Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Gravity well visibility in haptic interfaces for motion-impaired

Haptic computer interfaces provide users with feedback through the sense of touch, thereby allowing users to feel a graphical user interface. Force feedback gravity wells, i.e. attractive basins that can pull the cursor toward a target, are one type of haptic effect that have been shown to provide improvements in "point and click" tasks. For motion-impaired users, gravity wells could improve times by as much as 50%. It has been reported that the presentation of information to multiple sensory modalities, e.g. haptics and vision, can provide performance benefits. However, previous studies investigating the use of force feedback gravity wells have generally not provided visual representations of the haptic effect. Where force fields extend beyond clickable targets, the addition of visual cues may affect performance. This paper investigates how the performance of motion-impaired computer users is affected by having visual representations of force feedback gravity wells presented on-screen. Results indicate that the visual representation does not affect times and errors in a "point and click" task involving multiple targets.

Simulated anthropogenic changes in the Brewer–Dobson circulation, including its extension to high latitudes

Recent studies using comprehensive middle atmosphere models predict a strengthening of the Brewer-Dobson circulation in response to climate change. To gain confidence in the realism of this result it is important to quantify and understand the contributions from the different components of stratospheric wave drag that cause this increase. Such an analysis is performed here using three 150-yr transient simulations from the Canadian Middle Atmosphere Model (CMAM), a Chemistry-Climate Model that simulates climate change and ozone depletion and recovery. Resolved wave drag and parameterized orographic gravity wave drag account for 60% and 40%, respectively, of the long-term trend in annual mean net upward mass flux at 70 hPa, with planetary waves accounting for 60% of the resolved wave drag trend. Synoptic wave drag has the strongest impact in northern winter, where it accounts for nearly as much of the upward mass flux trend as planetary wave drag. Owing to differences in the latitudinal structure of the wave drag changes, the relative contribution of resolved and parameterized wave drag to the tropical upward mass flux trend over any particular latitude range is highly sensitive to the range of latitudes considered. An examination of the spatial structure of the climate change response reveals no straightforward connection between the low-latitude and high-latitude changes: while the model results show an increase in Arctic downwelling in winter, they also show a decrease in Antarctic downwelling in spring. Both changes are attributed to changes in the flux of stationary planetary wave activity into the stratosphere.

Vertical propagation of information in a middle atmosphere data assimilation system by gravity-wave drag feedbacks

The mesospheric response to the 2002 Antarctic Stratospheric Sudden Warming (SSW) is analysed using the Canadian Middle Atmosphere Model Data Assimilation System (CMAM-DAS), where it represents a vertical propagation of information from the observations into the data-free mesosphere. The CMAM-DAS simulates a cooling in the lowest part of the mesosphere which is accomplished by resolved motions, but which is extended to the mid- to upper mesosphere by the response of the model's non-orographic gravity-wave drag parameterization to the change in zonal winds. The basic mechanism is that elucidated by Holton consisting of a net eastward wave-drag anomaly in the mesosphere during the SSW, although in this case there is a net upwelling in the polar mesosphere. Since the zonal-mean mesospheric response is shown to be predictable, this demonstrates that variations in the mesospheric state can be slaved to the lower atmosphere through gravity-wave drag.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.