability. 
 
 
 
Fig. 1. Role of the obliquity angle, . Temporal evolution of the normalized energy, G(t).  is the 
cross-flow angle between the streamwise and the chordwise directions, k is the polar wavenumber.  
 
References 
[1] Tayor, M. J., Peake, N. 1997, J. Fluid Mech. 355, 359–381. 
[2] Breuer, K. S., Kuraishi, T. 1994, Phys. Fluids 6, 1983-1994. 
[3] Corbett, P., Bottaro, A. 2000, J. Fluid Mech. 435, 1-23. 
[4]    Scarsoglio, S., Tordella, D., Criminale, W. O. 2009, Stud. Applied Math. 123, 153–173. 
[5]    Scarsoglio, S., Tordella, D., Criminale, W. O. 2010, Phys. Rev. E 81, 036326/1-9. 


Role of the obliquity angle on the perturbed cross-flow boundary layer

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