Solar signal propagation: the role of gravity waves and stratospheric sudden warmings

We use a troposphere‐stratosphere model of intermediate complexity to study the atmospheric response to an idealized solar forcing in the subtropical upper stratosphere during Northern Hemisphere (NH) early winter. We investigate two conditions that could influence poleward and downward propagation of the response: (1) the representation of gravity wave effects and (2) the presence/absence of stratospheric sudden warmings (SSWs). We also investigate how the perturbation influences the timing and frequency of SSWs. Differences in the poleward and downward propagation of the response within the stratosphere are found depending on whether Rayleigh friction (RF) or a gravity wave scheme (GWS) is used to represent gravity wave effects. These differences are likely related to differences in planetary wave activity in the GWS and RF versions, as planetary wave redistribution plays an important role in the downward and poleward propagation of stratospheric signals. There is also remarkable sensitivity in the tropospheric response to the representation of the gravity wave effects. It is most realistic for GWS. Further, tropospheric responses are systematically different dependent on the absence/presence of SSWs. When only years with SSWs are examined, the tropospheric signal appears to have descended from the stratosphere, while the signal in the troposphere appears disconnected from the stratosphere when years with SSWs are excluded. Different troposphere‐stratosphere coupling mechanisms therefore appear to be dominant for years with and without SSWs. The forcing does not affect the timing of SSWs, but does result in a higher occurrence frequency throughout NH winter. Quasi‐Biennial Oscillation effects were not included.

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.

The interaction of flexural-gravity waves with periodic geometries

A periodic structure of finite extent is embedded within an otherwise uniform two-dimensional system consisting of finite-depth fluid covered by a thin elastic plate. An incident harmonic flexural-gravity wave is scattered by the structure. By using an approximation to the corresponding linearised boundary value problem that is based on a slowly varying structure in conjunction with a transfer matrix formulation, a method is developed that generates the whole solution from that for just one cycle of the structure, providing both computational savings and insight into the scattering process. Numerical results show that variations in the plate produce strong resonances about the ‘Bragg frequencies’ for relatively few periods. We find that certain geometrical variations in the plate generate these resonances above the Bragg value, whereas other geometries produce the resonance below the Bragg value. The familiar resonances due to periodic bed undulations tend to be damped by the plate.

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.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.