Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite-element velocity/surface-elevation pairs that are used to approximate the linear shallow-water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P0-P1, RT0 and P-P1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results.

Cross section of a resonant-mass detector for scalar gravitational waves

Gravitationally coupled scalar fields, originally introduced by Jordan, Brans and Dicke to account for a non-constant gravitational coupling, are a prediction of many non-Einsteinian theories of gravity not excluding perturbative formulations of string theory. In this paper, we compute the cross sections for scattering and absorption of scalar and tensor gravitational waves by a resonant-mass detector in the framework of the Jordan-Brans-Dicke theory. The results are then specialized to the case of a detector of spherical shape and shown to reproduce those obtained in general relativity in a certain limit. Eventually we discuss the potential detectability of scalar waves emitted in a spherically symmetric gravitational collapse.

On some properties of traveling water waves with vorticity

We prove that for a large class of vorticity functions the crests of any corresponding traveling gravity water wave of finite depth are necessarily points of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure everywhere in the fluid is larger than the atmospheric pressure. A related a priori estimate for waves with nonnegative vorticity is also given.

On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

On the momentum fluxes associated with mountain waves in directionally sheared flows

The direct impact of mountain waves on the atmospheric circulation is due to the deposition of wave momentum at critical levels, or levels where the waves break. The first process is treated analytically in this study within the framework of linear theory. The variation of the momentum flux with height is investigated for relatively large shears, extending the authors’ previous calculations of the surface gravity wave drag to the whole atmosphere. A Wentzel–Kramers–Brillouin (WKB) approximation is used to treat inviscid, steady, nonrotating, hydrostatic flow with directional shear over a circular mesoscale mountain, for generic wind profiles. This approximation must be extended to third order to obtain momentum flux expressions that are accurate to second order. Since the momentum flux only varies because of wave filtering by critical levels, the application of contour integration techniques enables it to be expressed in terms of simple 1D integrals. On the other hand, the momentum flux divergence (which corresponds to the force on the atmosphere that must be represented in gravity wave drag parameterizations) is given in closed analytical form. The momentum flux expressions are tested for idealized wind profiles, where they become a function of the Richardson number (Ri). These expressions tend, for high Ri, to results by previous authors, where wind profile effects on the surface drag were neglected and critical levels acted as perfect absorbers. The linear results are compared with linear and nonlinear numerical simulations, showing a considerable improvement upon corresponding results derived for higher Ri.

Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization

The Canadian Middle Atmosphere Model is used to examine the sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. Momentum conservation requires that the parameterized gravity wave momentum flux at the top of the model be zero and corresponds to the physical boundary condition of no momentum flux at the top of the atmosphere. Allowing momentum flux to escape the model domain violates momentum conservation. Here the impact of momentum conservation in two sets of model simulations is investigated. In the first set, the simulation of present-day climate for two model-lid height configurations, 0.001 and 10 hPa, which are identical below 10 hPa, is considered. The impact of momentum conservation on the climate with the model lid at 0.001 hPa is minimal, which is expected because of the small amount of gravity wave momentum flux reaching 0.001 hPa. When the lid is lowered to 10 hPa and momentum is conserved, there is only a modest impact on the climate in the Northern Hemisphere; however, the Southern Hemisphere climate is more adversely affected by the deflection of resolved waves near the model lid. When momentum is not conserved in the 10-hPa model the climate is further degraded in both hemispheres, particularly in winter at high latitudes, and the impact of momentum conservation extends all the way to the surface. In the second set of simulations, the impact of momentum conservation and model-lid height on the modeled response to ozone depletion in the Southern Hemisphere is considered, and it is found that the response can display significant sensitivity to both factors. In particular, both the lower-stratospheric polar temperature and surface responses are significantly altered when the lid is lowered, with the effect being most severe when momentum is not conserved. The implications with regard to the current round of Intergovernmental Panel on Climate Change model projections are discussed.

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.

The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

ENSO related variation of equatorial MRG and Rossby waves and forcing from higher latitudes

The contrasting behaviour of westward-moving mixed Rossby-gravity (WMRG) and the first Rossby (R1) waves in El Niño (EN) and La Niña (LN) seasons is documented with a focus on the Northern Hemisphere winter. The eastward-moving variance in the upper troposphere is dominated by WMRG and R1 structures that appear to be Doppler-shifted by the flow and are referred to as WMRG-E and R1-E. In the East Pacific and Atlantic the years with stronger equatorial westerly winds have the stronger WMRG and WMRG- E. In the East Pacific, R1 is also a maximum in LN. However, R1-E exhibits an eastward-shift between LN and EN. The changes with ENSO phase provide a test-bed for the understanding of these waves. In the East Pacific and Atlantic, the stronger WMRG-E and WMRG with stronger westerlies are in accord with the dispersion relation with simple Doppler-shifting by the zonal flow. The possible existence of free waves can also explain stronger R1 in EN in the Eastern Hemisphere. 1-D free wave propagation theory based on wave activity conservation is also important for R1. However, this theory is unable to explain the amplitude maxima for other waves observed in the strong equatorial westerly regions in the Western Hemisphere, and certainly not their ENSO-related variation. The forcing of equatorial waves by higher latitude wave activity and its variation with ENSO phase is therefore examined. Propagation of extratropical eastward-moving Rossby wave activity through the westerly ducts into the equatorial region where it triggers WMRG-E is favoured in the stronger westerlies, in LN in the East Pacific and EN in the Atlantic. It is also found that WMRG is forced by Southern Hemisphere westward-moving wavetrains arching into the equatorial region where they are reflected. The most significant mechanism for both R1 and R1-E appear to be lateral forcing by subtropical wavetrains.

Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

In this work, a new theoretical mechanism is presented in which equatorial Rossby and inertio-gravity wave modes may interact with each other through resonance with the diurnal cycle of tropical deep convection. We have adopted the two-layer incompressible equatorial primitive equations forced by a parametric heating that roughly represents deep convection activity in the tropical atmosphere. The heat source was parametrized in the simplest way according to the hypothesis that it is proportional to the lower-troposphere moisture convergence, with the background moisture state function mimicking the structure of the ITCZ. In this context, we have investigated the possibility of resonant interaction between equatorially trapped Rossby and inertio-gravity modes through the diurnal cycle of the background moisture state function. The reduced dynamics of a single resonant duo shows that when this diurnal variation is considered, a Rossby wave mode can undergo significant amplitude modulations when interacting with an inertio-gravity wave mode, which is not possible in the context of the resonant triad non-linear interaction. Therefore, the results suggest that the diurnal variation of the ITCZ can be a possible dynamical mechanism that leads the Rossby waves to be significantly affected by high frequency modes.

Alfven waves as a driving mechanism in stellar winds

Alfven waves have been invoked as an important mechanism of particle acceleration in stellar winds of cool stars. After their identification in the solar wind they started to be studied in winds of stars located in different regions of the FIR diagram. We discuss here some characteristics of these waves and we present a direct application in the acceleration of late-type stellar winds. (C) 2009 COSPAR. Published by Elsevier Ltd. All rights reserved.

Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Implementation of an F-statistic all-sky search for continuous gravitational waves in Virgo VSR1 data

We present an implementation of the F-statistic to carry out the first search in data from the Virgo laser interferometric gravitational wave detector for periodic gravitational waves from a priori unknown, isolated rotating neutron stars. We searched a frequency f(0) range from 100 Hz to 1 kHz and the frequency dependent spindown f(1) range from -1.6(f(0)/100 Hz) x 10(-9) Hz s(-1) to zero. A large part of this frequency-spindown space was unexplored by any of the all-sky searches published so far. Our method consisted of a coherent search over two-day periods using the F-statistic, followed by a search for coincidences among the candidates from the two-day segments. We have introduced a number of novel techniques and algorithms that allow the use of the fast Fourier transform (FFT) algorithm in the coherent part of the search resulting in a fifty-fold speed-up in computation of the F-statistic with respect to the algorithm used in the other pipelines. No significant gravitational wave signal was found. The sensitivity of the search was estimated by injecting signals into the data. In the most sensitive parts of the detector band more than 90% of signals would have been detected with dimensionless gravitational-wave amplitude greater than 5 x 10(-24).

Magnetic and gravity measurements on North-South profiles across the Grosse Meteor Bank, North Atlantic

During the first section of the "Meteor" cruise No. 2 a profile was run from the Azores to the south across the flanks of the Mid-Atlantic Ridge with a chain of seamounts. The profile extended between the Cruiser (living) and the Hyeres seamounts, which, according to our soundings, form a connected massif, and across the centre of the Grosse Meteor Bank (30°N, 28.5 °W). These seamounts rise from a depth of more than 4000 m up till close to the surface of the sea forming there a large almost flat plateau. In the case of the Grosse Meteor Bank, this plateau has a N-S extension of approx. 30 nautical miles and an E-W extension of approx. 20 nautical miles and reaches a height of 275 m in water depth. The gravity measurements yielded a density of the topographic masses of 2.6 g/cm**3 for the Grosse Meteor Bank. Magnitude and shape of the measured free-air anomaly are very well shown in a model computation with this density. The theoretical gravity effects of the seismically detected swell of cristalline rock and of the Moho depression (mountain root) are not indicated by the observational data. It can, therefore, be assumed that the latter two neutralize each other. It seems, accordingly, that there is no local isostatic compensation of the topographic masses. Hence, the density of 2.6 g/cm**3 obtained would be about the true density of rock. In connection with the mean velocity of P waves (Aric et al., 1968) obtained by seismic refraction methods it must be concluded that the material of the 1200-4000 m thick surface layer of the Grosse Meteor Bank consists of consolidated sediments. This finding is supported by the total intensity of the Earth's magnetic field over the Grosse Meteor Bank. On the assumption of a homogeneous magnetization in the direction of the present Earth's field, the computed anomaly of the massif deviates considerably from the measured anomaly while the magnetic field of the seismically detected crystalline body is capable of interpreting the observed data. Deviating from the prevailing interpretation of the seamounts' plateau as a volcanic cone with submarine abrasion, the Grosse Meteor Bank and the seamounts in the vicinity are assumed to be of continental origin. The questions whether these seamounts submerged later on or whether the sealevel has risen subsequently are, therefore, largely nonexistent.