Travelling waves in a model of species migration

A model of species migration is presented which takes the form of a reaction-diffusion system. We consider special limits of this model in which we demonstrate the existence of travelling wave solutions. These solutions can be used to describe the migration of cells, bacteria, and some organisms. © 2000 Elsevier Science Ltd. All rights reserved.

Electron acceleration and parallel electric fields due to kinetic Alfvén waves in plasma with similar thermal and Alfvén speeds

We investigate electron acceleration due to shear Alfven waves in a collissionless plasma for plasma parameters typical of 4–5RE radial distance from the Earth along auroral field lines. Recent observational work has motivated this study, which explores the plasma regime where the thermal velocity of the electrons is similar to the Alfven speed of the plasma, encouraging Landau resonance for electrons in the wave fields. We use a self-consistent kinetic simulation model to follow the evolution of the electrons as they interact with a short-duration wave pulse, which allows us to determine the parallel electric field of the shear Alfven wave due to both electron inertia and electron pressure effects. The simulation demonstrates that electrons can be accelerated to keV energies in a modest amplitude sub-second period wave. We compare the parallel electric field obtained from the simulation with those provided by fluid approximations.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

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.

Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs

Wave solutions to a mechanochemical model for cytoskeletal activity are studied and the results applied to the waves of chemical and mechanical activity that sweep over an egg shortly after fertilization. The model takes into account the calcium-controlled presence of actively contractile units in the cytoplasm, and consists of a viscoelastic force equilibrium equation and a conservation equation for calcium. Using piecewise linear caricatures, we obtain analytic solutions for travelling waves on a strip and demonstrate uiat the full nonlinear system behaves as predicted by the analytic solutions. The equations are solved on a sphere and the numerical results are similar to the analytic solutions. We indicate how the speed of the waves can be used as a diagnostic tool with which the chemical reactivity of the egg surface can be measured.

Ion acceleration at both the interior and exterior Alfvén waves associated with the magnetopause reconnection site: Signatures in cusp precipitation

We present evidence for the acceleration of magnetospheric ions by reflection off two Alfvén waves, launched by the reconnection site into the inflow regions on both sides of the reconnecting magnetopause. The “exterior” wave stands in the inflow from the magnetosheath and is the magnetopause, in the sense that the majority of the field rotation occurs there. The other, “interior” wave stands in the inflow region on the magnetospheric side of the boundary. The population reflected by the interior wave is the more highly energized of the two and appears at low altitudes on open field lines, immediately equatorward of the cusp precipitation. In addition, we identify the population of magnetosheath ions transmitted across the exterior Alfvén wave, as well as a population of magnetospheric ions which are accelerated, after transmission through the interior wave, by reflection off the exterior wave. The ion populations near the X line are modeled and, with allowance for time-of-flight effects, are also derived from observations in the dayside auroral ionosphere. Agreement between observed and theoretical spectra is very good and the theory also explains the observed total fluxes and average energies of the precipitations poleward of the open/closed field line boundary. The results offer a physical interpretation of all the various classifications of precipitation into the dayside ionosphere (central plasma sheet, dayside boundary plasma sheet, void, low-latitude boundary layer, cusp, and mantle) and allow the conditions in both the magnetosphere and the magnetosheath adjacent to the X line to be studied.

Simple M-factor algorithm for improved estimation of the basic maximum usable frequency of radio waves reflected from the ionospheric F-region

The equations of Milsom are evaluated, giving the ground range and group delay of radio waves propagated via the horizontally stratified model ionosphere proposed by Bradley and Dudeney. Expressions for the ground range which allow for the effects of the underlying E- and F1-regions are used to evaluate the basic maximum usable frequency or M-factors for single F-layer hops. An algorithm for the rapid calculation of the M-factor at a given range is developed, and shown to be accurate to within 5%. The results reveal that the M(3000)F2-factor scaled from vertical-incidence ionograms using the standard URSI procedure can be up to 7.5% in error. A simple addition to the algorithm effects a correction to ionogram values to make these accurate to 0.5%.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

Extracting planetary waves from geomagnetic time series using Empirical Mode Decomposition

Empirical Mode Decomposition is presented as an alternative to traditional analysis methods to decompose geomagnetic time series into spectral components. Important comments on the algorithm and its variations will be given. Using this technique, planetary wave modes of 5-, 10-, and 16-day mean periods can be extracted from magnetic field components of three different stations in Germany. In a second step, the amplitude modulation functions of these wave modes can be shown to contain significant contribution from solar cycle variation through correlation with smoothed sunspot numbers. Additionally, the data indicate connections with geomagnetic jerk occurrences, supported by a second set of data providing reconstructed near-Earth magnetic field for 150 years. Usually attributed to internal dynamo processes within the Earth's outer core, the question of who is impacting whom will be briefly discussed here.

A route to systematic error in forecasts of Rossby waves

Recent work has shown that both the amplitude of upper-level Rossby waves and the tropopause sharpness decrease with forecast lead time for several days in some operational weather forecast systems. In this contribution, the evolution of error growth in a case study of this forecast error type is diagnosed through analysis of operational forecasts and hindcast simulations. Potential vorticity (PV) on the 320-K isentropic surface is used to diagnose Rossby waves. The Rossby-wave forecast error in the operational ECMWF high-resolution forecast is shown to be associated with errors in the forecast of a warm conveyor belt (WCB) through trajectory analysis and an error metric for WCB outflows. The WCB forecast error is characterised by an overestimation of WCB amplitude, a location of the WCB outflow regions that is too far to the southeast, and a resulting underestimation of the magnitude of the negative PV anomaly in the outflow. Essentially the same forecast error development also occurred in all members of the ECMWF Ensemble Prediction System and the Met Office MOGREPS-15 suggesting that in this case model error made an important contribution to the development of forecast error in addition to initial condition error. Exploiting this forecast error robustness, a comparison was performed between the realised flow evolution, proxied by a sequence of short-range simulations, and a contemporaneous forecast. Both the proxy to the realised flow and the contemporaneous forecast a were produced with the Met Office Unified Model enhanced with tracers of diabatic processes modifying potential temperature and PV. Clear differences were found in the way potential temperature and PV are modified in the WCB between proxy and forecast. These results demonstrate that differences in potential temperature and PV modification in the WCB can be responsible for forecast errors in Rossby waves.

Rayleigh scattering by hexagonal ice crystals and the interpretation of dual-polarisation radar measurements

Dual-polarisation radar measurements provide valuable information about the shapes and orientations of atmospheric ice particles. For quantitative interpretation of these data in the Rayleigh regime, common practice is to approximate the true ice crystal shape with that of a spheroid. Calculations using the discrete dipole approximation for a wide range of crystal aspect ratios demonstrate that approximating hexagonal plates as spheroids leads to significant errors in the predicted differential reflectivity, by as much as 1.5 dB. An empirical modification of the shape factors in Gans's spheroid theory was made using the numerical data. The resulting simple expressions, like Gans's theory, can be applied to crystals in any desired orientation, illuminated by an arbitrarily polarised wave, but are much more accurate for hexagonal particles. Calculations of the scattering from more complex branched and dendritic crystals indicate that these may be accurately modelled using the new expression, but with a reduced permittivity dependent on the volume of ice relative to an enclosing hexagonal prism.

Predictability of frontal waves and cyclones

The statistical properties and skill in predictions of objectively identified and tracked cyclonic features (frontal waves and cyclones) are examined in MOGREPS-15, the global 15-day version of the Met Office Global and Regional Ensemble Prediction System (MOGREPS). The number density of cyclonic features is found to decline with increasing lead-time, with analysis fields containing weak features which are not sustained past the first day of the forecast. This loss of cyclonic features is associated with a decline in area averaged enstrophy with increasing lead time. Both feature number density and area averaged enstrophy saturate by around 7 days into the forecast. It is found that the feature number density and area averaged enstrophy of forecasts produced using model versions that include stochastic energy backscatter saturate at higher values than forecasts produced without stochastic physics. The ability of MOGREPS-15 to predict the locations of cyclonic features of different strengths is evaluated at different spatial scales by examining the Brier Skill (relative to the analysis climatology) of strike probability forecasts: the probability that a cyclonic feature center is located within a specified radius. The radius at which skill is maximised increases with lead time from 650km at 12h to 950km at 7 days. The skill is greatest for the most intense features. Forecast skill remains above zero at these scales out to 14 days for the most intense cyclonic features, but only out to 8 days when all features are included irrespective of intensity.