The impact of multiple layering on internal wave transmission

Abstract

Given the ubiquity of layering in environmental stratifications, an interesting example being double-diffusive staircase structures in the Arctic Ocean, we present the results of a joint theoretical and laboratory experimental study investigating the impact of multiple layering on internal wave propagation. We first present results for a simplified model that demonstrates the non-trivial impact of multiple layering. Thereafter, utilizing a weakly viscous linear model that can handle arbitrary vertical stratifications, we perform a comparison of theory with experiments. We conclude by applying this model to a case study of a staircase stratification profile obtained from the Arctic Ocean, finding a rich landscape of transmission behaviour.

Internal wave transmission through a thermohaline staircase

“…This is on the horizontal scale of internal waves generated by storms. Thus, consistent with the assertion of Ghaemsaidi et al [22], this work predicts that density staircases may act as an effective filter allowing waves with longer horizontal wavelength and larger frequencies to transmit through to the abyss. Shorter waves may reflect or transmit substantially.…”

“…In particular, taking f = 0.01N 0 , ω = 1.05f 0 , and R = 0.1, the lower bound is λ T l 1.6 × 10 3 D. So for inertia gravity waves incident upon a staircase of total depth 30 m [22], the waves transmit with little reflection if their horizontal wavelength is larger than 50 km. This is on the horizontal scale of internal waves generated by storms.…”

“…This analytic study was extended to examine the influence of shear [17]. Further numerical studies examined the transmission of waves through more complex stratification [18][19][20][21][22] and large-amplitude effects were also considered [23]. However, in all these studies except Ref.…”

“…However, in all these studies except Ref. [22] the background stratification considered involved far fewer layers than occurs in a typical thermohaline staircase. Ghaemsaidi et al [22] in part considered the transmission of waves across two well-mixed regions bounded by finite-depth stratified layers through theory, numerics, and experiments.…”

“…[22] the background stratification considered involved far fewer layers than occurs in a typical thermohaline staircase. Ghaemsaidi et al [22] in part considered the transmission of waves across two well-mixed regions bounded by finite-depth stratified layers through theory, numerics, and experiments. They found that incident waves passing through multiple layers could result in transmission spikes in incident vertical wave number and frequency space occurring as a result of interference patterns between evanescent waves within the mixed regions and propagating waves within the stratified layers.…”