Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

The small open-economy New Keynesian Phillips Curve: empirical evidence and implied inflation dynamics

In this paper we apply GMM estimation to assess the relevance of domestic versus external determinants of CPI inflation dynamics in a sample of OECD countries typically classified as open economies. The analysis is based on a variant of the small open-economy New Keynesian Phillips Curve derived in Galí and Monacelli (Rev Econ Stud 72:707–734, 2005), where the novel feature is that expectations about fluctuations in the terms of trade enter explicitly. For most countries in our sample the expected relative change in the terms of trade emerges as the more relevant inflation driver than the contemporaneous domestic output gap.

Sleeping with half open eyes: dreams and realities in The Cry of the Owl

This article is a close analysis of The Cry of the Owl (Thraves, 2009). It is also part of larger project to bring together traditions of detailed criticism with those of production history, which culminates in second article on the film due to be published in 2011. The detail of the argument concerns analysing a range of the film’s key signifying systems, with a particular interest in the way the film explores the gap between images / impressions and characters’ realities; engages in a complex way with generic traditions and modes of address; establishes complex patterns of connection and contrast through blocking, camera strategies and narrative structure.

A potential lag between the open solar magnetic source flux and solar EUV and X-ray emissions as measured by the Earth's ionosphere during total solar eclipses

Measurements of the ionospheric E-region during total solar eclipses have been used to provide information about the evolution of the solar magnetic field and EUV and X-ray emissions from the solar corona and chromosphere. By measuring levels of ionisation during an eclipse and comparing these measurements with an estimate of the unperturbed ionisation levels (such as those made during a control day, where available) it is possible to estimate the percentage of ionising radiation being emitted by the solar corona and chromosphere. Previously unpublished data from the two eclipses presented here are particularly valuable as they provide information that supplements the data published to date. The eclipse of 23 October 1976 over Australia provides information in a data gap that would otherwise have spanned the years 1966 to 1991. The eclipse of 4 December 2002 over Southern Africa is important as it extends the published sequence of measurements. Comparing measurements from eclipses between 1932 and 2002 with the solar magnetic source flux reveals that changes in the solar EUV and X-ray flux lag the open source flux measurements by approximately 1.5 years. We suggest that this unexpected result comes about from changes to the relative size of the limb corona between eclipses, with the lag representing the time taken to populate the coronal field with plasma hot enough to emit the EUV and X-rays ionising our atmosphere.

Scorch marks from the sky

Daily sunshine duration is commonly reported at weather stations. Beyond the basic duration report, more information is available from scorched cards of Campbell-Stokes sunshine recorders, such as the estimation of direct-beam solar irradiance. Sunshine cards therefore potentially provide information on sky state, as inferred from solar-radiation data. Some sites have been operational since the late 19th century, hence sunshine cards potentially provide underexploited historical data on sky state. Sunshine cards provide an example of an archive source yielding data beyond the measurements originally sought.

The dependence of clear-sky outgoing longwave radiation on surface temperature and relative humidity

A simulation of the earth's clear-sky long-wave radiation budget is used to examine the dependence of clear-sky outgoing long-wave radiation (OLR) on surface temperature and relative humidity. the simulation uses the European Centre for Medium-Range Weather Forecasts global reanalysed fields to calculate clear-sky OLR over the period from January 1979 to December 1993, thus allowing the seasonal and interannual time-scales to be resolved. the clear-sky OLR is shown to be primarily dependent on temperature changes at high latitudes and on changes in relative humidity at lower latitudes. Regions exhibiting a ‘super-greenhouse’ effect are identified and are explained by considering the changes in the convective regime associated with the Hadley circulation over the seasonal cycle, and with the Walker circulation over the interannual time-scale. the sensitivity of clear-sky OLR to changes in relative humidity diminishes with increasing relative humidity. This is explained by the increasing saturation of the water-vapour absorption bands with increased moisture. By allowing the relative humidity to vary in specified vertical slabs of the troposphere over an interannual time-scale it is shown that changes in humidity in the mid troposphere (400 to 700 hPa) are of most importance in explaining clear-sky OLR variations. Relative humidity variations do not appear to affect the positive thermodynamic water-vapour feedback significantly in response to surface temperature changes.

Centennial changes in the heliospheric magnetic field and open solar flux: the consensus view from geomagnetic data and cosmogenic isotopes and its implications

Svalgaard and Cliver (2010) recently reported a consensus between the various reconstructions of the heliospheric field over recent centuries. This is a significant development because, individually, each has uncertainties introduced by instrument calibration drifts, limited numbers of observatories, and the strength of the correlations employed. However, taken collectively, a consistent picture is emerging. We here show that this consensus extends to more data sets and methods than reported by Svalgaard and Cliver, including that used by Lockwood et al. (1999), when their algorithm is used to predict the heliospheric field rather than the open solar flux. One area where there is still some debate relates to the existence and meaning of a floor value to the heliospheric field. From cosmogenic isotope abundances, Steinhilber et al. (2010) have recently deduced that the near-Earth IMF at the end of the Maunder minimum was 1.80 ± 0.59 nT which is considerably lower than the revised floor of 4nT proposed by Svalgaard and Cliver. We here combine cosmogenic and geomagnetic reconstructions and modern observations (with allowance for the effect of solar wind speed and structure on the near-Earth data) to derive an estimate for the open solar flux of (0.48 ± 0.29) × 1014 Wb at the end of the Maunder minimum. By way of comparison, the largest and smallest annual means recorded by instruments in space between 1965 and 2010 are 5.75 × 1014 Wb and 1.37 × 1014 Wb, respectively, set in 1982 and 2009, and the maximum of the 11 year running means was 4.38 × 1014 Wb in 1986. Hence the average open solar flux during the Maunder minimum is found to have been 11% of its peak value during the recent grand solar maximum.

How is open solar magnetic flux lost over the solar cycle?

The Sun's open magnetic field, magnetic flux dragged out into the heliosphere by the solar wind, varies by approximately a factor of 2 over the solar cycle. We consider the evolution of open solar flux in terms of a source and loss term. Open solar flux creation is likely to proceed at a rate dependent on the rate of photospheric flux emergence, which can be roughly parameterized by sunspot number or coronal mass ejection rate, when available. The open solar flux loss term is more difficult to relate to an observable parameter. The supersonic nature of the solar wind means open solar flux can only be removed by near-Sun magnetic reconnection between open solar magnetic field lines, be they open or closed heliospheric field lines. In this study we reconstruct open solar flux over the last three solar cycles and demonstrate that the loss term may be related to the degree to which the heliospheric current sheet (HCS) is warped, i.e., locally tilted from the solar rotation direction. This can account for both the large dip in open solar flux at the time of sunspot maximum as well as the asymmetry in open solar flux during the rising and declining phases of the solar cycle. The observed cycle-to-cycle variability is also well matched. Following Sheeley et al. (2001), we attribute modulation of open solar flux by the degree of warp of the HCS to the rate at which opposite polarity open solar flux is brought together by differential rotation.