Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc

TVL₁ Planarity Regularization for 3D Shape Approximation

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within. This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy

Linear image reconstruction by Sobolev norms on the bounded domain

The reconstruction problem is usually formulated as a variational problem in which one searches for that image that minimizes a so called prior (image model) while insisting on certain image features to be preserved. When the prior can be described by a norm induced by some inner product on a Hilbert space the exact solution to the variational problem can be found by orthogonal projection. In previous work we considered the image as compactly supported in and we used Sobolev norms on the unbounded domain including a smoothing parameter ¿>¿0 to tune the smoothness of the reconstruction image. Due to the assumption of compact support of the original image components of the reconstruction image near the image boundary are too much penalized. Therefore we minimize Sobolev norms only on the actual image domain, yielding much better reconstructions (especially for ¿¿»¿0). As an example we apply our method to the reconstruction of singular points that are present in the scale space representation of an image

Global generalized solutions for Maxwell-alpha and Euler-alpha equations

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit

How large are projected 21st century storm track changes?

Projected changes in the extra-tropical wintertime storm tracks are investigated using the multi-model ensembles from both the third and fifth phases of the World Climate Research Programme's Coupled Model Intercomparison Project (CMIP3 and CMIP5). The aim is to characterize the magnitude of the storm track responses relative to their present-day year-to-year variability. For the experiments considered, the ‘middle-of-the-road’ scenarios in each CMIP, there are regions of the Northern Hemisphere where the responses of up to 40% of the models exceed half of the inter-annual variability, and for the Southern Hemisphere there are regions where up to 60% of the model responses exceed half of the inter-annual variability

Variability of the winter wind waves and swell in the North Atlantic and North Pacific as revealed by the Voluntary Observing Ship data

This paper analyses secular changes and interannual variability in the wind wave, swell, and significant wave height (SWH) characteristics over the North Atlantic and North Pacific on the basis of wind wave climatology derived from the visual wave observations of voluntary observing ship (VOS) officers. These data are available from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS) collection of surface meteorological observations for 1958–2002, but require much more complicated preprocessing than standard meteorological variables such as sea level pressure, temperature, and wind. Visual VOS data allow for separate analysis of changes in wind sea and swell, as well as in significant wave height, which has been derived from wind sea and swell estimates. In both North Atlantic and North Pacific midlatitudes winter significant wave height shows a secular increase from 10 to 40 cm decade−1 during the last 45 yr. However, in the North Atlantic the patterns of trend changes for wind sea and swell are quite different from each other, showing opposite signs of changes in the northeast Atlantic. Trend patterns of wind sea, swell, and SWH in the North Pacific are more consistent with each other. Qualitatively the same conclusions hold for the analysis of interannual variability whose leading modes demonstrate noticeable differences for wind sea and swell. Statistical analysis shows that variability in wind sea is closely associated with the local wind speed, while swell changes can be driven by the variations in the cyclone counts, implying the importance of forcing frequency for the resulting changes in significant wave height. This mechanism of differences in variability patterns of wind sea and swell is likely more realistic than the northeastward propagation of swells from the regions from which the wind sea signal originates

A regime analysis of Atlantic winter jet variability applied to evaluate HadGEM3-GC2

The behaviour of the eddy-driven jet over the Atlantic sector during the winter season is analyzed for the ERA-Interim reanalysis and the coupled and atmosphere-only configuration of HadGEM3-GC2—the climate model in use at the Met Office. The trimodal distribution that characterizes the jet-stream structure in terms of its preferred locations is reproduced with good accuracy by the model, although a distinct bias towards the high-latitude position is observed. Two different scenarios are found to contribute to this bias. One occurs when the jet shifts from its southern regime, whereby it settles too far north and for too long compared with the reanalysis. The other is associated with the exit from the central latitude regime, with too many events shifting poleward rather than equatorward. Excessively large lower tropospheric eddy heat fluxes during these transitions may account for the jet errors, even though the heat fluxes do not exhibit a climatological bias. Interestingly, these biases are weaker when the atmosphere model is forced with observed sea-surface temperatures (SSTs), suggesting that either it is vital to have the correct SST distribution or ocean–atmosphere coupling plays a key role in the biases. Additional analysis revealed that the Pacific jet exit is biased south in the coupled model and that this contributes to the Atlantic bias. Anomalously warm SSTs in the Gulf Stream region may be acting together with the Pacific bias in fostering anomalous activity in low-level eddy heat fluxes

Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy