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.

On the interpretation of Andrews’ theorem

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

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.

Understanding the spatial mass transfer behaviour of a pulsating jet HMV system: vortex generation and characterisation

The flow patterns generated by a pulsating jet used to study hydrodynamic modulated voltammetry (HMV) are investigated. It is shown that the pronounced edge effect reported previously is the result of the generation of a vortex ring from the pulsating jet. This vortex behaviour of the pulsating jet system is imaged using a number of visualisation techniques. These include a dye system and an electrochemically generated bubble stream. In each case a toroidal vortex ring was observed. Image analysis revealed that the velocity of this motion was of the order of 250 mm s−1 with a corresponding Reynolds number of the order of 1200. This motion, in conjunction with the electrode structure, is used to explain the strong ‘ring and halo’ features detected by electrochemical mapping of the system reported previously.

The influence of stratospheric vortex displacements and splits on surface climate

A strong link exists between stratospheric variability and anomalous weather patterns at the earth’s surface. Specifically, during extreme variability of the Arctic polar vortex termed a “weak vortex event,” anomalies can descend from the upper stratosphere to the surface on time scales of weeks. Subsequently the outbreak of cold-air events have been noted in high northern latitudes, as well as a quadrupole pattern in surface temperature over the Atlantic and western European sectors, but it is currently not understood why certain events descend to the surface while others do not. This study compares a new classification technique of weak vortex events, based on the distribution of potential vorticity, with that of an existing technique and demonstrates that the subdivision of such events into vortex displacements and vortex splits has important implications for tropospheric weather patterns on weekly to monthly time scales. Using reanalysis data it is found that vortex splitting events are correlated with surface weather and lead to positive temperature anomalies over eastern North America of more than 1.5 K, and negative anomalies over Eurasia of up to −3 K. Associated with this is an increase in high-latitude blocking in both the Atlantic and Pacific sectors and a decrease in European blocking. The corresponding signals are weaker during displacement events, although ultimately they are shown to be related to cold-air outbreaks over North America. Because of the importance of stratosphere–troposphere coupling for seasonal climate predictability, identifying the type of stratospheric variability in order to capture the correct surface response will be necessary.

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.

Power transfer in velocity-vortex acceleration

A theoretical model is presented of an electron acceleration-as-oscillator method derived from the work of Joseph Larmor unified with J. Clerk Maxwell’s theory of vorticity for the displacement of radiation into free-space at an antenna interface.

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.