It is known that the sub critical flow of a stratified fluid past a barrier produce motions upstream of the barrier. Sub critical flow may be defined as a flow for which the Froude number based on channel height is less than 1/π, so that one
or more stationary lee waves would be present. Some of the upstream motions do not decompose with the distance upstream. These ‘columnar’ modes have zero frequency and a sinusoidal structure in the direction of the density gradient; they effectively lead to a continuous change in upstream conditions. If the barrier is two-dimensional (i.e. of infinite extent in the direction perpendicular to the upstream flow and the direction of density gradient), inviscid theories show that the length of the upstream
region affected by the columnar modes increases without bound as t->infinity. Non-zero viscosity (and/or diffusivity) will, however, limit the region affected, since the wave amplitudes will then slowly decay.