The generation and propagation of planetary Rossby waves

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Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth.Comment: 18 pages, 6 figures, 1 tabl

NASA/MSFC FY88 Global Scale Atmospheric Processes Research Program Review

Interest in environmental issues and the magnitude of the environmental changes continues. One way to gain more understanding of the atmosphere is to make measurements on a global scale from space. The Earth Observation System is a series of new sensors to measure globally atmospheric parameters. Analysis of satellite data by developing algorithms to interpret the radiance information improves the understanding and also defines requirements for these sensors. One measure of knowledge of the atmosphere lies in the ability to predict its behavior. Use of numerical and experimental models provides a better understanding of these processes. These efforts are described in the context of satellite data analysis and fundamental studies of atmospheric dynamics which examine selected processes important to the global circulation

Mountain-Wave Propagation under Transient Tropospheric Forcing: A DEEPWAVE Case Study

The impact of transient tropospheric forcing on the deep vertical mountain-wave propagation is investigated by a unique combination of in situ and remote sensing observations and numerical modeling. The temporal evolution of the upstream low-level wind follows approximately a cos2 shape and was controlled by a migrating trough and connected fronts. Our case study reveals the importance of the time-varying propagation conditions in the upper troposphere and lower stratosphere (UTLS). Upper-tropospheric stability, the wind profile, and the tropopause strength affected the observed and simulated wave response in the UTLS. Leg-integrated along-track momentum fluxes (-MFtrack) and amplitudes of vertical displacements of air parcels in the UTLS reached up to 130 kN m-1 and 1500 m, respectively. Their maxima were phase shifted to the maximum low-level forcing by ≈8 h. Small-scale waves (λx ≈ 20 - 30 km) were continuously forced, and their flux values depended on wave attenuation by breaking and reflection in the UTLS region. Only maximum flow over the envelope of the mountain range favored the excitation of longer waves that propagated deeply into the mesosphere. Their long propagation time caused a retarded enhancement of observed mesospheric gravity wave activity about 12–15 h after their observation in the UTLS. For the UTLS, we further compared observed and simulated MFtrack with fluxes of 2D quasi-steady runs. UTLS momentum fluxes seem to be reproducible by individual quasi-steady 2D runs, except for the flux enhancement during the early decelerating forcing phase

Mountain Wave Propagation under Transient Tropospheric Forcing: A DEEPWAVE Case Study

The impact of transient tropospheric forcing on the deep vertical mountain wave propagation is investigated by a unique combination of in-situ and remote-sensing observations and numerical modeling. The temporal evolution of the upstream low-level wind follows approximately a cos2 shape and was controlled by a migrating trough and connected fronts. Our case study reveals the importance of the time-varying propagation conditions in the upper troposphere, lower stratosphere (UTLS). Upper-tropospheric stability, the wind profile as well as the tropopause strength affected the observed and simulated wave response in the UTLS. Leg-integrated along-track momentum fluxes (−MFtrack) and amplitudes of vertical displacements of air parcels in the UTLS reached up to 130 kN m−1 and 1500 m, respectively. Their maxima were phase-shifted to the maximum low-level forcing by ≈ 8 h. Small-scale waves (λx ≈ 20–30 km) were continuously forced and their flux values depended on wave attenuation by breaking and reflection in the UTLS region

Complex Wavenumber Rossby Wave Ray Tracing

This paper presents a methodology for performing complex wavenumber ray tracing in which both wave trajectory and amplitude are calculated. This ray-tracing framework is first derived using a scaling in which the imaginary wavenumber component is assumed to be much smaller than the real wavenumber component. The approach, based on perturbation methods, is strictly valid when this scaling condition is met. The framework is then used to trace stationary barotropic Rossby waves in a number of settings. First, ray-traced Rossby wave amplitude is validated in a simple, idealized system for which exact solutions can be calculated. Complex wavenumber ray tracing is then applied to both solid-body rotation on a sphere and observed climatological upper-tropospheric fields. These ray-tracing solutions are compared with similarly forced solutions of the linearized barotropic vorticity equation (LBVE). Both real and complex wavenumber ray tracings follow trajectories matched by LBVE solutions. Complex wavenumber ray tracings on observed two-dimensional zonally asymmetric atmospheric fields are found to follow trajectories distinct from real wavenumber Rossby waves. For example, complex wavenumber ray tracings initiated over the eastern equatorial Pacific Ocean during boreal summer propagate northward and northeastward into the subtropics over the Atlantic Ocean, as well as southeastward into the Southern Hemisphere. Similarly initiated real wavenumber ray tracings remain within the deep tropics and propagate westward. These complex wavenumber Rossby wave trajectories and ray amplitudes are generally consistent with LBVE solutions, which indicates this methodology can identify Rossby wave effects distinct from traditional real wavenumber tracings.Keywords: Trajectories, Rossby waves, Stationary waves, Teleconnections, Nonlinear dynamics, atmospheric, Wave

Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters

In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak solution, we analyse its properties and illustrate the theoretical results through some numerical simulations by approximating the solutions to the full dissipative model for a particular synthetic piecewise continuous medium. In particular, we discover numerically a very interesting phenomenon of the appearance of a new wave at the singular point. For the acoustic problem this can be interpreted as an echo effect at the discontinuity interface of the medium

The drag exerted by weakly dissipative trapped lee waves on the atmosphere: application to Scorer's two-layer model

Although it is known that trapped lee waves propagating at low levels in a stratified atmosphere exert a drag on the mountains that generate them, the distribution of the corresponding reaction force exerted on the atmospheric mean circulation, defined by the wave momentum flux profiles, has not been established, because for inviscid trapped lee waves these profiles oscillate indefinitely downstream. A framework is developed here for the unambiguous calculation of momentum flux profiles produced by trapped lee waves, which circumvents the difficulties plaguing the inviscid trapped lee wave theory. Using linear theory, and taking Scorer's two-layer atmosphere as an example, the waves are assumed to be subject to a small dissipation, expressed as a Rayleigh damping. The resulting wave pattern decays downstream, so the momentum flux profile integrated over the area occupied by the waves converges to a well-defined form. Remarkably, for weak dissipation, this form is independent of the value of Rayleigh damping coefficient, and the inviscid drag, determined in previous studies, is recovered as the momentum flux at the surface. The divergence of this momentum flux profile accounts for the areally integrated drag exerted by the waves on the atmosphere. The application of this framework to this and other types of trapped lee waves potentially enables the development of physically based parametrizations of the effects of trapped lee waves on the atmosphere.info:eu-repo/semantics/publishedVersio

An equation for deriving spatial variations in carbonate production rates from sediment deposition rates and dilution: Application to Santa Maria Island, Azores

Knowledge of how carbonates are produced on shelves is needed for working out how these “carbonate factories” generate stratigraphy by providing particles for potential export or local deposition. Production rates can be derived straightforwardly in low-energy environments from one-dimensional analysis (age–depth variations) but rates are less easily derived for high-energy hydrodynamical environments where particles are transported away from their sites of production. This particularly affects knowledge of spatial variations in production rates, needed for working out controlling influences of light, hydrodynamics, and nutrient availability. We show here that, if a non-carbonate component of the sediment, such as terrigenous particles arising from coastal and subaerial erosion, is conserved and thus acts as a tracer, rates of carbonate production can in principle be derived from carbonate content data, if sediment transport fluxes can also be constrained. In the equation developed here, the spatial rate of change of carbonate content is caused by dilution of the terrigenous component by the newly produced carbonate and depends on the sediment transport flux. We investigate this idea using data from Santa Maria Island, Azores, an inactive volcanic island in a temperate environment. Geochemical, X-ray diffraction (XRD), and X-ray fluorescence (XRF) data of surface–sediment grab samples indicate nearly simple mixing trends between two components (volcanic rock and marine carbonate), as needed for our simple dilution-based equation to apply. High-resolution boomer seismic data reveal thicker (> 1 m) deposits in the mid- to outer shelf of the island, which we interpret as having been emplaced during the Holocene. These effectively provide time-averaged depositional fluxes and, assuming conservation of mass, can be used to constrain transport fluxes. The derived equation is used to predict the observed deposit thicknesses into the mid-shelf alongside coincident increasing carbonate percentages. The thicknesses are replicated only if carbonate production rates increase with depth and distance away from the coastline into the mid-shelf, quantifying the variation of production of such a nearshore environment for the first time. We speculate that mollusks dominating the production have a preference for sand that is less frequently or strongly agitated by waves, although nutrient availability from occasional upwelling may also regulate growth to create this trend.Peer reviewe