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M. G. Wurtele

Abstract

The Lagrangian “parcel method” of stability analysis is systematically presented and rendered rigorous in its application to nondivergent flow on a plane with constant Coriolis parameter. The method is applied in detail to two familiar models. (1) Zonal geostrophic current with linear horizontal shear. Here the parcel method is valid only for uniform initial disturbance (“infinite wave-length”), in which case the usual stability criterion applies, −ζg <f. Another particular solution has been given by Lord Kelvin. (2) Anticyclonic vortex with concentric circular contours. Here, the parcel-method stability criterion is −ζg < f/2 (as suggested by the balance equation) and is valid for any initial disturbance with balanced velocity field. So far, no non-symmetric solution to the balance equation for this pressure field has been discovered.

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M. G. Wurtele and Cheryl Clark

Abstract

Three relaxation schema are applied to Poisson equations with known solutions. It is found that the schema using larger stencils are not only, as might he expected, significantly more accurate, but also significantly more efficient, as measured both by number of scans required and by machine time consumed.

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M. G. Wurtele and Brian Finke

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No Abstract Available.

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J. G. EDINGER and M. G. WURTELE

Abstract

Extensive observations were made on aircraft flights in the marine layer over the Pacific Ocean off the coast of southern California. We interpret some of the cloud patterns as convective and some as gravity wave phenomena. The ship wave and the three-dimensional lee wave are observed and analyzed in terms of the accompanying soundings, as are other characteristic cloud structures. From photographs of glories in the stratus tops, angles of back-scattering can be determined with sufficient accuracy to identify cloud-drop size distributions in accordance with Mie scattering theory.

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R. D. Sharman and M. G. Wurtele

Abstract

The three-dimensional structure of lee waves is investigated using a combination of linear analysis and numerical simulation. The forcings are represented by flow over a single wave (monochromatic) in the along-stream direction but of limited extent in the cross-stream direction, and by flow over isolated obstacles. The flow structures considered are of constant static stability, and zero, positive, and negative basic-flow shears. Both nonhydrostatic and hydrostatic regimes are studied. Particular emphasis is placed on 1) the cross-stream structure of the waves, 2) the transition from three-dimensional to two-dimensional flow as the breadth of the obstacle is increased, 3) the criteria for three-dimensional nonhydrostatic to hydrostatic transitions, and 4) the effect of obstacle breadth-to-length aspect ratio on the wave drag for this linear system. It is shown that these aspects can in part be understood by relating the gravity waves produced by narrow-breadth obstacles to the “St. Andrew's Cross” for hydrostatic and nonhydrostatic uniform flow and for hydrostatic shear flow.

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R. D. Sharman and M. G. Wurtele

Abstract

Three-dimensional internal trapped lee wave modes produced by an isolated obstacle in a stratified fluid are shown to have dynamics analogous to surface ship waves on water of finite depth. Two models which allow for vertical trapping of wave energy are treated in detail: 1) uniform upstream flow and stratification bounded above by a rigid lid; and 2) a semi-infinite fluid of uniform stability, with wind velocity increasing exponentially with height. This second model is taken as representing the atmosphere.

Unlike the surface ship wave, both of these models allow for an infinity of wave modes, a finite number (possibly zero) of which both have transverse and diverging systems, the remainder of the infinite set consisting only of diverging waves. Each mode is contained within a characteristic wedge angle, and each mode amplitude is a function of height.

Pursuing lines of analysis similar to these established for the ship wave problem, we have produced formal asymptotic solutions to our models. However, because of the limitations of the approximations and the infinity of modes in the solution, these formal solutions have extremely limited quantitative value. Therefore, we have developed time-dependent numerical models for both surface ship waves and internal and atmospheric ship waves and present a variety of results.

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Ralph D. Reynolds, Roy L. Lamberth, and M. G. Wurtele

Abstract

A complex mountain lee wave was recorded by radar-tracked superpressure balloons at White Sands Missile Range on 6 May 1965 at a mean altitude of 3.5 km MSL; simultaneously, a very weak wave was recorded at 7 km. The lower complex wave showed variable wavelengths, amplitudes, and increasing vertical velocities with time.

Several of the better existing mountain wave theories were tested against the data to determine which theory or theories, if any, could explain the physical cause of the particular features of the complex wave.

It was found that existing theoretical models are too simplified to apply to the condition in the observed wave and explain only its grosser features. If our understanding of gravity waves is to be adequate to explain quantitatively what we are capable of observing quantitatively, we must begin the anlysis of more realistic models or turn to numerical integration of the relevant equations.

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M. G. Wurtele, A. Datta, and R. D. Sharman

Abstract

As is well known, the linear dynamic equations for gravity-inertia waves are characterized by three singular levels, one being the critical level at which flow speed and wave speed are equal, and the other two at which the flow speed is equal to ±f/k, where f is the Coriolis parameter and k the wave number, herein called Rossby singularities. This article discusses the propagation of two-dimensional gravity-inertial disturbances, both monochromatic and with continuous spectrum (i.e., lee waves), in a direction toward all of these singular levels. The study is conducted by analysis, which provides closed-form solutions to the linear equations, and by numerical simulation, which confirms the analysis and also exhibits nonlinearities where these are significant.

It is found that the Rossby singularity produces nonlinear reflection of a monochromatic wave, and comparisons are made with the case of the pure gravity wave (f = 0) reflected by a critical level. Unlike that situation, in the present problem the momentum flux is also singular at the reflecting level. However, this is no longer the case when the disturbance contains a continuous spectrum, as in a lee wave produced by a smooth isolated ridge. In this case, the problem is essentially linear, and a relatively simple analytic approximation to the solution is presented and verified by simulation. The critical level acts as a lid but produces no singular effects. However, certain types of forcing profiles are identified that, despite being themselves of small amplitude, do in fact lead to nonlinearities in the field.

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M. G. Wurtele, A. Datta, and R. D. Sharman

Abstract

When a gravity–inertia wave in two dimensions is generated by flow over a stationary boundary above the critical level, its vertical propagation will depend on whether it encounters the singular level at which kU/f is equal to unity. If so, the wave is cellular below this level and vertically propagating above it, with drag and momentum flux oscillating in time between positive and negative, with no steady state approached. This is demonstrated by simulation and explained by analysis as the result of near resonance. When the disturbance is excited by flow over an isolated ridge, the flow will, or will not, oscillate depending on its Rossby number and on the width of the ridge as scaled by the wavelengths of the oscillatory portion of the spectrum. In particular, the quasigeostrophic solution is highly oscillatory.

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M. G. WURTELE, JAN PAEGLE, and ANITA SIELECKI

Abstract

Open boundaries are desirable when the region of interest of a computation is a localized area of a much larger domain. Boundary conditions are developed for the linear storm-surge equations (without Coriolis effects) that permit disturbances to pass out of the region of computation with negligible reflection. These conditions, based on the concept of Riemann invariants, are applied in one- and two-space dimensions. Examples of the flow around a sea mound, a shelf, and an island are given. Selected comparisons are made with Sommerfeld's radiation condition, advanced by Vastano and Reid.

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