Internal wavepacket tunnelling across a thermohaline staircase

Due to double diffusive processes below the thermocline in the Arctic Ocean, vertical density profiles exhibit a staircase structure in which successive layers of near-uniform density are separated by sharp density jumps. Earlier work [Sutherland, PR Fluids (2016)] theoretically predicted the transmission and reflection of a vertically propagating internal gravity wave incident from above upon a density staircase with an arbitrary number of steps. That work assumed a plane incident wave, being monochromatic in wavenumber and frequency. For waves with given frequency, the transmission coefficient exhibited a series of spikes depending upon the depth of steps relative to the horizontal wavelength. Here we use numerical simulations to examine the transmission of a vertically propagating internal wavepacket that interacts transiently with a staircase. Rather than exhibit successive transmission spikes, the simulations show a smooth transition between perfect and zero transmission as the relative step size increases. This results from internal waves exciting leaky internal modes of the staircase that retransmit waves above and below the staircase slowly over time, as can be predicted by theory.