  A linear stability analysis is performed on a tilted parallel wake in a
strongly stratified fluid at low Reynolds numbers. A particular emphasis of the
present study is given to the understanding of the low-Froude-number mode
observed by the recent experiment (Meunier, J. Fluid Mech., vol. 699, 2012, pp.
174-197). In the limit of low Froude number, the linearised equations of motion
can be reduced to the Orr-Sommerfeld equation on the horizontal plane, except
the viscous term that contains vertical dissipation. Based on this equation, it
is proposed that the low-Froude-number mode would be a horizontal inflectional
instability, and should remain two dimensional at small tilting angles. To
support this claim, the asymptotic regime where this equation would be strictly
valid is subsequently discussed in relation to previous arguments on the proper
vertical length scale. Furthermore, the absolute and convective instability
analysis of parallel wake is performed, revealing qualitatively good agreement
with the experimental result. The low-Froude-number mode is found to be
stabilised on increasing Froude number, as is in the experiment. The emergence
of small vertical velocity at finite Froude number, the size of which is
proportional to the square of Froude number, plays the key role in the
stabilisation. It modifies the inflectional instability and is also associated
with the paradoxically stabilising buoyancy on increasing Froude number.
Lastly, we proposed some possible behaviours of the base flow when the tilting
angle changes, and they may provide a better approximation to produce the
behaviour consistent with the experiment.
