Internal waves near the buoyancy frequency in a narrow wave-guide

High-resolution temperature observations from the northern North Sea were used to study increased isotherm displacement variance above the internal wave spectral continuum near the background buoyancy frequency (N). Existing linear WKB-theories attributed such increase to internal reflection at a turning point within a moderately wide wave-guide or to resonant wave generation from outside the wave-guide. In contrast to linear theory and partially following previous suggestions, the present observations showed that in a narrow wave-guide this increase is due to just a few passages of near-monochromatic, mode-1 interfacial waves. Furthermore, it was observed for the first time that these interfacial waves can occasionally grow and increase their frequency (σ) until σ = NB ≪ N00, where N00 denotes the frequency of the thin interface of thickness Δz00 moving up and down and NB is the 5-day mean Eulerian background stratification. Maximum-displacement variance reached levels 2 decades above the long-term average value. The maximum-amplitude H of the σ ≈ NB-waves was half the vertical scale of the mean pycnocline (and inertial shear layer) ΔzB = 2H delineated by depths z for which N(z) ≥ NB, the ‘wave-guide’. As a result, the high-frequency waves partially determined the background stratification because further growth was not possible, leading to wave breaking at the edges of the wave-guide and thereby decreasing N. This mechanism for reduction of the pycnocline is different from accepted mechanisms such as boundary mixing and internal mixing following inertial shear. However, as it occurs within a finite thick pycnocline it may be responsible for much of the relatively slow turbulent exchange of nutrients across pycnoclines in shelf seas.