A surface Quasi‐Geostrophy based (eSQG) method to diagnose the vertical velocity field from Sea Surface Height (SSH) is assessed using high resolution simulations. These simulations concern a turbulent eddy field with large Rossby numbers and energetic wind‐driven motions. Results indicate that low‐frequency vertical velocities (and also horizontal motions) can be reconstructed within a range of scales between 20 km and 400 km from the surface down to 500 m. The only information needed is a single high‐resolution SSH snapshot and information on the large‐scale vertical stratification. Inertial motions are naturally filtered because they do not contaminate SSH as we demonstrate. These results are encouraging and further strengthen previous studies using the eSQG method. They indicate that access to high resolution SSH may represent a major advance to retrieve horizontal and vertical fluxes of any tracer in the upper ocean.

The authors analyze the 3D propagation of wind-forced near-inertial motions in a fully turbulent mesoscale eddy field with a primitive equation numerical model. Although the wind stress is uniform, the near-inertial motion field quickly becomes spatially heterogeneous, involving horizontal scales much smaller than the eddy scales. Analysis confirms that refraction by the eddy relative vorticity is the main mechanism responsible for the horizontal distortion of the near-inertial motions, which subsequently triggers their vertical propagation. An important result is the appearance of two maxima of near-inertial vertical velocity (both with rms values reaching 40 m day Ϫ1 ): one at a depth of 100 m and another unexpected one much below the main thermocline around 1700 m. The shallow maximum, captured by the highest vertical normal modes, involves near-inertial motions with a spatial heterogeneity close to the eddy vorticity gradient field. These characteristics match analytical results obtained with Young and Ben Jelloul's approach. The deep maximum, captured by the lowest vertical normal modes, involves superinertial motions with a frequency of twice the inertial frequency and much smaller horizontal scales. Because of these characteristics, not anticipated by previous analytical studies, these superinertial motions may represent an energy source for small-scale mixing through a mechanism not taken into account in the present study: the parametric subharmonic instability (PSI). This reveals a pathway by which wind energy may have a significant impact on small-scale mixing in the deep interior. Further studies that explicitly take into account PSI are needed to estimate this potential impact.

An overlooked conservation law for near-inertial waves (NIWs) propagating in a steady background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this concentration is a direct consequence of the decrease in spatial scales experienced by an initially homogeneous wave field. Scaling arguments and numerical simulations of a reduced-gravity model of mixed-layer NIWs confirm this interpretation and elucidate the influence of the strength of the background flow relative to the dispersion.

Summary The paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely drifting satellite‐tracked instruments. The time series models proposed are used to summarize large multivariate data sets and to infer important physical parameters of inertial oscillations and other ocean processes. Non‐stationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the data sets are large, we construct computationally efficient methods through the use of frequency domain modelling and estimation, with the data expressed as complex‐valued time series. We detail how practical issues related to sampling and model misspecification may be addressed by using semiparametric techniques for time series, and we demonstrate the effectiveness of our stochastic models through application to both real world data and to numerical model output.