The dynamics of perturbations to large-amplitude Internal Solitary Waves
(ISW) in two-layered flows with thin interfaces is analyzed by means of linear
optimal transient growth methods. Optimal perturbations are computed through
direct-adjoint iterations of the Navier-Stokes equations linearized around
inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation.
Optimal perturbations are found as a function of the ISW phase velocity c
(alternatively amplitude) for one representative stratification. These
disturbances are found to be localized wave-like packets that originate just
upstream of the ISW self-induced zone (for large enough c) of potentially
unstable Richardson number, Ri<0.25. They propagate through the base wave
as coherent packets whose total energy gain increases rapidly with c. The
optimal disturbances are also shown to be relevant to DJL solitary waves that
have been modified by viscosity representative of laboratory experiments. The
optimal disturbances are compared to the local WKB approximation for spatially
growing Kelvin-Helmholtz (K-H) waves through the Ri<0.25 zone. The WKB
approach is able to capture properties (e.g., carrier frequency, wavenumber and
energy gain) of the optimal disturbances except for an initial phase of
non-normal growth due to the Orr mechanism. The non-normal growth can be a
substantial portion of the total gain, especially for ISWs that are weakly
unstable to K-H waves. The linear evolution of Gaussian packets of linear free
waves with the same carrier frequency as the optimal disturbances is shown to
result in less energy gain than found for either the optimal perturbations or
the WKB approximation due to non-normal effects that cause absorption of
disturbance energy into the leading face of the wave.Comment: 33 pages, 22 figure
