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.

Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

The influence of bottom topography on the decay of modeled Agulhas rings

The influence of a large meridional submarine ridge on the decay of Agulhas rings is investigated with a 1 and 2-layer setup of the isopycnic primitive-equation ocean model MICOM. In the single-layer case we show that the SSH decay of the ring is primarily governed by bottom friction and secondly by the radiation of Rossby waves. When a topographic ridge is present, the effect of the ridge on SSH decay and loss of tracer from the ring is negligible. However, the barotropic ring cannot pass the ridge due to energy and vorticity constraints. In the case of a two-layer ring the initial SSH decay is governed by a mixed barotropic–baroclinic instability of the ring. Again, radiation of barotropic Rossby waves is present. When the ring passes the topographic ridge, it shows a small but significant stagnation of SSH decay, agreeing with satellite altimetry observations. This is found to be due to a reduction of the growth rate of the m = 2 instability, to conversions of kinetic energy to the upper layer, and to a decrease in Rossby-wave radiation. The energy transfer is related to the fact that coherent structures in the lower layer cannot pass the steep ridge due to energy constraints. Furthermore, the loss of tracer from the ring through filamentation is less than for a ring moving over a flat bottom, related to a decrease in propagation speed of the ring. We conclude that ridges like the Walvis Ridge tend to stabilize a multi-layer ring and reduce its decay.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

On the steadiness of separating meandering currents

The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

Simultaneous observations of reconnection pulses at Cluster and their effects on the cusp aurora seen at Chinese Yellow River Station

While the Cluster spacecraft were located near the high-latitude magnetopause, between 10:10 and 10:40 UT on 16 January 2004, three typical flux transfer event (FTE) signatures were observed. During this interval, simultaneous and conjugated all-sky camera measurements, recorded at Yellow River Station, Svalbard, are available at 630.0 and 557.7nm that show poleward-moving auroral forms (PMAFs), consistent with magnetic reconnection at dayside magnetopause. Simultaneous FTEs seen at the magnetopause mainly move northward, but having duskward (eastward) and tailward velocity components, roughly consistent with the observed direction of motion of the PMAFs in all-sky images. Between the PMAFs meridional keograms, extracted from the all-sky images, show intervals of lower intensity aurora which migrate equatorward just before the PMAFs intensify. This is strong evidence for an equatorward eroding and poleward moving open-closed boundary (OCB) associated with a variable magnetopause reconnection rate under variable IMF conditions. From the durations of the PMAFs we infer that the evolution time of FTEs is 5-11 minutes from its origin on magnetopause to its addition to the polar cap.

From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Synthesis and characterization of hyperbranched polyesters incorporating the AB(2) monomer 3,5-bis(3-hydroxylprop-1-ynyl)benzoic acid

The AB, monomer, 3,5-bis(3-hydroxylprop-1-ynyl)benzoic acid 1, has been synthesized using a Sonogashira cross-coupling with a palladium catalyst system developed for use with deactivated aryl halides. Numerous condensation methods have then been assessed in the homopolymerization of the acid-diol monomer 1 to afford hyperbranched polyesters. However, as a result of the thermal instability of the monomer, direct thermal polymerizations could not be employed. Alternative approaches using carbodiimide-coupling reagents enabled the production of soluble polyesters possessing molecular weights and degrees of branching ranging from 2500 to 11,000 and 0.22 to 0.33, respectively. (C) 2003 Elsevier Ltd. All rights reserved.

13C-2H correlation NMR spectroscopy studies of the in vivo transformations of natural products from Artemisia annua

13C-2H correlation NMR spectroscopy (13C-2H COSY) permits the identification of 13C and 2H nuclei which are connected to one another by a single chemical bond via the sizeable 1JCD coupling constant. The practical development of this technique is described using a 13C-2H COSY pulse sequence which is derived from the classical 13C-1H correlation experiment. An example is given of the application of 13C-2H COSY to the study of the biogenesis of natural products from the anti-malarial plant Artemisia annua, using a doubly-labelled precursor molecule. Although the biogenesis of artemisinin, the anti-malarial principle from this species, has been extensively studied over the past twenty years there is still no consensus as to the true biosynthetic route to this important natural product – indeed, some published experimental results are directly contradictory. One possible reason for this confusion may be the ease with which some of the metabolites from A. annua undergo spontaneous autoxidation, as exemplified by our recent in vitro studies of the spontaneous autoxidation of dihydroartemisinic acid, and the application of 13C-2H COSY to this biosynthetic problem has been important in helping to mitigate against such processes. In this in vivo application of 13C-2H COSY, [15-13C2H3]-dihydroartemisinic acid (the doubly-labelled analogue of the natural product from this species which was obtained through synthesis) was fed to A. annua plants and was shown to be converted into several natural products which have been described previously, including artemisinin. It is proposed that all of these transformations occurred via a tertiary hydroperoxide intermediate, which is derived from dihyroartemisinic acid. This intermediate was observed directly in this feeding experiment by the 13C-2H COSY technique; its observation by more traditional procedures (e.g., chromatographic separation, followed by spectroscopic analysis of the purified product) would have been difficult owing to the instability of the hydroperoxide group (as had been established previously by our in vitro studies of the spontaneous autoxidation of dihydroartemisinic acid). This same hydroperoxide has been reported as the initial product of the spontaneous autoxidation of dihydroartemisinic acid in our previous in vitro studies. Its observation in this feeding experiment by the 13C-2H COSY technique, a procedure which requires the minimum of sample manipulation in order to achieve a reliable identification of metabolites (based on both 13C and 2H chemical shifts at the 15-position), provides the best possible evidence for its status as a genuine biosynthetic intermediate, rather than merely as an artifact of the experimental procedure.

Marker placement to describe the wrist movements during activities of daily living in cyclical tasks

Objective. To describe the wrist kinematics during movement through free range of motion and activities of daily living using a cyclical task. Design. The wrist angles were initially calculated in a calibration trial and then in two selected activities of daily living (jar opening and carton pouring). Background. Existing studies which describe the wrist movement do not address the specific application of daily activities. Moreover, the data presented from subject to subject may differ simply because of the non-cyclical nature of the upper limbs movements. Methods. The coordinates of external markers attached to bone references on the forearm and dorsal side of the hand were obtained using an optical motion capture system. The wrist angles were derived from free motion trials and successively calculated in four healthy subjects for two specific cyclical daily activities (opening a jar and pouring from a carton). Results. The free motions trial highlighted the interaction between the wrist angles. Both the jar opening and the carton pouring activity showed a repetitive pattern for the three angles within the cycle length. In the jar-opening task, the standard deviation for the whole population was 10.8degrees for flexion-extension, 5.3degrees for radial-ulnar deviation and 10.4degrees for pronation-supination. In the carton-pouring task, the standard deviation for the whole population was 16.0degrees for flexion-extension, 3.4degrees for radial-ulnar deviation and 10.7degrees for pro nation-supination. Conclusion. Wrist kinematics in healthy subjects can be successfully described by the rotations about the axes of marker-defined coordinates systems during free range of motion and daily activities using cyclical tasks.

Visual motion interferes with lexical decision on motion words

Embodied theories of cognition propose that neural substrates used in experiencing the referent of a word, for example perceiving upward motion, should be engaged in weaker form when that word, for example ‘rise’, is comprehended. Motivated by the finding that the perception of irrelevant background motion at near-threshold, but not supra-threshold, levels interferes with task execution, we assessed whether interference from near-threshold background motion was modulated by its congruence with the meaning of words (semantic content) when participants completed a lexical decision task (deciding if a string of letters is a real word or not). Reaction times for motion words, such as ‘rise’ or ‘fall’, were slower when the direction of visual motion and the ‘motion’ of the word were incongruent — but only when the visual motion was at nearthreshold levels. When motion was supra-threshold, the distribution of error rates, not reaction times, implicated low-level motion processing in the semantic processing of motion words. As the perception of near-threshold signals is not likely to be influenced by strategies, our results support a close contact between semantic information and perceptual systems.

Syntheses, x-ray structures, photochemistry, redox properties, and DFT calculations of interconvertible fac- and mer-[Mn(SPS)(CO)3] isomers containing a flexible SPS-based pincer ligand

The lithium salt of the anionic SPS pincer ligand composed of a central hypervalent lambda(4)-phosphinine ring bearing two ortho-positioned diphenylphosphine sulfide side arms reacts with [Mn(CO)(5)Br] to give fac-[Mn(SPS)(CO)(3)], This isomer can be converted photochemicaily to mer-[Mn(SPS)(CO)(3)], with a very high quantum yield (0.80 +/- 0.05). The thermal backreaction is slow (taking ca. 8 h at room temperature), in contrast to rapid electrodecatalyzed mer-to-fac isomerization triggered by electrochemical reduction of mer-[Mn(SPS)(CO)(3)]. Both geometric isomers of [Mn(SPS)(CO)(3)] have been characterized by X-ray crystallography. Both isomers show luminescence from a low-lying (IL)-I-3 (SPS-based) excited state. The light emission of fac-[Mn(SPS)(CO)(3)] is largely quenched by the efficient photoisomerization occurring probably from a low-lying Mn-CO dissociative excited state. Density functional theory (DFT) and time-dependent DFT calculations describe the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of fac- and mer-[Mn(CO)(3)(SPS)] as ligand-centered orbitals, largely localized on the phosphinine ring of the SPS pincer ligand. In line with the ligand nature of its frontier orbitals, fac-[Mn(SPS)(CO)(3)] is electrochemically reversibly oxidized and reduced to the corresponding radical cation and anion, respectively. The spectroscopic (electron paramagnetic resonance, IR, and UV-vis) characterization of the radical species provides other evidence for the localization of the redox steps on the SIPS ligand. The smaller HOMO-LUMO energy difference in the case of mer-[Mn(CO)(3)(SPS)], reflected in the electronic absorption and emission spectra, corresponds with its lower oxidation potential compared to that of the fac isomer. The thermodynamic instability of mer-[Mn(CO)(3)(SPS)], confirmed by the DFT calculations, increases upon one-electron reduction and oxidation of the complex.

Baroclinic waves with parameterized effects of moisture interpreted using Rossby wave components

A theoretical framework is developed for the evolution of baroclinic waves with latent heat release parameterized in terms of vertical velocity. Both wave–conditional instability of the second kind (CISK) and large-scale rain approaches are included. The new quasigeostrophic framework covers evolution from general initial conditions on zonal flows with vertical shear, planetary vorticity gradient, a lower boundary, and a tropopause. The formulation is given completely in terms of potential vorticity, enabling the partition of perturbations into Rossby wave components, just as for the dry problem. Both modal and nonmodal development can be understood to a good approximation in terms of propagation and interaction between these components alone. The key change with moisture is that growing normal modes are described in terms of four counterpropagating Rossby wave (CRW) components rather than two. Moist CRWs exist above and below the maximum in latent heating, in addition to the upper- and lower-level CRWs of dry theory. Four classifications of baroclinic development are defined by quantifying the strength of interaction between the four components and identifying the dominant pairs, which range from essentially dry instability to instability in the limit of strong heating far from boundaries, with type-C cyclogenesis and diabatic Rossby waves being intermediate types. General initial conditions must also include passively advected residual PV, as in the dry problem.

Driving saccade to pursuit using image motion

Within the context of active vision, scant attention has been paid to the execution of motion saccades—rapid re-adjustments of the direction of gaze to attend to moving objects. In this paper we first develop a methodology for, and give real-time demonstrations of, the use of motion detection and segmentation processes to initiate capture saccades towards a moving object. The saccade is driven by both position and velocity of the moving target under the assumption of constant target velocity, using prediction to overcome the delay introduced by visual processing. We next demonstrate the use of a first order approximation to the segmented motion field to compute bounds on the time-to-contact in the presence of looming motion. If the bound falls below a safe limit, a panic saccade is fired, moving the camera away from the approaching object. We then describe the use of image motion to realize smooth pursuit, tracking using velocity information alone, where the camera is moved so as to null a single constant image motion fitted within a central image region. Finally, we glue together capture saccades with smooth pursuit, thus effecting changes in both what is being attended to and how it is being attended to. To couple the different visual activities of waiting, saccading, pursuing and panicking, we use a finite state machine which provides inherent robustness outside of visual processing and provides a means of making repeated exploration. We demonstrate in repeated trials that the transition from saccadic motion to tracking is more likely to succeed using position and velocity control, than when using position alone.

Simultaneous observations of reconnection pulses at Cluster and their effects on the cusp aurora observed at the Chinese Yellow River station

While the Cluster spacecraft were located near the high-latitude magnetopause, between 1010 and 1040 UT on 16 January 2004, three typical flux transfer event (FTE) signatures were observed. During this interval, simultaneous and conjugated all‐sky camera measurements, recorded at Yellow River Station, Svalbard, are available at 630.0 and 557.7 nm that show poleward‐moving auroral forms (PMAFs), consistent with magnetic reconnection at the dayside magnetopause. Simultaneous FTEs seen at the magnetopause mainly move northward, but having duskward (eastward) and tailward velocity components, roughly consistent with the observed direction of motion of the PMAFs in all‐sky images. Between the PMAFs meridional keograms, extracted from the all‐sky images, show intervals of lower intensity aurora which migrate equatorward just before the PMAFs intensify. This is strong evidence for an equatorward eroding and poleward moving open‐closed boundary associated with a variable magnetopause reconnection rate under variable IMF conditions. From the durations of the PMAFs, we infer that the evolution time of FTEs is 5–11 minutes from its origin on the magnetopause to its addition to the polar cap.