Solar rotation rate and its gradients during cycle 23

Available helioseismic data now span almost the entire solar activity cycle 23 making it possible to study solar-cycle related changes of the solar rotation rate in detail. In this paper we study how the solar rotation rate, in particular, the zonal flows change with time. In addition to the zonal flows that show a well known pattern in the solar convection zone, we also study changes in the radial and latitudinal gradients of the rotation rate, particularly in the shear layer that is present in the immediate sub-surface layers of the Sun. In the case of the zonal-flow pattern, we find that the band indicating fast rotating region close to the equator seems to have bifurcated around 2005. Our investigation of the rotation-rate gradients show that the relative variation in the rotation-rate gradients is about 20% or more of their average values, which is much larger than the relative variation in the rotation rate itself. These results can be used to test predictions of various solar dynamo models.Comment: To appear in ApJ. Fig 5 has been corrected in this versio

Solar Rotation Rate During the Cycle 24 Minimum in Activity

The minimum of solar cycle 24 is significantly different from most other minima in terms of its duration as well as its abnormally low levels of activity. Using available helioseismic data that cover epochs from the minimum of cycle 23 to now, we study the differences in the nature of the solar rotation between the minima of cycles 23 and 24. We find that there are significant differences between the rotation rates during the two minima. There are differences in the zonal-flow pattern too. We find that the band of fast rotating region close to the equator bifurcated around 2005 and recombined by 2008. This behavior is different from that during the cycle 23 minimum. By auto-correlating the zonal-flow pattern with a time shift, we find that in terms of solar dynamics, solar cycle 23 lasted for a period of 11.7 years, consistent with the result of Howe et al. (2009). The autocorrelation coefficient also confirms that the zonal-flow pattern penetrates through the convection zone.Comment: Accepted for publication in Ap

Temporal variations of solar rotation rate at high latitudes

Frequency splitting coefficients from Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) observations covering the period 1995--2001 are used to study temporal variations in the solar rotation rate at high latitudes. The torsional oscillation pattern in the Sun is known to penetrate to a depth of about $0.1R_\odot$ with alternate bands of faster and slower rotating plasma. At lower latitudes the bands move towards equator with time. At higher latitudes, however, the bands appear to move towards the poles. This is similar to the observed pole-ward movement of large scale magnetic fields at high latitudes. This also supports theoretical results of pole-ward moving bands at high latitudes in some mean field dynamo models. The polar rotation rate is found to decrease between 1995 and 1999 after which it has started increasing.Comment: To appear in ApJ Letter

Multi-criteria Analysis for the Selection of the Best Energy Efficient Option in Urban Water Systems

AbstractThis paper presents the application of multi-criteria decision analysis to select the best energy efficient option for a water supply system. The case study is a part of the Multi-Municipal Water Supply System (MMWSS) for the Algarve region in Portugal. There is a micro-hydropower plant installed in one of the two water treatment plants. The system has two operating schemes due to the seasonality of tourism: one for the high season from June to September; and the other one for the low season from October to May. The aim of the analysis is to compare the energy efficiency of the system for the two operating schemes and for different demands. Energy audits (i.e., hydraulic energy balance along the pipe system) are carried out for each option (pair operating scheme – demand). Different energy efficiency metrics are calculated and two different multi-criteria analysis methods are used and compared to rank the options. Results obtained are discussed and the main conclusions are presented

The Radial Distribution of Magnetic Helicity in the Solar Convective Zone: Observations and Dynamo Theory

We continue our attempt to connect observational data on current helicity in solar active regions with solar dynamo models. In addition to our previous results about temporal and latitudinal distributions of current helicity (Kleeorin et al. 2003), we argue that some information concerning the radial profile of the current helicity averaged over time and latitude can be extracted from the available observations. The main feature of this distribution can be presented as follows. Both shallow and deep active regions demonstrate a clear dominance of one sign of current helicity in a given hemisphere during the whole cycle. Broadly speaking, current helicity has opposite polarities in the Northern and Southern hemispheres, although there are some active regions that violate this polarity rule. The relative number of active regions violating the polarity rule is significantly higher for deeper active regions. A separation of active regions into `shallow', `middle' and `deep' is made by comparing their rotation rate and the helioseismic rotation law. We use a version of Parker's dynamo model in two spatial dimensions, that employs a nonlinearity based on magnetic helicity conservation arguments. The predictions of this model about the radial distribution of solar current helicity appear to be in remarkable agreement with the available observational data; in particular the relative volume occupied by the current helicity of "wrong" sign grows significantly with the depth.Comment: 12 pages, 8 Postscript figures, uses mn2e.cl

In--out intermittency in PDE and ODE models

We find concrete evidence for a recently discovered form of intermittency, referred to as in--out intermittency, in both PDE and ODE models of mean field dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in systems with invariant submanifolds and, as opposed to on--off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behaviour may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in--out intermittency are axisymmetric mean--field dynamo models which are often used to study the observed large scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at http://www.eurico.web.co

Modelling pellet flow in single extrusion with DEM

Plasticating single-screw extrusion involves the continuous conversion of loose solid pellets into a pressurized homogeneous melt that is pumped through a shaping tool. Traditional analyses of the solids conveying stage assume the movement of an elastic solid plug at a fixed speed. However, not only the corresponding predictions fail considerably, but it is also well known that, at least in the initial screw turns, the flow of loose individual pellets takes place. This study follows previous efforts to predict the characteristics of such a flow using the discrete element method. The model considers the development of normal and tangential forces resulting from the inelastic collisions between the pellets and between them and the neighbouring metallic surfaces. The algorithm proposed here is shown to be capable of capturing detailed features of the granular flow. The predictions of velocities in the cross- and down-channel directions and of the coordination number are in good agreement with equivalent reported results. The effect of pellet size on the flow features is also discussed

Changes in Solar Dynamics from 1995 to 2002

Data obtained by the GONG and MDI instruments over the last seven years are used to study how solar dynamics -- both rotation and other large scale flows -- have changed with time. In addition to the well known phenomenon of bands of faster and slower rotation moving towards the equator and pole, we find that the zonal flow pattern rises upwards with time. Like the zonal flows, the meridional flows also show distinct solar activity related changes. In particular, the anti-symmetric component of the meridional flow shows a decrease in speed with activity. We do not see any significant temporal variations in the dynamics of the tachocline region where the solar dynamo is believed to be operating.Comment: To appear in ApJ, March 1 200

On Predicting the Solar Cycle using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -- this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic mean-field models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap

Application of hydraulic transients for leak detection in water supply systems

Abstract The current paper reports the investigation of two transient-based techniques for leak detection in water pipe systems using physical data collected in the laboratory and in quasi-field conditions. The first is the analysis of the leak reflected wave during a transient event and the second is inverse transient analysis (ITA). This was approached through the development of an inverse transient analysis tool and the collection of transient data for the testing and validation of this model. Two experimental programmes were carried out at Imperial College and in cooperation with Thames Water for the validation and testing of these techniques. Evaluation of the presence, location and size of leaks was carried out using the collected data. Transient-based techniques have been shown to be successful in the detection and location of leaks and leak location uncertainties depended on the leak size and location, flow regime and location where the transient event was generated. These leak detection methods are very promising for identifying the general area of the trunk main with leakage, and can be combined with other leak location techniques (e.g. acoustic equipment) to more precisely pinpoint the leak position. Transient-based techniques are particularly important for the diagnosis, monitoring and control of existing water supply systems, not only to detect leaks, but also to better understand the causes of pipe bursts and accidents, particularly when these are due to natural transient events