The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0

The counterpropagating Rossby wave perspective on Kelvin Helmholtz instability as a limiting case of a Rayleigh shear layer with zero width

The Kelvin Helmholtz (KH) problem, with zero stratification, is examined as a limiting case of the Rayleigh model of a single shear layer whose width tends to zero. The transition of the Rayleigh modal dispersion relation to the KH one, as well as the disappearance of the supermodal transient growth in the KH limit, are both rationalized from the counterpropagating Rossby wave perspective.

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

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.

Flow structure and variability in the subtropical Indian Ocean: Instability of the South Indian Ocean Countercurrent

The origin of the eddy variability around the 25°S band in the Indian Ocean is investigated. We have found that the surface circulation east of Madagascar shows an anticyclonic subgyre bounded to the south by eastward flow from southwest Madagascar, and to the north by the westward flowing South Equatorial Current (SEC) between 15° and 20°S. The shallow, eastward flowing South Indian Ocean Countercurrent (SICC) extends above the deep reaching, westward flowing SEC to 95°E around the latitude of the high variability band. Applying a two-layer model reveals that regions of large vertical shear along the SICC-SEC system are baroclinically unstable. Estimates of the frequencies (3.5–6 times/year) and wavelengths (290–470 km) of the unstable modes are close to observations of the mesoscale variability derived from altimetry data. It is likely then that Rossby wave variability locally generated in the subtropical South Indian Ocean by baroclinic instability is the origin of the eddy variability around 25°S as seen, for example, in satellite altimetry.

Instability of surface-temperature filaments in strain and shear

The effects of uniform straining and shearing on the stability of a surface quasi-geostrophic temperature filament are investigated. Straining is shown to stabilize perturbations for wide filaments but only for a finite time until the filament thins to a critical width, after which some perturbations can grow. No filament can be stabilized in practice, since there are perturbations that can grow large for any strain rate. The optimally growing perturbations, defined as solutions that reach a certain threshold amplitude first, are found numerically for a wide range of parameter values. The radii of the vortices formed through nonlinear roll-up are found to be proportional to θ/s, where θ is the temperature anomaly of the filament and s the strain rate, and are not dependent on the initial size of the filament. Shearing is shown to reduce the normal-mode growth rates, but it cannot stabilize them completely when there are temperature discontinuities in the basic state; smooth filaments can be stabilized completely by shearing and a simple scaling argument provides the shear rate required. Copyright © 2010 Royal Meteorological Society

Recent advances in capillary electrophoresis methods for food analysis

This review article addresses recent advances in the analysis of foods and food components by capillary electrophoresis (CE). CE has found application to a number of important areas of food analysis, including quantitative chemical analysis of food additives, biochemical analysis of protein composition, and others. The speed, resolution and simplicity of CE, combined with low operating costs, make the technique an attractive option for the development of improved methods of food analysis for the new millennium.

Development of a capillary electrophoresis method for the simultaneous analysis of artificial sweeteners, preservatives and colours in soft drinks

A rapid capillary electrophoresis method was developed simultaneously to determine artificial sweeteners, preservatives and colours used as additives in carbonated soft drinks. Resolution between all additives occurring together in soft drinks was successfully achieved within a 15-min run-time by employing the micellar electrokinetic chromatography mode with a 20 mM carbonate buffer at pH 9.5 as the aqueous phase and 62 mM sodium dodecyl sulfate as the micellar phase. By using a diode-array detector to monitor the UV-visible range (190-600 nm), the identity of sample components, suggested by migration time, could be confirmed by spectral matching relative to standards.

The development and application of capillary electrophoresis methods for food analysis

Capillary electrophoresis (CE) offers the analyst a number of key advantages for the analysis of the components of foods. CE offers better resolution than, say, high-performance liquid chromatography (HPLC), and is more adept at the simultaneous separation of a number of components of different chemistries within a single matrix. In addition, CE requires less rigorous sample cleanup procedures than HPLC, while offering the same degree of automation. However, despite these advantages, CE remains under-utilized by food analysts. Therefore, this review consolidates and discusses the currently reported applications of CE that are relevant to the analysis of foods. Some discussion is also devoted to the development of these reported methods and to the advantages/disadvantages compared with the more usual methods for each particular analysis. It is the aim of this review to give practicing food analysts an overview of the current scope of CE.

Nomenclature in the dock. Overclassification leads to instability: a case study in the horticulturally important genus Cyclamen (Myrsinaceae)

Nine different classifications have been produced in the last 70 years for the horticulturally valuable genus Cyclamen, a small genus with fewer than 30 species. These classifications, generated by intuitive methods and cladistic analyses, incorporated a total of four infrageneric ranks above that of species and were based on data from morphology, cytology and DNA sequencing. Our results, based on cladistic analyses of three independent data sources − nrDNA ITS, cpDNA trnL intron and morphological data − reveal good resolution only in nrDNA sequence data. However, when these three data sources are combined they provide stronger resolution and support for three major clades, only one of which, subgenus Psilanthum, has been consistently supported in previous classifications. The differing infrageneric classifications produced in Cyclamen result from varying taxon sampling, differing interpretation of morphological data, changes in the sources and analysis of data, and inconsistent application of names. Extensive subdivision of small genera in the absence of adequate data that could provide evidence for consistent patterns of relationship is premature and leads to a proliferation of names.© 2004 The Linnean Society of London, Botanical Journal of the Linnean Society, 2004, 146, 339-349.

Capillary flow behavior of worm-like micelles studied by small-angle X-ray scattering and small angle light scattering

A novel capillary flow device has been developed and applied to study the orientation of worm-like micelles, among other systems. Small-angle X-ray scattering (SAXS) data from micelles formed by a Pluronic block copolymer in aqueous salt solution provides evidence for the formation of worm-like micelles, which align under flow. A transition from a rod-like form factor to a less persistent conformation is observed under flow. Flow alignment of worm-like micelles formed by the low molar mass amphiphile system cetyl pyridinium chloride+sodium salicylate is studied for comparative purposes. Here, inhomogenous flow at the micron scale is revealed by streaks in the small-angle light scattering pattern perpendicular to the flow direction. Copyright (c) 2006 John Wiley & Sons, Ltd.