Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Electron trapping in shear Alfvén waves that power the aurora

Results from 1D Vlasov drift-kinetic plasma simulations reveal how and where auroral electrons are accelerated along Earth’s geomagnetic field. In the warm plasma sheet, electrons become trapped in shear Alfven waves, preventing immediate wave damping. As waves move to regions with larger vTe=vA, their parallel electric field decreases, and the trapped electrons escape their influence. The resulting electron distribution functions compare favorably with in situ observations, demonstrating for the first time a self-consistent link between Alfven waves and electrons that form aurora.

Sponge layer feedbacks in middle-atmosphere models

Middle-atmosphere models commonly employ a sponge layer in the upper portion of their domain. It is shown that the relaxational nature of the sponge allows it to couple to the dynamics at lower levels in an artificial manner. In particular, the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating is shown to induce a drag force in the sponge that modifies the response expected from the “downward control” arguments of Haynes et al. [1991]. In the case of an imposed local force the sponge acts to divert a fraction of the mean meridional mass flux upward, which for realistic parameter values is approximately equal to exp(−Δz/H), where Δz is the distance between the forcing region and the sponge layer and H is the density scale height. This sponge-induced upper cell causes temperature changes that, just below the sponge layer, are of comparable magnitude to those just below the forcing region. In the case of an imposed local diabatic heating, the sponge induces a meridional circulation extending through the entire depth of the atmosphere. This circulation causes temperature changes that, just below the sponge layer, are of opposite sign and comparable in magnitude to those at the heating region. In both cases, the sponge-induced temperature changes are essentially independent of the height of the imposed force or diabatic heating, provided the latter is located outside the sponge, but decrease exponentially as one moves down from the sponge. Thus the effect of the sponge can be made arbitrarily small at a given altitude by placing the sponge sufficiently high; e.g., its effect on temperatures two scale heights below is roughly at the 10% level, provided the imposed force or diabatic heating is located outside the sponge. When, however, an imposed force is applied within the sponge layer (a highly plausible situation for parameterized mesospheric gravity-wave drag), its effect is almost entirely nullified by the sponge-layer feedback and its expected impact on temperatures below largely fails to materialize. Simulations using a middle-atmosphere general circulation model are described, which demonstrate that this sponge-layer feedback can be a significant effect in parameter regimes of physical interest. Zonally symmetric (two dimensional) middle-atmosphere models commonly employ a Rayleigh drag throughout the model domain. It is shown that the long-term zonally symmetric response to an imposed extratropical local force or diabatic heating, in this case, is noticeably modified from that expected from downward control, even for a very weak drag coefficient

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

DK-1D: a drift-kinetic simulation tool for modelling the shear Alfvén wave and its interaction with collisionless plasma

We present a highly accurate tool for the simulation of shear Alfven waves (SAW) in collisionless plasma. SAW are important in space plasma environments because for small perpendicular scale lengths they can support an electric field parallel to the ambient magnetic field. Electrons can be accelerated by the parallel electric field and these waves have been implicated as the source of vibrant auroral displays. However, the parallel electric field carried by SAW is small in comparison to the perpendicular electric field of the wave, making it difficult to measure directly in the laboratory, or by satellites in the near-Earth plasma environment. In this paper, we present a simulation code that provides a means to study in detail the SAW-particle interaction in both space and laboratory plasma. Using idealised, small-amplitude propagating waves with a single perpendicular wavenumber, the simulation code accurately reproduces the damping rates and parallel electric field amplitudes predicted by linear theory for varying temperatures and perpendicular scale lengths. We present a rigorous kinetic derivation of the parallel electric field strength for small-amplitude SAW and show that commonly-used inertial and kinetic approximations are valid except for where the ratio of thermal to Alfv\'{e}n speed is between 0.7 and 1.0. We also present nonlinear simulations of large-amplitude waves and show that in cases of strong damping, the damping rates and parallel electric field strength deviate from linear predictions when wave energies are greater than only a few percent of the plasma kinetic energy, a situation which is often observed in the magnetosphere. The drift-kinetic code provides reliable, testable predictions of the parallel electric field strength which can be investigated directly in the laboratory, and will help to bridge the gap between studies of SAW in man-made and naturally occuring plasma.

On Rossby waves modified by weak sinusoidal shear

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flow U 0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear, U 0γ2 0/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Mean motions induced by baroclinic instability in a jet

A study is made of the zonal-mean motions induced by a growing baroclinic wave in several contexts, under the framework of three different analysis schemes: the conventional Eulerian mean (EM), the transformed Eulerian mean (TEM), and the generalized Lagrangian mean (GLM). The effect of meridional shear in the initial jet on these induced mean motions is considered by treating the instability problem in the context of the two-layer model. The conceptual simplicity of the TEM formulation is shown to be useful in diagnosing the dynamics of instability, much as it has been found helpful in many problems of wave, mean-flow interaction. In addition, it is found that the TEM vertical velocity is a very good indicator of the GLM vertical velocity. However, the GLM meridional velocity is always convergent towards the centre of instability activity, and is not at all well represented by the nondivergent TEM meridional velocity. In comparing the results with Uryu's (1979) calculation of the GLM circulation induced by a growing Eady wave, it is found that the inclusion of meridional jet shear in the present work leads to some strikingly different effects in the GLM zonal wind acceleration. In the case of pure baroclinic instability treated by Uryu, the Eulerian and Stokes accelerations nearly cancel each other in the centre of the channel, leaving a weak Lagrangian acceleration opposed to the Eulerian one. In the more general case of mixed baroclinic-barotropic instability, however, the Eulerian and Stokes accelerations can reinforce one another, leading to a very strong Lagrangian zonal wind

Wave activity in the tropical tropopause layer in seven reanalysis and four chemistry climate model data sets

Sub-seasonal variability including equatorial waves significantly influence the dehydration and transport processes in the tropical tropopause layer (TTL). This study investigates the wave activity in the TTL in 7 reanalysis data sets (RAs; NCEP1, NCEP2, ERA40, ERA-Interim, JRA25, MERRA, and CFSR) and 4 chemistry climate models (CCMs; CCSRNIES, CMAM, MRI, and WACCM) using the zonal wave number-frequency spectral analysis method with equatorially symmetric-antisymmetric decomposition. Analyses are made for temperature and horizontal winds at 100 hPa in the RAs and CCMs and for outgoing longwave radiation (OLR), which is a proxy for convective activity that generates tropopause-level disturbances, in satellite data and the CCMs. Particular focus is placed on equatorial Kelvin waves, mixed Rossby-gravity (MRG) waves, and the Madden-Julian Oscillation (MJO). The wave activity is defined as the variance, i.e., the power spectral density integrated in a particular zonal wave number-frequency region. It is found that the TTL wave activities show significant difference among the RAs, ranging from ∼0.7 (for NCEP1 and NCEP2) to ∼1.4 (for ERA-Interim, MERRA, and CFSR) with respect to the averages from the RAs. The TTL activities in the CCMs lie generally within the range of those in the RAs, with a few exceptions. However, the spectral features in OLR for all the CCMs are very different from those in the observations, and the OLR wave activities are too low for CCSRNIES, CMAM, and MRI. It is concluded that the broad range of wave activity found in the different RAs decreases our confidence in their validity and in particular their value for validation of CCM performance in the TTL, thereby limiting our quantitative understanding of the dehydration and transport processes in the TTL.

Cross-layer design for multiuser MIMO MRC systems with feedback constraints

Cross-layer techniques represent efficient means to enhance throughput and increase the transmission reliability of wireless communication systems. In this paper, a cross-layer design of aggressive adaptive modulation and coding (A-AMC), truncated automatic repeat request (T-ARQ), and user scheduling is proposed for multiuser multiple-input-multiple-output (MIMO) maximal ratio combining (MRC) systems, where the impacts of feedback delay (FD) and limited feedback (LF) on channel state information (CSI) are also considered. The A-AMC and T-ARQ mechanism selects the appropriate modulation and coding schemes (MCSs) to achieve higher spectral efficiency while satisfying the service requirement on the packet loss rate (PLR), profiting from the feasibility of using different MCSs to retransmit a packet, which is destined to a scheduled user selected to exploit multiuser diversity and enhance the system's performance in terms of both transmission efficiency and fairness. The system's performance is evaluated in terms of the average PLR, average spectral efficiency (ASE), outage probability, and average packet delay, which are derived in closed form, considering transmissions over Rayleigh-fading channels. Numerical results and comparisons are provided and show that A-AMC combined with T-ARQ yields higher spectral efficiency than the conventional scheme based on adaptive modulation and coding (AMC), while keeping the achieved PLR closer to the system's requirement and reducing delay. Furthermore, the effects of the number of ARQ retransmissions, numbers of transmit and receive antennas, normalized FD, and cardinality of the beamforming weight vector codebook are studied and discussed.

Cross-layer design for MIMO systems over spatially correlated and keyhole Nakagami-m fading channels

Cross-layer design is a generic designation for a set of efficient adaptive transmission schemes, across multiple layers of the protocol stack, that are aimed at enhancing the spectral efficiency and increasing the transmission reliability of wireless communication systems. In this paper, one such cross-layer design scheme that combines physical layer adaptive modulation and coding (AMC) with link layer truncated automatic repeat request (T-ARQ) is proposed for multiple-input multiple-output (MIMO) systems employing orthogonal space--time block coding (OSTBC). The performance of the proposed cross-layer design is evaluated in terms of achievable average spectral efficiency (ASE), average packet loss rate (PLR) and outage probability, for which analytical expressions are derived, considering transmission over two types of MIMO fading channels, namely, spatially correlated Nakagami-m fading channels and keyhole Nakagami-m fading channels. Furthermore, the effects of the maximum number of ARQ retransmissions, numbers of transmit and receive antennas, Nakagami fading parameter and spatial correlation parameters, are studied and discussed based on numerical results and comparisons. Copyright © 2009 John Wiley & Sons, Ltd.

Cross-layer design of enhanced AMC with truncated ARQ protocols

Using a cross-layer approach, two enhancement techniques applied for adaptive modulation and coding (AMC) with truncated automatic repeat request (T-ARQ) are investigated, namely, aggressive AMC (A-AMC) and constellation rearrangement (CoRe). Aggressive AMC selects the appropriate modulation and coding schemes (MCS) to achieve higher spectral efficiency, profiting from the feasibility of using different MCSs for retransmitting a packet, whereas in the CoRe-based AMC, retransmissions of the same data packet are performed using different mappings so as to provide different degrees of protection to the bits involved, thus achieving mapping diversity gain. The performance of both schemes is evaluated in terms of average spectral efficiency and average packet loss rate, which are derived in closed-form considering transmission over Nakagami-m fading channels. Numerical results and comparisons are provided. In particular, it is shown that A-AMC combined with T-ARQ yields higher spectral efficiency than the AMC-based conventional scheme while keeping the achieved packet loss rate closer to the system's requirement, and that it can achieve larger spectral efficiency objectives than that of the scheme using AMC along with CoRe.

Trade-offs and responsiveness of the single-layer urban canopy parametrization in WRF: an offline evaluation using the MOSCEM optimization algorithm and field observations

For an increasing number of applications, mesoscale modelling systems now aim to better represent urban areas. The complexity of processes resolved by urban parametrization schemes varies with the application. The concept of fitness-for-purpose is therefore critical for both the choice of parametrizations and the way in which the scheme should be evaluated. A systematic and objective model response analysis procedure (Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm) is used to assess the fitness of the single-layer urban canopy parametrization implemented in the Weather Research and Forecasting (WRF) model. The scheme is evaluated regarding its ability to simulate observed surface energy fluxes and the sensitivity to input parameters. Recent amendments are described, focussing on features which improve its applicability to numerical weather prediction, such as a reduced and physically more meaningful list of input parameters. The study shows a high sensitivity of the scheme to parameters characterizing roof properties in contrast to a low response to road-related ones. Problems in partitioning of energy between turbulent sensible and latent heat fluxes are also emphasized. Some initial guidelines to prioritize efforts to obtain urban land-cover class characteristics in WRF are provided. Copyright © 2010 Royal Meteorological Society and Crown Copyright.