We give an algorithmic introduction to Lagrangian coherent structures (LCSs) using a newly developed computational engine, LCS Tool. LCSs are most repelling, attracting and shearing material lines that form the centerpieces of observed tracer patterns in two-dimensional unsteady dynamical systems. LCS Tool implements the latest geodesic theory of LCSs for two-dimensional flows, uncovering key transport barriers in unsteady flow velocity data as explicit solutions of differential equations. After a review of the underlying theory, we explain the steps and numerical methods used by LCS Tool, and illustrate its capabilities on three unsteady fluid flow examples.

The properties of waves generated by a vertically oscillating sphere in a uniformly stratified fluid are examined both theoretically and experimentally. Existing predictions for the wave amplitude and phase structure are modified to account for the effects of viscous attenuation. As with waves generated by an oscillating cylinder, the main effect of attenuation is to broaden the two peaks of the amplitude envelope on either flank of the wave beam so that far from the sphere the wave beam exhibits a single peak with a maximum along the centreline. The transition distance from bimodal to unimodal wave beam structure is shown to occur closer to the source than the corresponding distance calculated for the oscillating circular cylinder. For laboratory experiments, a recently developed 'synthetic schlieren' method is adapted so that quantitative measurements may be made of an axisymmetric wave field. This non-intrusive technique allows us to evaluate the amplitude of the waves everywhere in space and time. Experiments are performed to examine the amplitude of waves generated by small and large spheres oscillating with a range of amplitudes and frequencies. The wave amplitude is found to scale linearly with the oscillation amplitude A for A/a as large as 0.27, where a is the radius of the sphere. Generally good agreement between theory and experiment is found for the small sphere experiments. However, the theory overpredicts both the amplitude and the bimodal-to-unimodal transition distance for waves generated by the large sphere.

The importance of coupling between the atmosphere and the ocean for forecasting on time scales of hours to weeks has been demonstrated for a range of physical processes. Here, the authors evaluate the impact of an interactive air–sea coupling between an operational global deterministic medium-range weather forecasting system and an ice–ocean forecasting system. This system was developed in the context of an experimental forecasting system that is now running operationally at the Canadian Centre for Meteorological and Environmental Prediction. The authors show that the most significant impact is found to be associated with a decreased cyclone intensification, with a reduction in the tropical cyclone false alarm ratio. This results in a 15% decrease in standard deviation errors in geopotential height fields for 120-h forecasts in areas of active cyclone development, with commensurate benefits for wind, temperature, and humidity fields. Whereas impacts on surface fields are found locally in the vicinity of cyclone activity, large-scale improvements in the mid-to-upper troposphere are found with positive global implications for forecast skill. Moreover, coupling is found to produce fairly constant reductions in standard deviation error growth for forecast days 1–7 of about 5% over the northern extratropics in July and August and 15% over the tropics in January and February. To the authors’ knowledge, this is the first time a statistically significant positive impact of coupling has been shown in an operational global medium-range deterministic numerical weather prediction framework.

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Abstract. Synthetic schlieren is a new technique that allows one easily and inexpensively to visualise density variations, such as those caused by internal waves propagating in a density stratified fluid. In the special case of twodimensional internal waves (for example, those created by an oscillating cylinder), synthetic schlieren allows one to measure non-intrusively the wave amplitudes everywhere in space and time. The technique works by measuring the apparent displacement of points in a digitised image (such as a grid of horizontal lines), which is observed by a CCD camera through the experimental test section. Synthetic schlieren is sufficiently sensitive that it can measure sub-pixel-scale disturbances.In this work, we report on the first step toward measuring fully three-dimensional disturbances. We perform laboratory experiments in which internal waves are generated in a uniformly salt-stratified fluid by a vertically oscillating sphere. Theory predicts that the resulting wave-field is in the form of two cones emanating above and below the sphere. Using inverse tomographic techniques, we exploit the axisymmetry of the wave-field to relate the apparent displacement of pixels in an image to the wave amplitudes.