This study investigated the correspondence between the near-surface drifters from a mass drifter deployment near Martha's Vineyard, Massachusetts, and the surface current observations from a network of three high-resolution, high-frequency radars to understand the effects of the radar temporal and spatial resolution on the resulting Eulerian current velocities and Lagrangian trajectories and their predictability. The radar-based surface currents were found to be unbiased in direction but biased in magnitude with respect to drifter velocities. The radar systematically underestimated velocities by approximately 2 cm s 21 due to the smoothing effects of spatial and temporal averaging. The radar accuracy, quantified by the domain-averaged rms difference between instantaneous radar and drifter velocities, was found to be about 3.8 cm s
21. A Lagrangian comparison between the real and simulated drifters resulted in the separation distances of roughly 1 km over the course of 10 h, or an equivalent separation speed of approximately 2.8 cm s21 . The effects of the temporal and spatial radar resolution were examined by degrading the radar fields to coarser resolutions, revealing the existence of critical scales (1.5-2 km and 3 h) beyond which the ability of the radar to reproduce drifter trajectories decreased more rapidly. Finally, the importance of the different flow components present during the experiment-mean, tidal, locally wind-driven currents, and the residual velocities-was analyzed, finding that, during the study period, a combination of tidal, locally wind-driven, and mean currents were insufficient to reliably reproduce, with minimal degradation, the trajectories of real drifters. Instead, a minimum combination of the tidal and residual currents was required.
Hamiltonian systems that locally violate the twist condition arise in many applications. Numerical simulations reveal that, when systems of this type are perturbed, the degenerate or nontwist tori are remarkably stable. This phenomenon, which we refer to as strong Kolmogorov-Arnold-Moser (KAM) stability, is shown to be linked to very small resonance widths near degenerate tori. Quantitative estimates of degenerate resonance widths are derived and bifurcations of degenerate resonances are described. Strong KAM stability leads to robust transport barriers, which are important in all of the many applications in which Hamilitonians with the nontwist property arise.
The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the earth's summer hemisphere subtropical stratosphere.
Sound propagation is considered in range-independent environments and environments consisting of a range-independent background on which a weak range-dependent perturbation is superimposed. Recent work on propagation of both types of environment, involving both ray-and mode-based wavefield descriptions, have focused on the importance of α, a ray-based "stability parameter," and β, a mode-based "waveguide invariant." It is shown that, when β is evaluated using asymptotic mode theory, β = α. Using both ray and mode concepts, known results relating to the manner by which α (or β) controls both the unperturbed wavefield structure and the stability of the perturbed wavefield are briefly reviewed.
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