Localised continental shelf waves: geometric effects and resonant forcing

Alongshore variations in coastline curvature or offshore depth profile can create localised regions of shelf-wave propagation with modes decaying outside these regions. These modes, termed localised continental shelf waves (`CSWs) here, exist only at certain discrete frequencies lying below the local maximum frequency, and above the far-field maximum frequency, for propagating shelf waves. The purpose of this paper is to obtain these frequencies and construct, both analytically and numerically, and discuss `CSWs for shelves with arbitrary alongshore variations in offshore depth profile and coastline curvature. If the shelf curvature changes by a small fraction of its value over the shelf section of interest or an alongshore perturbation in offshore depth profile varies slowly over the same length scale then `CSWs can be constructed using WKBJ theory. Two subcases are described: (i) if the propagating region is sufficiently long that the offshore structure of the `CSW varies appreciably alongshore then the frequency and alongshore structure are found from a sequence of local problems; (ii) if the propagating region is sufficiently short that the alongshore change in offshore structure of the `CSW is small then the alongshore modal structure is given in an explicit, uniformly valid form. A separate asymptotic theory is required for curvature perturbations to shelves that are otherwise straight rather than curved. Comparison with highly accurately numerically determined `CSWs shows that both theories are extremely accurate, with the WKBJ theory having a significantly wider range of applicability. An idealised model for the generation of `CSWs is also suggested. A localised time-periodic wind stress generates an evanescent continental shelf wave in the far field of a localised mode where the coast is almost straight and the response on the shelf is obtained numerically. If the forcing frequency is close to that of an `CSW then the wind stress excites energetic motions in the region of maximum curvature, creating a significant localised response possibly far from the forcing region

Localisation of coastal trapped waves by longshore variations in bottom topography

Variations in shelf geometry mean that a coastal trapped wave mode can propagate within some finite length of shelf but be evanescent outside this region. This paper constructs such geographically localised coastal trapped waves using a WKBJ approximation. Comparison with full numerical solutions of the non-linear differential eigenvalue problem demonstrates that the approximation is extremely accurate. The asymptotic and full numerical models are then used to examine the parameters and geometries that govern the existence of these modes

Meanders and eddies from topographic transformation of coastal-trapped waves

This paper describes how topographic variations can transform a small-amplitude, linear, coastal-trapped wave (CTW) into a nonlinear wave or an eddy train. The dispersion relation for CTWs depends on the slope of the shelf. Provided the cross-shelf slope varies sufficiently slowly along the shelf, the local structure of the CTWadapts to the local geometry and the wave transformation can be analyzed by theWentzel-Kramers- Brillouin-Jeffreys (WKBJ) method. Two regions of parameter space are straightforward: adiabatic transmission (where, at the incident wave frequency, a long wave exists everywhere along the shelf) and short-wave reflection (where somewhere on the shelf no long wave exists at the incident frequency, but the stratification is sufficiently weak that a short reflected wave can coexist with the incident wave). This paper gives the solutions for these two cases but concentrates on a third parameter regime, which includes all sufficiently strongly stratified flows, where neither of these behaviors is possible and theWKBJ method fails irrespective of how slowly the topography changes. Fully nonlinear integrations of the equation for the advection of the bottom boundary potential vorticity show that the incident wave in this third parameter regime transforms into a nonlinear wave when topographic variations are gradual or into an eddy train when the changes are abrupt. © 2014 American Meteorological Society

Learning Shape Priors for Single-View 3D Completion and Reconstruction

The problem of single-view 3D shape completion or reconstruction is challenging, because among the many possible shapes that explain an observation, most are implausible and do not correspond to natural objects. Recent research in the field has tackled this problem by exploiting the expressiveness of deep convolutional networks. In fact, there is another level of ambiguity that is often overlooked: among plausible shapes, there are still multiple shapes that fit the 2D image equally well; i.e., the ground truth shape is non-deterministic given a single-view input. Existing fully supervised approaches fail to address this issue, and often produce blurry mean shapes with smooth surfaces but no fine details. In this paper, we propose ShapeHD, pushing the limit of single-view shape completion and reconstruction by integrating deep generative models with adversarially learned shape priors. The learned priors serve as a regularizer, penalizing the model only if its output is unrealistic, not if it deviates from the ground truth. Our design thus overcomes both levels of ambiguity aforementioned. Experiments demonstrate that ShapeHD outperforms state of the art by a large margin in both shape completion and shape reconstruction on multiple real datasets.Comment: ECCV 2018. The first two authors contributed equally to this work. Project page: http://shapehd.csail.mit.edu

Preliminary interpretation of Titan plasma interaction as observed by the Cassini Plasma Spectrometer: Comparisons with Voyager 1

The Cassini Plasma Spectrometer (CAPS) instrument observed the plasma environment at Titan during the Cassini orbiter's TA encounter on October 26, 2004. Titan was in Saturn's magnetosphere during the Voyager 1 flyby and also during the TA encounter. CAPS measurements from this encounter are compared with measurements made by the Voyager 1 Plasma Science Instrument (PLS). The comparisons focus on the composition and nature of ambient and pickup ions. They lead to: A) the major ion components of Saturn's magnetosphere in the vicinity of Titan are H+, H-2(+) and O+/CH4+ ions; B) finite gyroradius effects are apparent in ambient O+ ions as the result of their absorption by Titan's extended atmosphere; C) the principal pickup ions are composed of H+, H-2(+), N+/CH2+, CH4+, and N-2(+); D) the pickup ions are in narrow energy ranges; and E) there is clear evidence of the slowing down of background ions due to pickup ion mass loading