On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

The vertical structure of oceanic Rossby waves: a comparison of high-resolution model data to theoretical vertical structures

Tests of the new Rossby wave theories that have been developed over the past decade to account for discrepancies between theoretical wave speeds and those observed by satellite altimeters have focused primarily on the surface signature of such waves. It appears, however, that the surface signature of the waves acts only as a rather weak constraint, and that information on the vertical structure of the waves is required to better discriminate between competing theories. Due to the lack of 3-D observations, this paper uses high-resolution model data to construct realistic vertical structures of Rossby waves and compares these to structures predicted by theory. The meridional velocity of a section at 24° S in the Atlantic Ocean is pre-processed using the Radon transform to select the dominant westward signal. Normalized profiles are then constructed using three complementary methods based respectively on: (1) averaging vertical profiles of velocity, (2) diagnosing the amplitude of the Radon transform of the westward propagating signal at different depths, and (3) EOF analysis. These profiles are compared to profiles calculated using four different Rossby wave theories: standard linear theory (SLT), SLT plus mean flow, SLT plus topographic effects, and theory including mean flow and topographic effects. Our results support the classical theoretical assumption that westward propagating signals have a well-defined vertical modal structure associated with a phase speed independent of depth, in contrast with the conclusions of a recent study using the same model but for different locations in the North Atlantic. The model structures are in general surface intensified, with a sign reversal at depth in some regions, notably occurring at shallower depths in the East Atlantic. SLT provides a good fit to the model structures in the top 300 m, but grossly overestimates the sign reversal at depth. The addition of mean flow slightly improves the latter issue, but is too surface intensified. SLT plus topography rectifies the overestimation of the sign reversal, but overestimates the amplitude of the structure for much of the layer above the sign reversal. Combining the effects of mean flow and topography provided the best fit for the mean model profiles, although small errors at the surface and mid-depths are carried over from the individual effects of mean flow and topography respectively. Across the section the best fitting theory varies between SLT plus topography and topography with mean flow, with, in general, SLT plus topography performing better in the east where the sign reversal is less pronounced. None of the theories could accurately reproduce the deeper sign reversals in the west. All theories performed badly at the boundaries. The generalization of this method to other latitudes, oceans, models and baroclinic modes would provide greater insight into the variability in the ocean, while better observational data would allow verification of the model findings.

Climate impacts on river flow: projections for the Medway catchment UK with UKCP09 and CATCHMOD

The potential impact of climate change on areas of strategic importance for water resources remains a concern. Here, river flow projections for the River Medway, above Teston in southeast England are presented, which is just such an area of strategic importance. The river flow projections use climate inputs from the Hadley Centre Regional Climate Model (HadRM3) for the time period 1960–2080 (a subset of the early release UKCP09 projections). River flow predictions are calculated using CATCHMOD, the main river flow prediction tool of the Environment Agency (EA) of England and Wales. In order to use this tool in the best way for climate change predictions, model setup and performance are analysed using sensitivity and uncertainty analysis. The model's representation of hydrological processes is discussed and the direct percolation and first linear storage constant parameters are found to strongly affect model results in a complex way, with the former more important for low flows and the latter for high flows. The uncertainty in predictions resulting from the hydrological model parameters is demonstrated and the projections of river flow under future climate are analysed. A clear climate change impact signal is evident in the results with a persistent lowering of mean daily river flows for all months and for all projection time slices. Results indicate that a projection of lower flows under future climate is valid even taking into account the uncertainties considered in this modelling chain exercise. The model parameter uncertainty becomes more significant under future climate as the river flows become lower. This has significant implications for those making policy decisions based on such modelling results. Copyright © 2010 John Wiley & Sons, Ltd.

Flow structure and near-field dispersion in arrays of building-like obstacles

Dispersion in the near-field region of localised releases in urban areas is difficult to predict because of the strong influence of individual buildings. Effects include upstream dispersion, trapping of material into building wakes and enhanced concentration fluctuations. As a result, concentration patterns are highly variable in time and mean profiles in the near field are strongly non-Gaussian. These aspects of near-field dispersion are documented by analysing data from direct numerical simulations in arrays of building-like obstacles and are related to the underlying flow structure. The mean flow structure around the buildings is found to exert a strong influence over the dispersion of material in the near field. Diverging streamlines around buildings enhance lateral dispersion. Entrainment of material into building wakes in the very near field gives rise to secondary sources, which then affect the subsequent dispersion pattern. High levels of concentration fluctuations are also found in this very near field; the fluctuation intensity is of order 2 to 5.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels

A lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries. The mass conservation for the boundary condition is tested in detail. The viscous flow in elastic vessels is simulated with a pressure-radius relationship similar to that of the Pulmonary blood vessels. The numerical results for steady flow agree with the analytical prediction to very high accuracy, and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally. The model is expected to find many applications for studying blood flows in large distensible arteries, especially in those suffering from atherosclerosis. stenosis. aneurysm, etc.

Resonance response of electrorheological fluids in vertical oscillation squeeze flow

The resonance effect of microcrystalline cellulose/castor oil electrorheological (ER) suspensions was studied in a compressed oscillatory squeeze flow under external electric fields. The resonance frequency first increases linearly with increasing external held, and then shift to high-field plateau. The amplitudes of resonance peak increase sharply with the applied fields in the range of 0.17-1.67kV/mm. The phase difference of the reduced displacement relative to the excitation force inverses in the case of resonance. A viscoelasticity model of the ER suspensions, which offers both the equivalent stiffness and the viscous damping, should be responsible for the appearance of resonance. The influence of the electric field on the resonance frequency and the resonance hump is consistent qualitatively with the interpretation of our proposed model. Storage modulus G' was presented for the purpose of investigating this influence.

A comparison between ion characteristics observed by the POLAR and DMSP spacecraft in the high-latitude magnetosphere

We study here the injection and transport of ions in the convection-dominated region of the Earth’s magnetosphere. The total ion counts from the CAMMICE MICS instrument aboard the POLAR spacecraft are used to generate occurrence probability distributions of magnetospheric ion populations. MICS ion spectra are characterised by both the peak in the differential energy flux, and the average energy of ions striking the detector. The former permits a comparison with the Stubbs et al. (2001) survey of He2+ ions of solar wind origin within the magnetosphere. The latter can address the occurrences of various classifications of precipitating particle fluxes observed in the topside ionosphere by DMSP satellites (Newell and Meng, 1992). The peak energy occurrences are consistent with our earlier work, including the dawn-dusk asymmetry with enhanced occurrences on the dawn flank at low energies, switching to the dusk flank at higher energies. The differences in the ion energies observed in these two studies can be explained by drift orbit effects and acceleration processes at the magnetopause, and in the tail current sheet. Near noon at average ion energies of _1 keV, the cusp and open LLBL occur further poleward here than in the Newell and Meng survey, probably due to convectionrelated time-of-flight effects. An important new result is that the pre-noon bias previously observed in the LLBL is most likely due to the component of this population on closed field lines, formed largely by low energy ions drifting earthward from the tail. There is no evidence here of mass and momentum transfer from the solar wind to the LLBL by nonreconnection coupling. At higher energies (_2–20 keV), we observe ions mapping to the auroral oval and can distinguish between the boundary and central plasma sheets. We show that ions at these energies relate to a transition from dawnward to duskward dominated flow, this is evidence of how ion drift orbits in the tail influence the location and behaviour of the plasma populations in the magnetosphere.

Variability of dayside high latitude convection associated with a sequence of auroral transients

10 second resolution ionospheric convection data covering the invariant latitude range from 71° to 76°, obtained by using the EISCAT UHF and VHF radars, are combined with optical data from Ny Ålesund during a sequence of auroral transients in the post-noon sector (∼ 15 MLT). Satellite observations of polar cap convection patterns suggest negative BZ and BY components of the interplanetary magnetic field. Burst-like enhancements of westward (sunward) post-noon convection were accompanied by eastward moving auroral forms at higher latitudes, above the convection reversal boundary. In this case the background convection was weak, whereas the integrated potential drop across the radar field-of-view associated with the westward flow bursts was typically ∼ 20-35 kV. The auroral phenomenon consists of a series of similar events with a mean repetition period of 8 min. A close correlation between the auroral activity and convection enhancements in the cleft ionosphere is demonstrated.

Modelling the high-latitude ionosphere for time-varying plasma convection

The paper discusses how variations in the pattern of convective plasma flows should beincluded in self-consistent time-dependent models of the coupled ionosphere-thermosphere system. The author shows how these variations depend upon the mechanism by which the solar wind flow excites the convection. The modelling of these effects is not just of relevance to the polar ionosphere. This is because the influence of convection is not confined to high latitudes: the resultant heating and composition changes in the thermosphere are communicated to lower latitudes by the winds which are also greatly modified by the plasma convection. These thermospheric changes alter the global distribution of plasma by modulatingthe rates of the chemical reactions which areresponsible for the loss of plasma. Hence the modelling of these high-latitude processes is of relevanceto the design and operation of HF communication, radar and navigation systems worldwide.

Periodic auroral events at the high-latitude convection reversal in the 16 MLT region

Combined optical and radar observations of two breakup-like auroral events near the polar cap boundary, within 74–76° MLAT and 1210 – 1240 UT (roughly 1540 – 1610 MLT) on 9 Jan. 1989 are reported. A two-component structure of the auroral phenomenon is indicated, with a local intensification of the pre-existing arc as well as a separate, tailward moving discrete auroral event on the poleward side of the background aurora, close to the reversal between well-defined zones of sunward and tailward ion flows. The all-sky TV observations do not indicate a connection between the two components, which also show different optical spectral composition. The 16 MLT background arc is located on sunward convecting field lines, as opposed to the 12–14 MLT auroral emission observed on this day. Although the magnetospheric plasma source (s) of the 16 MLT events are not easily identified from these ground-based data alone, it is suggested that the lower and higher latitude components, may map to the plasma sheet boundary layer and along open field lines to the magnetopause boundary, respectively. The events occur at the time of enhancements of westward ionospheric ion flow and corresponding eastward electrojet current south of 74° MLAT. Thus, they seem to be very significant events, involving periodic (10 min period), tailward moving filaments of field-aligned current/discrete auroral emission at the 16 MLT polar cap boundary.

The excitation of plasma convection in the high-latitude ionosphere

Recent observations of ionospheric flows by ground-based radars, in particular by the European Incoherent Scatter (EISCAT) facility using the “Polar” experiment, together with previous analyses of the response of geomagnetic disturbance to variations of the interplanetary magnetic field (IMF), suggest that convection in the high-latitude ionosphere should be considered to be the sum of two intrinsically time-dependent patterns, one driven by solar wind-magnetosphere coupling at the dayside magnetopause, the other by the release of energy in the geomagnetic tail (mainly by dayside and nightside reconnection, respectively). The flows driven by dayside coupling are largest on the dayside, where they usually dominate, are associated with an expanding polar cap area, and are excited and decay on ∼10-min time scales following southward and northward turnings of the IMF, respectively. The latter finding indicates that the production of new open flux at the dayside magnetopause excites magnetospheric and ionospheric flow only for a short interval, ∼10 min, such that the flow driven by this source subsequently decays on this time scale unless maintained by the production of more open flux tubes. Correspondingly, the flows excited by the release of energy in the tail, mainly during substorms, are largest on the nightside, are associated with a contracting polar cap boundary, and are excited on ∼1-hour time scales following a southward turn of the IMF. In general, the total ionospheric flow will be the sum of the flows produced by these two sources, such that due to their different response times to changes in the IMF, considerable variations in the flow pattern can occur for a given direction and strength of the IMF. Consequently, the ionospheric electric field cannot generally be regarded as arising from a simple mapping of the solar wind electric field along open flux tubes.

Comparisons between EISCAT observations and model calculations of the high latitude ionosphere

Calculations using a numerical model of the convection dominated high latitude ionosphere are compared with observations made by EISCAT as part of the UK-POLAR Special Programme. The data used were for 24–25 October 1984, which was characterized by an unusually steady IMF, with Bz < 0 and By > 0; in the calculations it was assumed that a steady IMF implies steady convection conditions. Using the electric field models of Heppner and Maynard (1983) appropriate to By > 0 and precipitation data taken from Spiroet al. (1982), we calculated the velocities and electron densities appropriate to the EISCAT observations. Many of the general features of the velocity data were reproduced by the model. In particular, the phasing of the change from eastward to westward flow in the vicinity of the Harang discontinuity, flows near the dayside throat and a region of slow flow at higher latitudes near dusk were well reproduced. In the afternoon sector modelled velocity values were significantly less than those observed. Electron density calculations showed good agreement with EISCAT observations near the F-peak, but compared poorly with observations near 211 km. In both cases, the greatest disagreement occurred in the early part of the observations, where the convection pattern was poorly known and showed some evidence of long term temporal change. Possible causes for the disagreement between observations and calculations are discussed and shown to raise interesting and, as yet, unresolved questions concerning the interpretation of the data. For the data set used, the late afternoon dip in electron density observed near the F-peak and interpreted as the signature of the mid-latitude trough is well reproduced by the calculations. Calculations indicate that it does not arise from long residence times of plasma on the nightside, but is the signature of a gap between two major ionization sources, viz. photoionization and particle precipitation.

Response time of the high-latitude dayside ionosphere to sudden changes in the north-south component of the IMF

The time scale of the response of the high-latitude dayside ionospheric flow to changes in the North-South component of the interplanetary magnetic field (IMF) has been investigated by examining the time delays between corresponding sudden changes. Approximately 40 h of simultaneous IMF and ionospheric flow data have been examined, obtained by the AMPTE-UKS and -IRM spacecraft and the EISCAT “Polar” experiment, respectively, in which 20 corresponding sudden changes have been identified. Ten of these changes were associated with southward turnings of the IMF, and 10 with northward turnings. It has been found that the corresponding flow changes occurred simultaneously over the whole of the “Polar” field-of-view, extending more than 2° in invariant latitude, and that the ionospheric response delay following northward turnings is the same as that following southward turnings, though the form of the response is different in the two cases. The shortest response time, 5.5 ± 3.2 min, is found in the early- to mid-afternoon sector, increasing to 9.5 ± 3.0 min in the mid-morning sector, and to 9.5 ± 3.1 min near to dusk. These times represent the delays in the appearance of perturbed flows in the “Polar” field-of-view following the arrival of IMF changes at the subsolar magnetopause. Overall, the results agree very well with those derived by Etemadi et al. (1988, Planet. Space Sci.36, 471) from a general cross-correlation analysis of the IMF Bz and “Polar” beam-swinging vector flow data.

Vertical ion flow in the polar ionosphere

Outflowing ions from the polar ionosphere fall into two categories: the classical polar wind and the suprathermal ion flows. The flows in both these categories vary a great deal with altitude. The classical polar wind is supersonic at high altitude: at ∼3 RE geocentric, the observed polar wind is H+ dominated and has a Mach number of 2.5–5.1. At 400–600 km, thermal and suprathermal upward O+ ion fluxes frequently occur at the poleward edge of the nightside auroral oval during magnetically active times. Above 500 km, ions are accelerated transverse to the local geomagnetic field. At 1400 km, transversely accelerated ions are frequently observed in winter nights but rarely appear in the summer. In the dayside cleft above ∼2000 km, ions of all species are transversely heated and upwell with significant number and heat fluxes, forming a cleft ion fountain as they convect across the polar cap. Upwelling ions are observed most (least) frequently in the summer (winter). At yet higher altitudes, energetic (>10 eV to several kiloelectron volts) upflowing H+ and O+ ions are frequently observed, their active time occurrence frequency being as high as 0.7 at auroral latitudes and 0.3 in the polar cap. Their composition, intensity, and angular characteristics vary quantitatively with solar activity, being O+ dominant and more intense near solar maximum. Their resulting ion outflow is dominated by ions below 1 keV and reaches 3.5×10^26 O+ and 7×10^25 H+ ions s^{−1} at magnetically active times (Kp≥5) near solar maximum. In comparison, the estimated polar wind ion outflow at times of moderate solar activity is 7×10^25H+ and 4×10^24 He+ ions s^{−1}. The estimated <10-eV cleft ion fountain flow is 3.8×10^25 O+ and 8.6×10^23 H+ ions s^{−1} near solar maximum.