TY - JOUR
T1 - The linear stability of a Stokes layer subjected to high-frequency perturbations
AU - Thomas, Christian
AU - Blennerhassett, P. J.
AU - Bassom, Andrew P.
AU - Davies, Christopher
PY - 2015/2/1
Y1 - 2015/2/1
N2 - Quantitative results for the linear stability of planar Stokes layers subject to small, high-frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a 1 % perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60 %, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.
AB - Quantitative results for the linear stability of planar Stokes layers subject to small, high-frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a 1 % perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60 %, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.
KW - boundary layer stability
KW - boundary layers
UR - http://www.scopus.com/inward/record.url?scp=84927152750&partnerID=8YFLogxK
U2 - 10.1017/jfm.2014.710
DO - 10.1017/jfm.2014.710
M3 - Article
AN - SCOPUS:84927152750
SN - 0022-1120
VL - 764
SP - 193
EP - 218
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -