The effect of ocean current on internal waves

In a fluid whose density changes with the height, either abruptly at a sharp surface of discontinuity or gradually, it is possible to have internal wave motions whose amplitude is greatest at the density discontinuity or, in the case of a gradual density change, somewhere in the interior of the fluid and not at the free upper surface where the surface waves have their maximum amplitude...

The motion of atmospheric disturbances on the spherical Earth

When the perturbations of the pressure distribution due to rapidly moving cyclones are eliminated by plotting charts of the mea1;1 distribution of the pressure for a number of days, centres of larger dimensions 13,nd of a more permanent character appear, as has been shown by the work carried out by Rossby and his collaborators (7). On winter maps of the northern hemisphere, as a rule at least five of these perturbations are found: the Icelandic and the Aleutian Lows, the Azores, Asiatic and Pacific Highs. They can hardly be considered as mere perturbations of the general circulation, but must rather be regarded as important parts of it, as is evidenced by their semipermanent character. Nevertheless, they will in the following sometimes be referred to as perturbations or disturbances, since they are treated mathematically as perturbations of an undisturbed current

The motion of atmospheric disturbances

In a recent paper Rossby has discussed the effect of the latitudinal variation of the Coriolis force on the propagation of oceanic and atmospheric disturbances (2). He showed that the velocity c of a disturbance in an incompressible atmosphere on a plane earth when only the effect of the latitudinal variation of the Coriolis force is considered is given with sufficient accuracy by the formula..

Vertical distribution of temperature and humidity over the Caribbean Sea

The observations presented and discussed in this paper were obtained as part of a research project conducted under contract NObs-2083 with the Bureau of Ships of the U. S. Navy by the Woods Hole Oceanographic Institution. The observations and their original reduction were carried out under the direction of Jeffries Wyman. The airplane soundings were undertaken by Kenneth McCasland and Alfred Woodcock. The sea surface temperature was measured on the surface ships by David F. Barnes and Roger Patterson. The necessary airplane (PBY-SA) and surface boats (PC's) were made available by the U. S. Navy. All observations were made during the spring of 1946 at about 19.5°N latitude, 66°W longitude, north of San Juan, Puerto Rico, and at about lO°N latitude, 79.5°W longitude, north of Coco Solo, Panama. An extensive preliminary report on the results of the expedition with a limited circulation was prepared by Wyman and his collaborators during the summer of 1946. The present paper deals with certain phases of the work in a more detailed fashion. Special attention is given to the temperature and humidity distributions in the vertical and to their interpretation in the light of meteorological principles. A discussion of atmospheric turbulence based on airplane measurements has already been published elsewhere (Langwell, 1948), and an application of the airplane soundings to the theory of cumulus clouds has been studied by Stommel (1947). The second and third chapters of this publication deal with the description of observational techniques used by the expedition, with the methods of reduction and present the data on which the later discussion is based. It has been thought desirable to publish these data in extenso because they may be of interest to other meteorologists in view of the sparsity of upper-air observations in this region. The actual preparation of Chapters II and III is largely the work of Bunker and Stommel. In order to show how the observations made off Puerto Rico fit into the general pattern of climatic and weather conditions in the Caribbean area Chapter iv presents a survey of the climate of this region and of the weather conditions during the time when the observations were taken. This Chapter was contributed by Joanne Malkus. It is pertinent to include in this general introduction the conclusion drawn in Chapter IV namely that the weather situations encountered represented, in general, a relatively undisturbed trade-wind regime of early spring. The homogeneous layer of nearly dry-adiabatic lapse-rate of temperature and almost constant mixing ratio is one of the most characteristic phenomena in the lowest atmosphere of this region. It is also of utmost importance for the energy budget of the hydrosphere and the atmosphere. Therefore, a special discussion of this layer by Bunker is given in Chapter V. Because of the nearly dry-adiabatic lapse-rate in the homogeneous layer most of the heat transfer between water and air in the trade-wind zone must be in the form of latent heat of vaporization, a conclusion whose thermodynamic implications were discussed thoroughly by Ficker (1936). For this reason the distribution of water vapor deserves special attention, and Chapter VI deals with this variable as a problem in turbulent mass exchange. The analysis presented in this chapter is due to Haurwitz and Stommel

General Relativistic Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate transformation. As an application, we show that the results recently obtained by Rezzolla and Yoshida (2001) in the analysis of Newtonian Rossby-Haurwitz waves of a slowly and differentially rotating, fluid shell apply also in General Relativity, at first order in the angular velocity.Comment: 4 pages. Comment to Class. Quantum Grav. 18(2001)L8

Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the presence of differential rotation. The results obtained indicate that the eigenvalue problem is never singular and that, at least for the case of a thin-shell, the analogues of r modes can be found for arbitrarily large degrees of differential rotation. This work clarifies the puzzling results obtained in calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ

Plasma Depletion and Mirror Waves Ahead of Interplanetary Coronal Mass Ejections

We find that the sheath regions between fast interplanetary coronal mass ejections (ICMEs) and their preceding shocks are often characterized by plasma depletion and mirror wave structures, analogous to planetary magnetosheaths. A case study of these signatures in the sheath of a magnetic cloud (MC) shows that a plasma depletion layer (PDL) coincides with magnetic field draping around the MC. In the same event, we observe an enhanced thermal anisotropy and plasma beta as well as anti-correlated density and magnetic fluctuations which are signatures of mirror mode waves. We perform a superposed epoch analysis of ACE and Wind plasma and magnetic field data from different classes of ICMEs to illuminate the general properties of these regions. For MCs preceded by shocks, the sheaths have a PDL with an average duration of 6 hours (corresponding to a spatial span of about 0.07 AU) and a proton temperature anisotropy ${T_{\perp p}\over T_{\parallel p}}\simeq 1.2$ -1.3, and are marginally unstable to the mirror instability. For ICMEs with preceding shocks which are not MCs, plasma depletion and mirror waves are also present but at a reduced level. ICMEs without shocks are not associated with these features. The differences between the three ICME categories imply that these features depend on the ICME geometry and the extent of upstream solar wind compression by the ICMEs. We discuss the implications of these features for a variety of crucial physical processes including magnetic reconnection, formation of magnetic holes and energetic particle modulation in the solar wind.Comment: fully refereed, accepted for publication in J. Geophys. Re

Coastal Tropical Convection in a Stochastic Modeling Framework

Recent research has suggested that the overall dependence of convection near coasts on large-scale atmospheric conditions is weaker than over the open ocean or inland areas. This is due to the fact that in coastal regions convection is often supported by meso-scale land-sea interactions and the topography of coastal areas. As these effects are not resolved and not included in standard cumulus parametrization schemes, coastal convection is among the most poorly simulated phenomena in global models. To outline a possible parametrization framework for coastal convection we develop an idealized modeling approach and test its ability to capture the main characteristics of coastal convection. The new approach first develops a decision algorithm, or trigger function, for the existence of coastal convection. The function is then applied in a stochastic cloud model to increase the occurrence probability of deep convection when land-sea interactions are diagnosed to be important. The results suggest that the combination of the trigger function with a stochastic model is able to capture the occurrence of deep convection in atmospheric conditions often found for coastal convection. When coastal effects are deemed to be present the spatial and temporal organization of clouds that has been documented form observations is well captured by the model. The presented modeling approach has therefore potential to improve the representation of clouds and convection in global numerical weather forecasting and climate models.Comment: Manuscript submitted for publication in Journal of Advances in Modeling Earth System

PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems

Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency near that of hand-coded Fortran and scales to the largest supercomputers. This is achieved by using Python for most of the code while employing automatically-wrapped Fortran kernels for computationally intensive routines, and using Python bindings to interface with a parallel computing library and other numerical packages. The software described here is PyClaw, a Python-based structured grid solver for general systems of hyperbolic PDEs \cite{pyclaw}. PyClaw provides a powerful and intuitive interface to the algorithms of the existing Fortran codes Clawpack and SharpClaw, simplifying code development and use while providing massive parallelism and scalable solvers via the PETSc library. The package is further augmented by use of PyWENO for generation of efficient high-order weighted essentially non-oscillatory reconstruction code. The simplicity, capability, and performance of this approach are demonstrated through application to example problems in shallow water flow, compressible flow and elasticity