  A theoretical and numerical analysis of the linear stability of the boundary
layer flow under a solitary wave is presented. In the present work, the
nonlinear boundary layer equations are solved. The result is compared to the
linear boundary layer solution in Liu et al. (2007) reveal- ing that both
profiles are disagreeing more than has been found before. A change of frame of
reference has been used to allow for a classical linear stability analysis
without the need to redefine the notion of stability for this otherwise
unsteady flow. For the linear stability the Orr-Sommerfeld equation and the
parabolic stability equation were used. The results are compared to key results
of inviscid stability theory and validated by means of a direct numerical
simulation using a Legendre-Galerkin spectral ele- ment Navier-Stokes solver.
Special care has been taken to ensure that the numerical results are valid.
Linear stability predicts that the boundary layer flow is unstable for the
entire parameter range considered, confirm- ing qualitatively the results by
Blondeaux et al. (2012). As a result of this analysis the stability of this
flow cannot be described by a critical Reynolds number unlike what is atempted
in previous publications. This apparent contradiction can be resolved by
looking at the amplification factor responsible for the amplification of the
perturbation. For lower Reynolds numbers, the boundary layer flow becomes
unstable in the de- celeration region of the flow. For higher Reynolds numbers,
instability arises also in the acceleration region of the flow, confirming,
albeit only qualitatively, an observation in the experiments by Sumer et al.
(2010).
