Amplitude equations for Rayleigh-Benard convective rolls far from threshold

An extension of the amplitude method is proposed. An iterative algorithm is developed to build an amplitude equation model that is shown to provide precise quantitative results even far from the linear instability threshold. The method is applied to the study of stationary Rayleigh-Benard thermoconvective rolls in the nonlinear regime. In particular, the generation of second and third spatial harmonics is analyzed. Comparison with experimental results and direct numerical calculations is also made and a very good agreement is found.Peer reviewe

Use of the continuity equation for transesophageal Doppler assessment of severity of proximal left coronary artery stenosis: a quantitative coronary angiography validation study

AbstractObjectives. We tested the value of transesophageal Doppler echocardiography (TEDE) for quantitating proximal left coronary artery (LCA) stenosis by using the continuity equation.Background. The continuity equation applied to a stenosis states that the ratio of the time–velocity integral (TVI) of prestenotic to stenotic flow velocities is equal to the ratio of stenotic to prestenotic cross-sectional areas. TEDE allows the measurement of coronary blood flow velocities within the proximal part of the LCA.Methods. Forty-one patients with a stenosis of the proximal or mid left anterior descending coronary artery or with a nonostial stenosis of the left main coronary artery were studied. Coronary flow velocities were recorded by TEDE guided by color flow imaging. Prestenotic velocities were recorded by pulsed Doppler echocardiography and transstenotic velocities were recorded by pulsed or high pulse repetition frequency or continuous wave Doppler echocardiography. The prestenotic and transstenotic diastolic TVIs were calculated and the TEDE-derived percent area stenosis was calculated as (1 − TVI ratio) × 100. Quantitative angiography lesion analysis was performed using a computer-assisted automated edge-detection system.Results. TEDE recordings were successful in 35 of the 41 patients. A good linear correlation was found between TEDE and quantitative angiographically derived percent area stenosis (r = 0.89, p = 0.0001, SEE 5.7). However, TEDE measurements underestimated the actual percent area stenosis (slope of regression 0.54). A better agreement (slope 1.08) was obtained after dividing prestenotic velocity by 2 in the continuity equation, based on the assumption of a parabolic cross-sectional velocity profile in the prestenotic segment.Conclusions. TEDE may be used for quantitating stenosis of the proximal part of the LCA with the use of a modified continuity equation that takes into account the parabolic velocity profile in the normal prestenotic segment

Pulsed flows at the high-altitude cusp poleward boundary, and associated ionospheric convection and particle signatures, during a cluster - FAST - SuperDARN - sondrestrom conjunction under a southwest

Particle and magnetic field observations during a magnetic conjunction Cluster 1-FAST-Søndrestrøm within the field of view of SuperDARN radars on 21 January 2001 allow us to draw a detailed, comprehensive and self-consistent picture at three heights of signatures associated with transient reconnection under a steady south-westerly IMF (clock angle ≈130◦). Cluster 1 was outbound through the high altitude (∼12RE ) exterior northern cusp tailward of the bifurcation line (geomagnetic Bx>0) when a solar wind dynamic pressure release shifted the spacecraft into a boundary layer downstream of the cusp. The centerpiece of the investigation is a series of flow bursts observed there by the spacecraft, which were accompanied by strong field pertur- bations and tailward flow deflections. Analysis shows these to be Alfven waves. We interpret these flow events as being due to a sequence of reconnected flux tubes, with field-aligned currents in the associated Alfven waves carrying stresses to the underlying ionosphere, a view strengthened by the other observations. At the magnetic footprint of the region of Cluster flow bursts, FAST observed an ion energy- latitude disperison of the stepped cusp type, with individual cusp ion steps corresponding to individual flow bursts. Simultaneously, the SuperDARN Stokkseyri radar observed very strong poleward-moving radar auroral forms (PMRAFs) which were conjugate to the flow bursts at Cluster. FAST was traversing these PMRAFs when it observed the cusp ion steps. The Søndrestrøm radar observed pulsed ionospheric flows (PIFs) just poleward of the convection reversal boundary. As at Cluster, the flow was eastward (tailward), implying a coherent eastward (tailward) motion of the hypothesized open flux tubes. The joint Søndrestrøm and FAST observations indicate that the open/closed field line boundary was equatorward of the convection reversal boundary by ∼2 deg. The unprecedented accuracy of the conjunction argues strongly for the validity of the interpretation of the various signatures as resulting from transient reconnection. In particular, the cusp ion steps arise on this pass from this origin, in consonance with the original pulsating cusp model. The observations point to the need of extending current ideas on the response of the ionosphere to transient reconnection. Specifically, it argues in favor of re-establishing the high-latitude boundary layer downstream of the cusp as an active site of momentum transfer

Impact of the 26-30 May 2003 solar events on the earth ionosphere and thermosphere.

During the last week of May 2003, the solar active region AR 10365 produced a large number of flares, several of which were accompanied by Coronal Mass Ejections (CME). Specifically on 27 and 28 May three halo CMEs were observed which had a significant impact on geospace. On 29 May, upon their arrival at the L1 point, in front of the Earth's magnetosphere, two interplanetary shocks and two additional solar wind pressure pulses were recorded by the ACE spacecraft. The interplanetary magnetic field data showed the clear signature of a magnetic cloud passing ACE. In the wake of the successive increases in solar wind pressure, the magnetosphere became strongly compressed and the sub-solar magnetopause moved inside five Earth radii. At low altitudes the increased energy input to the magnetosphere was responsible for a substantial enhancement of Region-1 field-aligned currents. The ionospheric Hall currents also intensified and the entire high-latitude current system moved equatorward by about 10°. Several substorms occurred during this period, some of them - but not all - apparently triggered by the solar wind pressure pulses. The storm's most notable consequences on geospace, including space weather effects, were (1) the expansion of the auroral oval, and aurorae seen at mid latitudes, (2) the significant modification of the total electron content in the sunlight high-latitude ionosphere, (3) the perturbation of radio-wave propagation manifested by HF blackouts and increased GPS signal scintillation, and (4) the heating of the thermosphere, causing increased satellite drag. We discuss the reasons why the May 2003 storm is less intense than the October-November 2003 storms, although several indicators reach similar intensities

ESR and EISCAT observations of the response of the cusp and cleft to IMF orientation changes

International audienceWe report observations of the cusp/cleft ionosphere made on December 16th 1998 by the EISCAT (European incoherent scatter) VHF radar at Tromsø and the EISCAT Svalbard radar (ESR). We compare them with observations of the dayside auroral luminosity, as seen by meridian scanning photometers at Ny Ålesund and of HF radar backscatter, as observed by the CUTLASS radar. We study the response to an interval of about one hour when the interplanetary magnetic field (IMF), monitored by the WIND and ACE spacecraft, was southward. The cusp/cleft aurora is shown to correspond to a spatially extended region of elevated electron temperatures in the VHF radar data. Initial conditions were characterised by a northward-directed IMF and cusp/cleft aurora poleward of the ESR. A strong southward turning then occurred, causing an equatorward motion of the cusp/cleft aurora. Within the equatorward expanding, southward-IMF cusp/cleft, the ESR observed structured and elevated plasma densities and ion and electron temperatures. Cleft ion fountain upflows were seen in association with elevated ion temperatures and rapid eastward convection, consistent with the magnetic curvature force on newly opened field lines for the observed negative IMF By. Subsequently, the ESR beam remained immediately poleward of the main cusp/cleft and a sequence of poleward-moving auroral transients passed over it. After the last of these, the ESR was in the polar cap and the radar observations were characterised by extremely low ionospheric densities and downward field-aligned flows. The IMF then turned northward again and the auroral oval contracted such that the ESR moved back into the cusp/cleft region. For the poleward-retreating, northward-IMF cusp/cleft, the convection flows were slower, upflows were weaker and the electron density and temperature enhancements were less structured. Following the northward turning, the bands of high electron temperature and cusp/cleft aurora bifurcated, consistent with both subsolar and lobe reconnection taking place simultaneously. The present paper describes the large-scale behaviour of the ionosphere during this interval, as observed by a powerful combination of instruments. Two companion papers, by Lockwood et al. (2000) and Thorolfsson et al. (2000), both in this issue, describe the detailed behaviour of the poleward-moving transients observed during the interval of southward Bz, and explain their morphology in the context of previous theoretical work

The mechanical effects of short-circuit currents in open air substations.

SHort-circuit mechanical effects in substation is investigated by tests and simulations. Simplified equations are deduced to prepare standardisation of a procedure forthe design of substation against short-circuit mechanicle effects