Search Results (5)

We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as the “spline format”) on a spherical quasi-uniform longitude–latitude grid. It is a consistent longitude–latitude grid, and to verify the feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude–latitude grid, which may map a quasi-uniform longitude–latitude grid, a set of ideal, exact test schemes is adopted, which are recognized and proven to be effective internationally. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the polar area correctly, including the South Pole and North Pole. A non-hydrostatic, fully compressible dynamic core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution with the spline format and the benchmark reference solution with the linear format. Based on the findings, the non-hydrostatic dynamic core with the spline format is recommended for adoption. When simulated for the flow over an ideal mountain, through the “topographic gravity wave test”, the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition can be derived successfully. These may serve as the foundations for a global, unified spline-format numerical model in the future. Full article

A commercial unmanned aerial vehicle (UAV) is used for coastal submesoscale current estimation. The measurements were conducted in the Black Sea coastal area with a DJI Mavic quadcopter operated in self-stabilized mode at different look geometry (200–500-m altitude, 0–30${}^{\circ }$ incidence angle). The results of four flights during 2020–2021 are reported. Some scenes captured a train of or individual eddies, generated by a current flowing around a topographic obstacle (pier). The eddies were optically visible due to the mixing of clear and turbid waters in the experiment area. Wave dispersion analysis (WDA), based on dispersion shell signature recognition, is used to estimate the sea surface current in the upper 0.5-m-thick layer. The WDA-derived current maps are consistent with visible eddy manifestations. The alternative method, based on 4D-variational assimilation (4DVAR), agrees well with WDA and can complement it in calm wind conditions when waves are too short to be resolved by the UAV sensor. The error of reconstructed velocity due to the uncontrolled UAV motions is assessed from referencing to static land control points. At a 500-m altitude and 7–10 m s${}^{-1}$ wind speed (reported by a local weather station for 10-m height), the UAV drift velocity, or the bias of the current velocity estimate, is about $0.1$ m s${}^{-1}$, but can be reduced to $0.05$ m s${}^{-1}$ if the first 10 s of the UAV self-stabilization period are excluded from the analysis. The observed anticyclonic eddies (200–400 m in diameter with 0.15–0.30 m s${}^{-1}$ orbital velocity) have an unexpectedly high Rossby number, $\mathrm{Ro}$∼15, suggesting the importance of nonlinear centrifugal force for such eddies and their significant role in coastal vertical transport. Full article

Shelf break flows are often characterized by along-isobath jets with cross-shelf currents associated with tides and waves guided by variable topography. Here, we address the question: Can a superposition of such flows produce significant aperiodic cross-shelf transport? To answer this question, we use a barotropic analytic model for the jet based on a similarity solution of the shallow water equations over variable topography, a wave disturbance determined by the topography, and a diurnal tidal disturbance. We use standard Lagrangian methods to assess the cross-shelf transport, presenting the results, however, in a Eulerian frame, so as to be amenable to oceanographic observations. The relative roles of the different flow components in cross-shelf transport are assessed through an extensive parameter study. We find that a superposition of all three flow components can indeed produce consequential background aperiodic transport. An application of the model using recent observations from the Texas Shelf demonstrates that a combination of these background mechanisms can produce significant transport under realistic conditions. Full article

This paper explores the dynamical origin and physical characteristics of flow disturbances induced by ocean currents in interaction with shelf-incised submarine canyons. To this end, a process-oriented hydrodynamic model is applied in a series of case studies. The focus of studies is the canyon-upwelling process in which seawater is moved from the upper continental slope onto the shelf within a shelf-break canyon. Results reveal that the generation of canyon upwelling, to zero-order approximation, is a barotropic and friction-independent quasi-geostrophic process. Hence, the principle of conservation of potential vorticity for such flows is sufficient to explain the fundamental physical properties of the canyon-upwelling process. For instance, this principle explains the direction-dependence of the canyon-upwelling process. This principle also explains the formation of stationary topographic Rossby waves downstream from the canyon that can lead to far-field effects. Density effects, being of secondary influence to the canyon-upwelling process, result in the intensification of canyon-upwelling flows via the formation of narrow near-bottom density fronts and associated baroclinic geostrophic frontal flows. Findings of this work reveal that the apparently complex canyon-upwelling process is much more basic than previously thought. Full article

An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f and $f/H$ contours, where f is the Coriolis parameter and H is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an $f/H$ contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the $f/H$ contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies. Full article