Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

Can late-type active stars be explained by a dipole magnetic trap?

In this paper we review four different types of X-ray and/or radio observations of active late-type stars. We then consider if a single magnetic source configuration – a toroidal dipole magnetic trap – can possibly explain these various different observations. We conclude that, indeed, dipole magnetic confinement (similar to the magnetic configurations of the Earth's radiation belts and the case of Jupiter and the Io torus) can explain all the diverse observational data. We take this to be very strong observational support for this type of magnetic confinement scheme. We also consider that this magnetic configuration is only likely to be established and maintained in the most active stars.     

A concept for a superconducting tunnelling junction based spectrograph

We describe a multi-order spectrograph concept suitable for 8-m class telescopes, using the intrinsic spectral resolution of superconducting tunnelling junction detectors to sort the spectral orders. The spectrograph works at low orders, 1–5 or 1–6, and provides spectral coverage with a resolving power of   R ≃ 8000  from the atmospheric cut-off at 320 nm to the long-wavelength end of the infrared H or K band at 1800 nm or 2400 nm. We calculate that the spectrograph would provide substantial throughput and wavelength coverage, together with high time resolution and sufficient dynamic range. The concept uses currently available technology, or technologies with short development horizons, restricting the spatial sampling to two linear arrays; however, an upgrade path to provide more spatial sampling is identified. All of the other challenging aspects of the concept – the cryogenics, thermal baffling and magnetic field biasing – are identified as being feasible.     

Solar coronal heating by high-frequency dispersive Alfvén waves

It is shown that high-frequency dispersive kinetic Alfvén waves can cause significant electron heating in the solar corona. The heating is produced by collisionless electron Landau dissipation of the parallel electron current associated with high-frequency dispersive kinetic Alfvén waves, which have a parallel electric field.     

Proton acceleration in flares and magnetohydrodynamic solar activity

The possibility of accelerated protons in solar flares having a sharp change in their spectral index is discussed. The analysis is based on the Tsytovich (1982, 1984, 1987a, b, c) acceleration model by MHD turbulence, which is shown to have different resonant conditions for non-relativistic and relativistic particles. The different resonant condition is shown to result in a sharp change in the accelerated proton spectral index, even in the absence of any peculiarity in the spectra of the MHD turbulence. Time scales for accelerated protons to relativistic energies are also derived, and shown to be consistent with observations. We also show that the threshold energy for electron acceleration by low frequency MHD turbulence is much greater than for proton acceleration. The turbulence therefore preferentially accelerates protons.     

Improving the Coastal Mean Dynamic Topography by Geodetic Combination of Tide Gauge and Satellite Altimetry

Abstract

The ocean mean dynamic topography (MDT) is the surface representation of the ocean circulation. The MDT may be determined by the ocean approach, which involves temporal averaging of numerical ocean circulation model information, or by the geodetic approach, wherein the MDT is derived using the ellipsoidal height of the mean sea surface (MSS), or mean sea level (MSL) minus the geoid as the geoid. The ellipsoidal height of the MSS might be estimated either by satellite or coastal tide gauges by connecting the tide gauge datum to the Earth-centred reference frame. In this article we present a novel approach to improve the coastal MDT, where the solution is based on both satellite altimetry and tide gauge data using new set of 302 tide gauges with ellipsoidal heights through the SONEL network. The approach was evaluated for the Northeast Atlantic coast where a dense network of GNSS-surveyed tide gauges is available. The typical misfit between tide gauge and satellite or oceanographic MDT was found to be around 9?cm. This misfit was found to be mainly due to small scale geoid errors. Similarly, we found, that a single tide gauge places only weak constraints on the coastal dynamic topography.     

Evapotranspiration from the margin and moist playa of a closed desert valley

Two long term microclimate measurement stations with Bowen ratio capability have been used to study water cycling in a closed desert basin. Microclimate variables including the temperature and vapor pressure gradients were monitored continuously and were used to estimate the Bowen ratio, sensible and latent heat fluxes during 1986 and 1987. Despite having a water table that varied between the surface and 30 cm below the surface, the playa had little evaporation except after rainfall events. The very high osmotic pressure of the soil and salt crust caused most of the absorbed radiation to be partitioned to sensible heat. In contrast, along the margin the thin grass and brush cover transpired water freely, with the latent heat flux exceeding 60% of available energy for much of the season. The higher air temperatures above the playa raised potential evapotranspiration (ET) significantly higher than along the margin throughout the summer. The annual average actual ET of the playa was only 36% of the margin. During the drier summer period (May–October), this ratio decreased to < 28%. Immediately after a rainfall event, evaporation rates of the two sites were similar, but the playa rate was quickly reduced as the osmotic potential increased. During this study, the playa lost < 229 mm of subsurface water to evaporation annually, while > 638 mm were lost from the margin groundwater supply.

The 24-h solar and net radiation correlations were 0.80 and 0.94 for the playa and margin, respectively. The lower correlation for the playa resulted from the wide variation of albedo with surface moisture changes. The annual average albedo values for the playa and margin were 0.64 and 0.46, respectively.     

Comparison of upper ocean thermal conditions in the western North Pacific between two pentads: 1938–42 and 1978–82

In order to understand long-term changes in the temperature structure of the upper western North Pacific, we compared thermal conditions in two pentads, 1938–42 (P34) and 1978–82 (P78). The 1938–42 data were taken mostly by the Japanese Imperial Navy in a series of hydrographic surveys. The 1978–82 data were mostly XBT data taken as part of the TRANSPAC program. For each pentad, the data were interpolated to a set of standard depths, put through quality control procedures and averaged on a 1^o×1^o grid. A large area of the central subtropical gyre was warmer during P78, while the southern subtropical gyre, in the area of the North Equatorial Current was warmer during P34. This suggests that the transports of the Kuroshio and North Equatorial currents were larger during P78. Properties of North Pacific subtropical mode water (NPSTMW) were compared between pentads. It was found that NPSTMW was thicker, more uniform in temperature and more confined geographically during P34. A greater thickness is shown to result from stronger wintertime cooling during P34. Changes in the geographic extent of NPSTMW probably result from reduced advection by the Kuroshio current system during P34. The reason for the reduced advection maybe the Kuroshio was in a large meander state for a larger fraction of the earlier pentad, which can cut off advection west of the Izu Ridge.     

Odyssey: a solar system mission

The Solar System Odyssey mission uses modern-day high-precision experimental techniques to test the laws of fundamental physics which determine dynamics in the solar system. It could lead to major discoveries by using demonstrated technologies and could be flown within the Cosmic Vision time frame. The mission proposes to perform a set of precision gravitation experiments from the vicinity of Earth to the outer Solar System. Its scientific objectives can be summarized as follows: (1) test of the gravity force law in the Solar System up to and beyond the orbit of Saturn; (2) precise investigation of navigation anomalies at the fly-bys; (3) measurement of Eddington’s parameter at occultations; (4) mapping of gravity field in the outer solar system and study of the Kuiper belt. To this aim, the Odyssey mission is built up on a main spacecraft, designed to fly up to 13 AU, with the following components: (a) a high-precision accelerometer, with bias-rejection system, measuring the deviation of the trajectory from the geodesics, that is also giving gravitational forces; (b) Ka-band transponders, as for Cassini, for a precise range and Doppler measurement up to 13 AU, with additional VLBI equipment; (c) optional laser equipment, which would allow one to improve the range and Doppler measurement, resulting in particular in an improved measurement (with respect to Cassini) of the Eddington’s parameter. In this baseline concept, the main spacecraft is designed to operate beyond the Saturn orbit, up to 13 AU. It experiences multiple planetary fly-bys at Earth, Mars or Venus, and Jupiter. The cruise and fly-by phases allow the mission to achieve its baseline scientific objectives [(1) to (3) in the above list]. In addition to this baseline concept, the Odyssey mission proposes the release of the Enigma radio-beacon at Saturn, allowing one to extend the deep space gravity test up to at least 50 AU, while achieving the scientific objective of a mapping of gravity field in the outer Solar System [(4) in the above list].