A unified theory of available potential energy

Traditional derivations of available potential energy, in a variety of contexts, involve combining some form of mass conservation together with energy conservation. This raises the questions of why such constructions are required in the first place, and whether there is some general method of deriving the available potential energy for an arbitrary fluid system. By appealing to the underlying Hamiltonian structure of geophysical fluid dynamics, it becomes clear why energy conservation is not enough, and why other conservation laws such as mass conservation need to be incorporated in order to construct an invariant, known as the pseudoenergy, that is a positive‐definite functional of disturbance quantities. The available potential energy is just the non‐kinetic part of the pseudoenergy, the construction of which follows a well defined algorithm. Two notable features of the available potential energy defined thereby are first, that it is a locally defined quantity, and second, that it is inherently definable at finite amplitude (though one may of course always take the small‐amplitude limit if this is appropriate). The general theory is made concrete by systematic derivations of available potential energy in a number of different contexts. All the well known expressions are recovered, and some new expressions are obtained. The possibility of generalizing the concept of available potential energy to dynamically stable basic flows (as opposed to statically stable basic states) is also discussed.

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Balanced excitation and inhibition: Model based analysis of local field potentials

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin–Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5 Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

Government policy under price uncertainty: a source of volatility in illegal immigration

In this paper we provide an alternative explanation for why illegal immigration can exhibit substantial fluctuation. We develop a model economy in which migrants make decisions in the face of uncertain border enforcement and lump-sum transfers from the host country. The uncertainty is extrinsic in nature, a sunspot, and arises as a result of ambiguity regarding the commodity price of money. Migrants are restricted from participating in state-contingent insurance markets in the host country, whereas host country natives are not. Volatility in migration flows stems from two distinct sources: the tension between transfers inducing migration and enforcement discouraging it and secondly the existence of a sunspot. Finally, we examine the impact of a change in tax/transfer policies by the government on migration.

Evidence from Meteosat imagery of the interaction of sting jets with the boundary layer

Meteosat infra-red imagery for the Great Storm of October 1987 is analysed to show a series of very shallow arc-shaped and smaller chevron-shaped cloud features that were associated with damaging surface winds in the dry-slot region of this extra-tropical cyclone. Hypotheses are presented that attribute these low-level cloud features to boundary-layer convergence lines ahead of wind maxima associated with the downward transport of high momentum from overrunning, so-called sting-jet, flows originating in the storm's main cloud head. Copyright © 2004 Royal Meteorological Society.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

Shaken, not stirred: the impact of disasters on international trade

This paper examines the impact of major disasters on import and export flows using a gravity model (170 countries, 1962–2004). As a conservative estimate, an additional disaster reduces imports on average by 0.2% and exports by 0.1%. Despite the apparent persistence of bilateral trade volumes, we find that the driving forces determining the impact of disastrous events are the level of democracy and the geographical size of the affected country. The less democratic and the smaller a country the greater is its loss due to a catastrophe. In autocracies, exports and imports are significantly reduced. Had Togo been struck by a major disaster in 2000, it would have lost 6.2% of its imports and 3.7% of its exports. While democratic countries' exports suffer identical decreases, imports increase.

The influence of ocean flow on newly forming sea ice

The heat and mass balance of the Arctic Ocean is very sensitive to the growth and decay of sea ice and the interaction between the heat and salt fields in the oceanic boundary layer. The hydraulic roughness of sea ice controls the detailed nature of turbulent fluxes in the boundary layer and hence is an important ingredient in model parameterizations. We describe a novel mechanism for the generation of corrugations of the sea ice–ocean interface, present a mathematical analysis elucidating the mechanism, and present numerical calculations for geophysically relevant conditions. The mechanism relies on brine flows developing in the sea ice due to Bernoulli suction by flow of ocean past the interface. For oceanic shears at the ice interface of 0.2 s−1, we expect the corrugations to form with a wavelength dependent upon the permeability structure of the sea ice which is described herein. The mechanism should be particularly important during sea ice formation in wind-maintained coastal polynyas and in leads. This paper applies our earlier analyses of the fundamental instability to field conditions and extends it to take account of the anisotropic and heterogeneous permeability of sea ice.

Validity of the ice shelf water plume concept beneath Filchner-Ronne Ice Shelf

In winter, brine rejection from sea ice formation and export in the Weddell Sea, offshore of Filchner-Ronne Ice Shelf (FRIS), leads to the formation of High Salinity Shelf Water (HSSW). This dense water mass enters the cavity beneath FRIS by sinking southward down the sloping continental shelf towards the grounding line. Melting occurs when the HSSW encounters the ice shelf, and the meltwater released cools and freshens the HSSW to form a water mass known as Ice Shelf Water (ISW). If this ISW rises, the ‘ice pump’ is initiated (Lewis and Perkin, 1986), whereby the ascending ISW becomes supercooled and deposits marine ice at shallower locations due to the pressure increase in the in-situ freezing temperature. Sandh¨ager et al. (2004) were able to infer the thickness patterns of marine ice deposits at the base of FRIS (figure 1), so the primary aim of this work is to try to understand the ocean flows that determine these patterns. The plume model we use to investigate ISW flow is described fully by Holland and Feltham (accepted) so only a relatively brief outline is presented here. The plume is simulated by combining a parameterisation of ice shelf basal interaction and a multiplesize- class frazil dynamics model with an unsteady, depth-averaged reduced-gravity plume model. In the model an active region of ISW evolves above and within an expanse of stagnant ambient fluid, which is considered to be ice-free and has fixed profiles of temperature and salinity. The two main assumptions of the model are that there is a well-mixed layer underneath the ice shelf and that the ambient fluid outside the plume is stagnant with fixed properties. The topography of the ice shelf that the plume flows beneath is set to the FRIS ice shelf draft calculated by Sandh¨ager et al. (2004) masked with the grounding line from the Antarctic Digital Database (ADD Consortium, 2002). To initiate the plumes, we assume that the intrusion of dense HSSW initially causes melting at the points on the grounding line where the glaciological tributaries feeding FRIS go afloat.

Exploring the paradox of competence-creating subsidiaries: balancing bandwidth and dispersion in MNEs

This paper seeks to synthesise the various contributions to the special issue of Long Range Planning on competence-creating subsidiaries (CCS), and identifies avenues for future research. Effective competence-creation through a network of subsidiaries requires an appropriate balance between internal and external embeddedness. There are multiple types of firm-specific advantages (FSAs) essential to achieve this. In addition, wide-bandwidth pathways are needed with collaborators, suppliers, customers as well as internally within the MNE. Paradoxically, there is a natural tendency for bandwidth to shrink as dispersion increases. As distances (technological, organisational, and physical) become greater, there may be decreasing returns to R&D spread. Greater resources for knowledge integration and coordination are needed as intra-MNE and inter-firm R&D cooperation becomes more intensive and extensive. MNEs need to invest in mechanisms to promote wide-bandwidth knowledge flows, without which widely dispersed and networked MNEs can suffer from internal market failures.

A comparative performance analysis of TRMM 3B42 (TMPA) versions 6 and 7 for hydrological applications over Andean-Amazon river basins

The Tropical Rainfall Measuring Mission 3B42 precipitation estimates are widely used in tropical regions for hydrometeorological research. Recently, version 7 of the product was released. Major revisions to the algorithm involve the radar refl ectivity - rainfall rates relationship, surface clutter detection over high terrain, a new reference database for the passive microwave algorithm, and a higher quality gauge analysis product for monthly bias correction. To assess the impacts of the improved algorithm, we compare the version 7 and the older version 6 product with data from 263 rain gauges in and around the northern Peruvian Andes. The region covers humid tropical rainforest, tropical mountains, and arid to humid coastal plains. We and that the version 7 product has a significantly lower bias and an improved representation of the rainfall distribution. We further evaluated the performance of versions 6 and 7 products as forcing data for hydrological modelling, by comparing the simulated and observed daily streamfl ow in 9 nested Amazon river basins. We find that the improvement in the precipitation estimation algorithm translates to an increase in the model Nash-Sutcliffe effciency, and a reduction in the percent bias between the observed and simulated flows by 30 to 95%.