The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

Measuring motion with kinematically redundant accelerometer arrays: theory, simulation and implementation

This work presents two schemes of measuring the linear and angular kinematics of a rigid body using a kinematically redundant array of triple-axis accelerometers with potential applications in biomechanics. A novel angular velocity estimation algorithm is proposed and evaluated that can compensate for angular velocity errors using measurements of the direction of gravity. Analysis and discussion of optimal sensor array characteristics are provided. A damped 2 axis pendulum was used to excite all 6 DoF of the a suspended accelerometer array through determined complex motion and is the basis of both simulation and experimental studies. The relationship between accuracy and sensor redundancy is investigated for arrays of up to 100 triple axis (300 accelerometer axes) accelerometers in simulation and 10 equivalent sensors (30 accelerometer axes) in the laboratory test rig. The paper also reports on the sensor calibration techniques and hardware implementation.

Joint servoing for robust manipulator force control

An experimental and theoretical comparison is made of force control performance with different types of innerloop joint servoing techniques. The problem of disturbance rejection and sensitivity to plant dynamics variations (robustness) is addressed. Position, velocity, strain gauge derived joint torque, and current servos are designed and implemented on a specially instrumented industrial robot, and the end-effector force feedback performances achieved are compared. Joint strain derived torque servoing is found to provide the best overall robust force control performance. Experimental results of the robust hard-on-hard contact achieved with the novel force controller implementation based on joint torque sensing are provided. Conclusions are drawn on the force control performance achievable on a geared robot given the joint servoing technique.

Spontaneous generation and impact of inertia-gravity waves in a stratified, two-layer shear flow

Inertia-gravity waves exist ubiquitously throughout the stratified parts of the atmosphere and ocean. They are generated by local velocity shears, interactions with topography, and as geostrophic (or spontaneous) adjustment radiation. Relatively little is known about the details of their interaction with the large-scale flow, however. We report on a joint model/laboratory study of a flow in which inertia-gravity waves are generated as spontaneous adjustment radiation by an evolving large-scale mode. We show that their subsequent impact upon the large-scale dynamics is generally small. However, near a potential transition from one large-scale mode to another, in a flow which is simultaneously baroclinically-unstable to more than one mode, the inertia-gravity waves may strongly influence the selection of the mode which actually occurs.

Frost jacking of joint blocks above Cwm Idwal, in North Wales

The in situ development of ground ice is a major mechanism in rock breakdown. Where well-jointed rock has been streamlined through glacial abrasion, subsequent growth of subsurface intrusive ice may lead to the uplift of individual blocks and disruption of the ice erosional landform. This jacking' mechanism is likely to be a progressive process. Following climatic change and allied ground ice decay, the degree of subsequent settlement will be controlled by the degree to which individual blocks become wedged against their neighbours. Possibly the first example to be identified in Britain is described here. It dates from a severe phase of periglaciation occurring between the Last Glacial Maximum and the Flandrian Interglacial (c. 22-11.6 ka BP). Where identified in currently temperate regions, frost-jacked blocks may be interpreted as evidence for palaeopermafrost.

Frost jacking of joint blocks above Cwm Idwal, in North Wales

The in situ development of ground ice is a major mechanism in rock breakdown. Where well-jointed rock has been streamlined through glacial abrasion, subsequent growth of subsurface intrusive ice may lead to the uplift of individual blocks and disruption of the ice erosional landform. This jacking' mechanism is likely to be a progressive process. Following climatic change and allied ground ice decay, the degree of subsequent settlement will be controlled by the degree to which individual blocks become wedged against their neighbours. Possibly the first example to be identified in Britain is described here. It dates from a severe phase of periglaciation occurring between the Last Glacial Maximum and the Flandrian Interglacial (c. 22-11.6 ka BP). Where identified in currently temperate regions, frost-jacked blocks may be interpreted as evidence for palaeopermafrost.

Early social experience and individual differences in infants' joint attention

Fifty-nine healthy infants were filmed with their mothers and with a researcher at two, four, six and nine months in face-to-face play, and in toy-play at six and nine months. During toy-play at both ages, two indices of joint attention (JA)—infant bids for attention, and percent of time in shared attention—were assessed, along with other behavioural measures. Global ratings were made at all four ages of infants’ and mothers’ interactive style. The mothers varied in psychiatric history (e.g., half had experienced postpartum depression) and socioeconomic status, so their interactive styles were diverse. Variation in nine-month infant JA — with mother and with researcher — was predicted by variation in maternal behaviour and global ratings at six months, but not at two or four months. Concurrent adult behaviour also influenced nine-month JA, independent of infant ratings. Six-month maternal behaviours that positively predicted later JA (some of which remained important at nine months) included teaching, conjoint action on a toy, and global sensitivity. Other behaviours (e.g., entertaining) negatively predicted later JA. Findings are discussed in terms of social-learning and neurobiological accounts of JA emergence.