Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

Remarks concerning the double cascade as a necessary mechanism for the instability of steady equivalent-barotropic flows

n a recent paper, Petroniet al. claim that a necessary condition for the instability of two-dimensional steady flows is a «double cascade» of energy and enstrophy respectively to larger and to smaller scales of motion. It is shown here that the analytical reasoning employed by Petroniet al. is flawed and that their conclusions are incorrect. What is true is that in any scale interaction (whether an instability or not), neither energy nor enstrophy can be transferred in one spectral direction only, but this result is extremely well known.

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

Computer simulations of pyroclastic flows from dome collapse

We present a method of simulating both the avalanche and surge components of pyroclastic flows generated by lava collapsing from a growing Pelean dome. This is used to successfully model the pyroclastic flows generated on 12 May 1996 by the Soufriere Hills volcano, Montserrat. In simulating the avalanche component we use a simple 3-fold parameterisation of flow acceleration for which we choose values using an inverse method. The surge component is simulated by a 1D hydraulic balance of sedimentation of clasts and entrainment of air away from the avalanche source. We show how multiple simulations based on uncertainty of the starting conditions and parameters, specifically location and size (mass flux), could be used to map hazard zones.

The effect of climate policy on the impacts of climate change on river flows in the UK

This paper compares the effects of two indicative climate mitigation policies on river flows in six catchments in the UK with two scenarios representing un-mitigated emissions. It considers the consequences of uncertainty in both the pattern of catchment climate change as represented by different climate models and hydrological model parameterisation on the effects of mitigation policy. Mitigation policy has little effect on estimated flow magnitudes in 2030. By 2050 a mitigation policy which achieves a 2oC temperature rise target reduces impacts on low flows by 20-25% compared to a business-as-usual emissions scenario which increases temperatures by 4oC by the end of the 21st century, but this is small compared to the range in impacts between different climate model scenarios. However, the analysis also demonstrates that an early peak in emissions would reduce impacts by 40-60% by 2080 (compared with the 4oC pathway), easing the adaptation challenge over the long term, and can delay by several decades the impacts that would be experienced from around 2050 in the absence of policy. The estimated proportion of impacts avoided varies between climate model patterns and, to a lesser extent, hydrological model parameterisations, due to variations in the projected shape of the relationship between climate forcing and hydrological response.

Cross-border capital flows into real estate

This study investigates the determinants of cross-border capital flows into direct real estate markets. In particular, it investigates how existing institutional, regulatory and real estate specific barriers affect cross-border real estate inflows and outflows in a sample of 24 developed and emerging countries, and whether investors seek out targets with lower barriers and regulatory arbitrage. We do not find evidence of significant cross-border institutional or regulatory arbitrage in the real estate market. However, real estate market liquidity is found to be the most important driver of cross-border flows. While many of the institutional barriers included in this analysis do not appear to impact the level of real estate inflows significantly, their presence tends to suppress real estate capital outflows to other countries. Overall, easy access to financial markets, a good economic environment and transparent real estate markets may enhance real estate outflows, while returns and the macroeconomy are found to enhance domestic real estate investment.

Assessing the impacts of climate change on river flows in England using the UKCP09 climate change projections

This paper presents an assessment of the effects of climate change on river flow regimes in representative English catchments, using the UKCP09 climate projections. These comprise a set of 10,000 coherent climate scenarios, used here (i) to evaluate the distribution of potential changes in hydrological behaviour and (ii) to construct relationships between indicators of climate change and hydrological change. The study uses six catchments, and focuses on change in average flow, high flow (Q5) and low flow (Q95). There is a large range in hydrological change in each catchment between the plausible UKCP09 climate projections, with differences between catchments largely due to differences in catchment geology and baseline water balance. The range in change between the UKCP09 projections is in most catchments smaller than the range between changes with scenarios based on the CMIP3 ensemble of climate models, and earlier UK scenarios produce changes that tend towards the lower (drier) end of the UKCP09 range. The difference between emissions scenarios is small compared to the range across the 10,000 scenarios. Changes in high flows are largely driven by changes in winter precipitation, whilst changes in low flows are determined by changes in summer precipitation and temperature.

Time-dependent flows in the coupled solar wind-magnetosphere-ionosphere system

Concepts of time-dependent flow in the coupled solar wind-magnetosphere-ionosphere system are discussed and compared with the frequently-adopted steady-state paradigm. Flows are viewed as resulting from departures of the system from equilibrium excited by dayside and nightside reconnection processes, with the flows then taking the system back towards a new equilibrium configuration. The response of the system to reconnection impulses, continuous but unbalanced reconnection and balanced steady-state reconnection are discussed in these terms. It is emphasized that in the time-dependent case the ionospheric and interplanetary electric fields are generally inductively decoupled from each other; a simple mapping of the interplanetary electric field along equipotential field lines into the ionosphere occurs only in the electrostatic steady-state case.

Large-scale fields and flows in the magnetosphere-ionosphere system

Advances in our understanding of the large-scale electric and magnetic fields in the coupled magnetosphere-ionosphere system are reviewed. The literature appearing in the period January 1991–June 1993 is sorted into 8 general areas of study. The phenomenon of substorms receives the most attention in this literature, with the location of onset being the single most discussed issue. However, if the magnetic topology in substorm phases was widely debated, less attention was paid to the relationship of convection to the substorm cycle. A significantly new consensus view of substorm expansion and recovery phases emerged, which was termed the ‘Kiruna Conjecture’ after the conference at which it gained widespread acceptance. The second largest area of interest was dayside transient events, both near the magnetopause and the ionosphere. It became apparent that these phenomena include at least two classes of events, probably due to transient reconnection bursts and sudden solar wind dynamic pressure changes. The contribution of both types of event to convection is controversial. The realisation that induction effects decouple electric fields in the magnetosphere and ionosphere, on time scales shorter than several substorm cycles, calls for broadening of the range of measurement techniques in both the ionosphere and at the magnetopause. Several new techniques were introduced including ionospheric observations which yield reconnection rate as a function of time. The magnetospheric and ionospheric behaviour due to various quasi-steady interplanetary conditions was studied using magnetic cloud events. For northward IMF conditions, reverse convection in the polar cap was found to be predominantly a summer hemisphere phenomenon and even for extremely rare prolonged southward IMF conditions, the magnetosphere was observed to oscillate through various substorm cycles rather than forming a steady-state convection bay.