Characterization of internal tide incoherence : Eulerian versus Lagrangian perspectives

Abstract

The Lagrangian and Eulerian surface current signatures of a low-mode internal tide propagating through a turbulent balanced flow are compared in idealized numerical simulations. Lagrangian and Eulerian total (i.e., coherent plus incoherent) tidal amplitudes are found to be similar. Compared to Eulerian diagnostics, the Lagrangian tidal signal is more incoherent with comparable or smaller incoherence time scales and larger incoherent amplitudes. The larger level of incoherence in Lagrangian data is proposed to result from the deformation of an Eulerian internal tide signal induced by drifter displacements. Based on the latter hypothesis, a theoretical model successfully predicts Lagrangian autocovariances by relating Lagrangian and Eulerian autocovariances and the properties of the internal tides and jet. These results have implications for the separation of balanced flow and internal tides signals in the sea level data collected by the future Surface Water and Ocean Topography (SWOT) satellite mission.

Lagrangian versus Eulerian spectral estimates of surface kinetic energy over the global ocean

“…This is in line with the findings of Zaron and Elipot (2021), which noted that the drifter tidal peaks do not stand out above the background spectrum as strongly as in tide model predictions. Caspar-Cohen et al (2022) consistently demonstrated that the distortion of tidal internal waves induced by surface drifter motions, a process coined as apparent incoherence, leads to broader tidal peaks.…”

“…In regions of strong low-frequency flow, the ratio is significantly reduced, with a mean value smaller than 0.4, indicating a substantial underestimation of low-frequency KE from a Lagrangian perspective (Figure 5f). This underestimation results from a larger projection of spatial variability onto temporal one along particle trajectories in energetic regions (LaCasce, 2008;Caspar-Cohen et al, 2022). Indeed, nearby energetic current features, Lagrangian energy thus tends to underestimate Eulerian energy maxima in the core of these features (ratio below 0.5) and overestimate Eulerian energy on the surroundings (ratio above 0.5; Figure 5c).…”

“…This may explain the underestimation of Lagrangian diurnal KE in the Luzon Strait (approximately 20°N; Figure 4d), where the background flow is strong and divergent. Lastly, apparent incoherence is in general expected to be weaker at diurnal frequencies than at semidiurnal frequencies, due to the larger horizontal wavelength of diurnal tides (Caspar-Cohen et al, 2022).…”

“…Understanding and quantifying the differences caused by Lagrangian inherent sampling nature with respect to Eulerian is a key step to ensure the rationality of the mapping of high-frequency variance using the GDP data. At semidiurnal frequencies, Caspar-Cohen et al (2022) recently demonstrated that the displacement of surface drifters may distort low-mode internal tide signals which translated to wider spectral peaks, a mechanism coined "apparent incoherence".…”

Using Lagrangian filtering to remove waves from the ocean surface velocity field

“…This suggests that Lagrangian filtering is mostly removing the energy in the SSH field at the tidal and overtidal frequencies. Another possibility is that the transformation to the Lagrangian frame blurs the tidal peaks, spreading their energy over a broad range of frequencies (Caspar-Cohen et al, 2022).…”