[1] Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower-atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large-scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large-scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

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Gravity wave dynamics and effects in the middle atmosphere

This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

http://ieeexplore.ieee.org/iel5/10933/4065481/04065500.pdf

Surface Waves

Publisher Summary The chapter reviews the meteorological phenomena that are associated with topography. The study of airflow past mountains is complicated by the wide range of scales that must be considered. The ratios of the mountain width to each of the natural length scales are important in determining the physical regime of the flow. This idea is emphasized in the chapter by treating the effects of boundary layers and buoyancy. The theory of two-dimensional mountain waves with the help of its governing equations is presented and the observations of mountain waves are presented. The chapter also examines the influence of the boundary layer on mountain flows and slope winds and mountain and valley winds. It considers the perturbation to the wind flow caused by a mountain of intermediate scale where the rotation of the Earth cannot be neglected. For this the flow near mesoscale and synoptic-scale mountains, quasi-geostrophic flow over a mountain, the effect of inertia on the flow over mesoscale mountains, and theories of lee cyclogenesis are discussed. Finally the chapter describes planetary-scale mountain waves; a vertically integrated model of topographically forced planetary waves; the vertical structure of planetary waves; models of stationary planetary waves allowing meridional propagation and lateral; and variation in the background wind.

The Influence of Mountains on the Atmosphere

A completely new nonhydrostatic model system known as the Advanced Regional Prediction System (ARPS) has been developed in recent years at the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma. The ARPS is designed from the beginning to serve as an effective tool for basic and applied research and as a system suitable for explicit prediction of convective storms as well as weather systems at other scales. The ARPS includes its own data ingest, quality control and objective analysis packages, a data assimilation system which includes single-Doppler velocity and thermodynamic retrieval algorithms, the forward prediction component, and a self-contained post-processing, diagnostic and verification package. The forward prediction component of the ARPS is a three-dimensional, nonhydrostatic compressible model formulated in generalized terrain-following coordinates. Minimum approximations are made to the original governing equations. The split-explicit scheme is used to integrate the sound-wave containing equations, which allows the horizontal domain-decomposition strategy to be efficiently implemented for distributed-memory massively parallel computers. The model performs equally well on conventional shared-memory scalar and vector processors. The model employs advanced numerical techniques, including monotonic advection schemes for scalar transport and variance-conserving fourth-order advection for other variables. The model also includes state-of-the-art physics parameterization schemes that are important for explicit prediction of convective storms as well as the prediction of flows at larger scales. Unique to this system are the consistent code styling maintained for the entire model system and thorough internal documentation. Modern software engineering practices are employed to ensure that the system is modular, extensible and easy to use. The system has been undergoing real-time prediction tests at the synoptic through storm scales in the past several years over the continental United States as well as in part of Asia, some of which included retrieved Doppler radar data and hydrometeor types in the initial condition. As the first of a two-part paper series, we describe herein the dynamic and numerical framework of the model, together with the subgrid-scale turbulence and the PBL parameterization. The model dynamic and numerical framework is then verified using idealized and realistic mountain flow cases and an idealized density current. Other physics parameterization schemes will be described in Part II, which is followed by verification against observational data of the coupled soil-vegetation model, surface layer fluxes and the PBL parameterization. Applications of the model to the simulation of an observed supercell storm and to the prediction of a real case are also found in Part II. In the latter case, a long-lasting squall line developed and propagated across the eastern part of the United States following a historical number of tornado outbreak in the state of Arkansas.

/pdf/the-advanced-regional-prediction-system-arps-a-multi-scale-4ndsy21x71.pdf

The Advanced Regional Prediction System (ARPS) – A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification

This paper presents a general theoretical treatment of a new class of long stationary waves with finite amplitude. As the property in common amongst physical systems capable of manifesting these waves, the density of the (incompressible) fluid varies only within a layer whose thickness h is much smaller than the total depth, and it is h rather than the total depth that must be considered as the fundamental scale against which wave amplitude and length are to be measured. Internal-wave motions supported by the oceanic thermocline appear to be the most promising field of practical application for the theory, although applications to atmospheric studies are also a possibility.The waves in question differ in important respects from long waves of more familiar kinds, and in § 1 their character is discussed on the basis of a comparison with solitary-wave and cnoidal-wave theories on customary lines, such as apply to internal waves in fluids of limited depth. A summary of some simple experiments is included at the end of § 1. Then, in § 2, the comparatively easy example of two-fluid systems is examined, again to illustrate principles and to prepare the way for the main analysis in § 3. This proceeds to a second stage of approximation in powers of wave amplitude, and its leading result is an equation (3·51) determining, for arbitrary specifications of the density distribution, the form of the streamlines in the layer of heterogeneous fluid. Periodic solutions of this equation are obtained, and their properties are discussed with regard to the interpretation of internal bores and wave-resistance phenomena. Solutions representing solitary waves are then obtained in the form
 \[
 f(x) = a\lambda^2/(x^2+\lambda^2),
 \]
 where xis the horizontal co-ordinate and where aΛ = O(h2). (The latter relation between wave amplitude and length scale contrasts with the customary one, aΛ2 = O(h3)). The main analysis is developed with particular reference to systems in which the heterogeneous layer lies on a rigid horizontal bottom below an infinite expanse of homogeneous fluid; but in § 4 ways are given to apply the results to various other systems, including ones in which the heterogeneous layer is uppermost and is bounded by a free surface. Finally, in §5, three specific examples are treated: the density variation with depth is taken, respectively, to have a discontinuous, an exponential and a ‘tanh’ profile.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211206700103X

Internal waves of permanent form in fluids of great depth

The investigations of Parts I and II are extended to include experiments and theoretical considerations relating to the behavior of fluid systems with continuous gradients of density. The general equation of steady-state motion derived in Part I is integrated to yield the flow of a stratified fluid over an obstacle of finite dimensions. The results indicate a more or less complicated laminar wave motion for obstacles of maximum height below a certain value. Larger barriers cause an overdevelopment of the waves to a point where closed circulations and negative horizontal velocities appear. It is shown that this is accompanied by locally unstable distributions of density and eventual turbulence. If the height of the barrier is further increased, the velocity increases indefinitely in some parts of the field, becoming infinite for an obstacle of a certain size. No steady-state solution exists for larger barriers. The two critical values of the obstacle height depend primarily on the Froude number: If this number exceeds 1/π the solution exists and is stable for all obstacles; for small Froude numbers the barrier must be small if the solution is to exist or be stable. If the obstacle is small enough to permit laminar or moderately turbulent motion, the accompanying experiments verify all important features of the theory with remarkable fidelity. Larger obstacles cause considerable turbulence and blocking effects which propagate upstream, causing alternate maxima (jets) and minima of horizontal velocity in the vertical. DOI: 10.1111/j.2153-3490.1955.tb01171.x

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.2153-3490.1955.tb01171.x

Some Aspects of the Flow of Stratified Fluids

The following paper is the first of a series of two relating to the problem of internal oscillations of a fluid in a gravity field with vertical gradients of density and velocity. The theoretical analysis in this paper will be supplemented by a report on an experimental investigation along the same lines to be published in a future issue of this journal. The exact, steady-state equations of motion and continuity of a perfect liquid moving two-dimensionally, with an arbitrary vertical distribution of density and velocity, are integrated once to yield a second-order differential equation. This equation is examined with regard to uniqueness and stability of the motion. A criterion is developed giving a sufficient condition for the motion to be uniquely determined by the configuration of the topography over which the fluid moves. It appears, further, that the condition of uniqueness is also a condition that a certain integrated quantity, called the kinetic potential of the motion, be a maximum. The suggestion is offered that this may correspond to a form of fluid instability. A detailed study is made in the special cases of a uniform basic velocity, and a certain type of shearing flow. In either case, it is shown that an internal Froudc number of about 1/3 divides the motion into two states, one of which is called supercritical, the other subcritical. From several viewpoints, these regimes are analogous to the corresponding states of flow of water in a channel. In the subcritical state the flow is in the form of standing wave patterns. When flowing supercritically, conditions may be favorable for the formation of internal “hydraulic jumps”. DOI: 10.1111/j.2153-3490.1953.tb01035.x

https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v5i1.8563

Some Aspects of the Flow of Stratified Fluids: I. A Theoretical Investigation

A description is given of the flow of two superimposed layers of fluid over a barrier. This represents a partial experimental investigation of a problem considered theoretically in Part I. In general three regimes of motion are possible: If the velocities of the fluids are sufficiently small the interface is little disturbed except for a slight depression over the barrier. If the velocities are sufficiently high the interface swells symmetrically over the obstacle. At intermediate speeds a hydraulic jump occurs in the lee of the barrier and the lower layer increases in depth upstream. Two occurrences do not fit into the above description: If the obstacle is small compared to the depth of the lower layer, weak lee waves appear at low speeds, increasing in amplitude as the approach velocity of the fluid is increased. This seems to be the only case in which perturbation theory provides an adequate prediction of the flow. The second anomalous occurrence is the appearance of a “jump down” or hydraulic “drop” in the lee when the speed of the fluid is moderately high, the obstacle large, and the upper fluid relatively thin. The description of the experiments is supplemented by a theoretical discussion, employing the assumption of a hydrostatic pressure distribution. In general this theory provides a satisfactory explanation of the observed behavior. The paper concludes with a discussion of meteorological implications. DOI: 10.1111/j.2153-3490.1954.tb01100.x

https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v6i2.8731

Some Aspects of the Flow of Stratified Fluids: II. Experiments with a Two-Fluid System

The investigations of Parts I and II are extended to include experiments and theoretical considerations relating to the behavior of fluid systems with continuous gradients of density. The general e...

Some Aspects of the Flow of Stratified Fluids: 111. Continuous Density Gradients

A theoretical discussion is given of the solitary wave. Part I is concerned with the wave on a water surface; Part II considers the solitary wave at the interface of two superimposed liquids of different density, bounded above and below by rigid surfaces. In Part I higher approximations are obtained for the speed of propagation, and limits to the wave speed are derived from the momentum theorem. The results include a correction to the second approximation of Weinstein. In Part II the first two approximations to the wave speed are derived. The equations of the second approximation yield limits on the wave amplitude. DOI: 10.1111/j.2153-3490.1956.tb01249.x

https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v8i4.9035

Robert R. Long

Papers

Some Aspects of the Flow of Stratified Fluids

Some Aspects of the Flow of Stratified Fluids: I. A Theoretical Investigation

Some Aspects of the Flow of Stratified Fluids: II. Experiments with a Two-Fluid System

Some Aspects of the Flow of Stratified Fluids: 111. Continuous Density Gradients

Solitary Waves in the One- and Two-Fluid Systems