The interaction between the internal tide and the mesoscale circulation are studied from the internal tide energy budget perspective. To that end, the modal energy budget of the internal tide is diagnosed using a high resolution numerical simulation covering the North Atlantic. Compared to the topographic contribution, the advection of the internal tide by the background flow and the horizontal and vertical shear are found to be significant at global scale, while the buoyancy contribution is important locally. The advection of the internal tide by mesoscale currents is responsible for a net energy transfer from the large scale to smaller scale internal tide, without significant exchanges with the background flow. On the opposite, the shear of the mesoscale circulation and the buoyancy field are responsible for exchanges between the internal tide and the background flow. The importance of the shear increases in the northernmost part of the domain, and a partial compensation between the buoyancy and the shear contributions is found in some areas of the North Atlantic, such as in the Gulf Stream region. In addition, the temporal variability of the topographic, advection, mesoscale shear and buoyancy gradient induced energy transfers is investigated. The spring neap cycle is the dominant frequency for the topographic scattering, but other frequencies modulate this term in areas of strong mesoscale activity. Mesoscale induced energy fluxes are modulated by both the spring neap cycle and the variation in the mesoscale circulation patterns.

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 timescales and larger incoherent amplitudes. The larger level of incoherence in Lagrangian data is proposed to result from the deformation of 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.

The future wide-swath satellite altimeters, such as the upcoming Surface Water Ocean Topography (SWOT) mission, will provide instantaneous 2D measurements of sea level down to the spatial scale of O(10 km) for the first time. However, the validity of the geostrophic assumption for estimating surface currents from these instantaneous maps is not known a priori. In this study, we quantify the accuracy of geostrophy for the estimation of surface currents from a knowledge of instantaneous sea level using the hourly snapshots from a tide- and eddy-resolving global numerical simulation. Geostrophic balance is found to be the leading-order balance in frontal regions characterized by large kinetic energy, such as the western boundary currents and the Antarctic Circumpolar Current. Everywhere else, geostrophic approximation ceases to be a useful predictor of ocean velocity, which may result in significant high-frequency contamination of geostrophically computed velocities by fast variability (e.g., inertial and higher). As expected, the validity of geostrophy is shown to improve at low frequencies (typically$<$0.5 cpd). Global estimates of the horizontal momentum budget reveal that the tropical and mid-latitude regions where geostrophic balance fails are dominated by fast variability and turbulent stress divergence terms rather than higher-order geostrophic terms. These findings indicate that the estimation of velocity from geostrophy applied on SWOT instantaneous sea level maps may be challenging away from energetic areas.

The Lagrangian and Eulerian near-surface current signatures of a low-mode internal tide propagating through a turbulent jet are compared in an idealized numerical simulation. We estimate and compare internal tides’ stationary and nonstationary velocity amplitudes as well as non-stationarity timescales. We find Lagrangian internal tides total amplitude similar to Eulerian one. Lagrangian velocity are mostly nonstationary and Lagrangian non-stationary timescales are comparable to or smaller than Eulerian ones. This low-bias is proposed to be the result of the deformation of internal tide surface signal along the drift induced by lower frequency surface currents. A model based on the latter hypothesis successfully predicts Lagrangian autocovariance and highlights its dependence to Eulerian autocovariance and to the properties of the internal tides and jet. We address the implications of these results in the context of the Surface Water and Ocean Topography (SWOT) mission, for which the separation of mesoscale balanced flow and internal tides with data at the ocean’s surface was raised.