A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

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.

Mountain waves in two-layer sheared flows: Critical-level effects, wave reflection, and drag enhancement

Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too different from that predicted for an unbounded shear layer, while if it is small the differences are marked, with the drag being enhanced by a considerable factor at low Richardson numbers (Ri). The drag may be further enhanced by nonlinear processes, but its qualitative variation for relatively low Ri is essentially unchanged. However, nonlinear processes seem to interact constructively with shear, so that the drag for a noninfinite but relatively high Ri is considerably larger than the drag without any shear at all.

Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmosphere

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l_2/l_1 and of the corresponding dimensionless interface height l_1 H, for selected values of the dimensionless ridge width l_1 a and ratio of wind speeds in the two layers. When l_2/l_1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l_2/l_1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l_1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l_2/l_1 and slightly higher values of l_1 H than the propagating wave drag maxima. As l1a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l_2/l_1. These results are confirmed by numerical simulations for l_2/l_1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models.

The influence of the QBO on the propagation of equatorial waves into the stratosphere

The variation of stratospheric equatorial wave characteristics with the phase of the quasi-biennial oscillation (QBO) is investigated using ECMWF Re-Analysis and NOAA outgoing longwave radiation (OLR) data. The impact of the QBO phases on the upward propagation of equatorial waves is found to be consistent and significant. In the easterly phase, there is larger Kelvin wave amplitude but smaller westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave amplitude due to reduced propagation from the upper troposphere into the lower stratosphere, compared with the westerly phase. Differences in the wave amplitude exist in a deeper layer in summer than in winter, consistent with the seasonality of ambient zonal winds. There is a strong evidence of Kelvin wave amplitude peaking just below the descending westerly phase, suggesting that Kelvin waves act to bring the westerly phase downward. However, the corresponding evidence for WMRG and R1 waves is less clear. In the lower stratosphere there is zonal variation in equatorial waves. This reflects the zonal asymmetry of wave amplitudes in the upper troposphere, the source for the lower-stratospheric waves. In easterly winters the upper-tropospheric WMRG and R1 waves over the eastern Pacific region appear to be somewhat stronger compared to climatology, perhaps because of the accumulation of waves that are unable to propagate upward into the lower stratosphere. Vertical propagation features of these waves are generally consistent with theory and suggest a mixture of Doppler shifting by ambient flows and filtering. Some lower-stratosphere equatorial waves have a connection with preceding tropical convection, especially for Kelvin and R1 waves in winter.

Gap junction-mediated spontaneous Ca(2+) waves in differentiated cholinergic SN56 cells

Neuronal gap junctions are receiving increasing attention as a physiological means of intercellular communication, yet our understanding of them is poorly developed when compared to synaptic communication. Using microfluorimetry, we demonstrate that differentiation of SN56 cells (hybridoma cells derived from murine septal neurones) leads to the spontaneous generation of Ca(2+) waves. These waves were unaffected by tetrodotoxin (1microM), but blocked by removal of extracellular Ca(2+), or addition of non-specific Ca(2+) channel inhibitors (Cd(2+) (0.1mM) or Ni(2+) (1mM)). Combined application of antagonists of NMDA receptors (AP5; 100microM), AMPA/kainate receptors (NBQX; 20microM), nicotinic AChR receptors (hexamethonium; 100microM) or inotropic purinoceptors (brilliant blue; 100nM) was also without effect. However, Ca(2+) waves were fully prevented by carbenoxolone (200microM), halothane (3mM) or niflumic acid (100microM), three structurally diverse inhibitors of gap junctions, and mRNA for connexin 36 was detected by PCR. Whole-cell patch-clamp recordings revealed spontaneous inward currents in voltage-clamped cells which we inhibited by Cd(2+), Ni(2+) or niflumic acid. Our data suggest that differentiated SN56 cells generated spontaneous Ca(2+) waves which are propagated by intercellular gap junctions. We propose that this system can be exploited conveniently for the development of neuronal gap junction modulators.

A diagnostic study of waves on the tropopause

The spatial structure and phase velocity of tropopause disturbances localized around the subpolar jet in the Southern Hemisphere are investigated using 6-hourly European Centre for Medium-Range Weather Forecasts reanalysis data covering 15 yr (1979–93). The phase velocity and phase structure of the tropopause disturbances are in good agreement with those of an edge wave vertically trapped at the tropopause. However, the vertical distribution of the ratio of potential to kinetic energy exhibits maxima above and below the tropopause and a minimum around the tropopause, in contradiction to edge wave theory for which the ratio is unity throughout the troposphere and stratosphere. This difference in vertical structure between the observed tropopause disturbances and edge wave theory is attributed to the effects of a finite-depth tropopause together with the next-order corrections in Rossby number to quasigeostrophic dynamics

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed.

Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere

During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.

Physicality, difference, and the challenge of representation: Werner Herzog in the Light of the new waves

This chapter looks into the gap between presentational realism and the representation of physical experience in Werner Herzog's work so as to retrieve the indexical trace – or the absolute materiality of death. To that end, it draws links between Herzog and other directors akin to realism in its various forms, including surrealism. In particular, it focuses on François Truffaut and Glauber Rocha, representing respectively the Nouvelle Vague and the Cinema Novo, whose works had a decisive weight on Herzog’s aesthetic choices to the point of originating distinct phases of his outputs. The analyses, though restricted to a small number of films, intends to re-evaluate Herzog’s position within, and contribution to, film history.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. 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 an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

The role of baroclinic waves in the initiation of tropical cyclones across the southern Indian Ocean

Cases where tropical storms are initiated simultaneously along one latitude are investigated. It is argued that such structure arises as part of a baroclinic wave. A case from February 2008 is examined using European Centre for Medium-Range Forecasts (ECMWF) analyses; the birth of three tropical cyclones in the low-level cyclonic regions to the east of upper-level troughs suggests that the wave was instrumental for initiation. Archived satellite imagery and storm warnings reveal that baroclinic waves over the southern Indian Ocean accompany tropical cyclogenesis twice a season on average, mainly in late summer, when breaking Rossby waves on the subtropical westerly jet are closest to the Intertropical Convergence Zone (ITCZ). Copyright © 2012 Royal Meteorological Society

The correlation of ULF waves and auroral intensity before, during and after substorm expansion phase onset

We present case studies of the evolution of magnetic wave amplitudes and auroral intensity through the late growth phase and the expansion phase of the substorm cycle. We present strong evidence that substorm-related auroral enhancements are clearly and demonstrably linked to ULF wave amplitudes observed at the same location. In most cases, we find that the highest correlations are observed when the magnetometer time series is advanced in time, indicating that the ULF wave amplitudes start to grow before measured auroral intensities, though interestingly this is not always the case. Further we discuss the four possible reasons that may be able to explain both the timing and the high correlations between these two phenomena, including: a simple coincidence, an artifact of instrumental effects, the response of the ionosphere to magnetic waves and auroral particle precipitation, and finally that ULF waves and auroral particle precipitation are physically linked. We discount coincidence and instrumental effects since in the studies presented here they are unlikely or in general will contribute negligible effects, and we find that the ionospheric response to waves and precipitation can explain some, but not all of the results contained within this paper. Specifically, ionospheric response to substorm waves and auroral precipitation cannot explain that the result that previous studies have shown, that onset of ULF wave activity and the onset of auroral particle precipitation occur at the same time and in the same location. This leaves the possibility that ULF waves and auroral particles are physically linked.