Second-order wave structure in supersonic flows
Mathematical analysis of wave structure in supersonic flow
Caughey, D. A.↗
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Basic studies of baroclinic flows
A fully nonlinear 3-dimensional numerical model (GEOSIM), previously developed and validated for several cases of geophysical fluid flow, has been used to investigate the dynamical behavior of laboratory experiments of fluid flows similar to those of the Earth's atmosphere. The phenomena investigated are amplitude vacillation, and the response of the fluid system to uneven heating and cooling. The previous year's work included hysteresis in the transition between axisymmetric and wave flow. Investigation is also continuing of the flows in the Geophysical Fluid Flow Cell (GFFC), a low-gravity Spacelab experiment. Much of the effort in the past year has been spent in validation of the model under a wide range of external parameters including nonlinear flow regimes. With the implementation of a 3-dimensional upwind differencing scheme, higher spectral resolution, and a shorter time step, the model has been found capable of predicting the majority of flow regimes observed in one complete series of baroclinic annulus experiments of Pfeffer and co-workers. Detailed analysis of amplitude vacillation has revealed that the phase splitting described in the laboratory experiments occurs in some but not all cases. Through the use of animation of the models output, a vivid 3-dimensional view of the phase splitting was shown to the audience of the Southeastern Geophysical Fluid Dynamics Conference in March of this year. A study on interannual variability was made using GEOSIM with periodic variations in the thermal forcing. Thus far, the model has not predicted a chaotic behavior as observed in the experiments, although there is a sensitivity in the wavenumber selection to the initial conditions. Work on this subject, and on annulus experiments with non-axisymmetric thermal heating, will continue. The comparison of GEOSIM's predictions will result from the Spacelab 3 GFFC experiments continued over the past year, on a 'back-burner' basis. At this point, the study (in the form of a draft of a journal article) is nearly completed. The results from GEOSIM compared very well with the experiments, and the use of the model allows the demonstration of flow mechanics that were not possible with the experimental data. For example, animation of the model output shows that the forking of the spiral bands is a transient phenomenon, due to the differential east-west propagation of convection bands from different latitudes.
Miller, Timothy L.↗
On the nonlinear characteristics of the axisymmetric flow regime: Cylindrical and spherical systems
The physical relationship between steady axisymmetric flows that might be observed in the atmosphere and in laboratory vessels is investigated theoretically. This is accomplished by comparing both the nonlinear structure and the thermal forcing mechanisms in two truncated spectral models of flow in the atmosphere and the rotating laboratory cylinder, respectively. Under statically stable conditions, the response of the internally forced spherical model (which is developed here from a set of new orthonormal basis functions) exhibits steady behavior different from that in the externally forced cylindrical model. Two regions of multiple steady solutions occur in the cylindrical model, under stable conditions, that are not found in the spherical one. The possible physical relevance of these multiple solutions is investigated by determining their location in parameter space with respect to the classical Hadley-Rossby transition curve. The results suggest that the wave flow regime, in an annulus, might develop catastrophically when an upper symmetric flow ceases to exist.
Higgins, R. W.↗
Aerodynamic Evidence Pertaining to the Entry of Tektites into the Earth's Atmosphere
Evidence is presented which shows that the Australian and Java tektites entered the earth's atmosphere and experienced ablation by severe aerodynamic heating in hypervelocity flight. The laboratory experiments on hypervelocity ablation have reproduced ring-wave flow ridges and coiled circumferential flanges like those found on certain of these tektites. Systematic striae distortions exhibited in a thin layer beneath the front surface of australites also are reproduced in the laboratory ablation experiments, and are shown to correspond to the calculated distortions for aerodynamic ablation of a glass. About 98 percent of Australian tektites represent aerodynamically stable configurations during the ablative portion of an entry trajectory. Certain meteorites exhibit surface features similar to those on tektites.
AERODYNAMIC HEATING↗
Contributions to Proceedings from the NATO Advanced Research Workshop on the Seismology of the Sun and the Distant Stars
Advanced research results on the seismology of the Sun and distant stars is presented. Topics presented include: (1) detection of global convective wave flows; (2) observation of low degree p-mode oscillations; and (3) techniques for spectral deconvolution.
Source record↗
The Acoustic Air-Jet Generator
This paper describes the development history, operation, and working principle of an acoustic air-jet generator, which can be used to produce high intensity, high frequency acoustic waves. Flow imaging experiments of the system are shown, and applications of the system for various fluid flows are presented. While previous articles on this system have been written in English by the author, this article provides the only documented explanation and implementation of the focusing schlieren system used for flow imaging of the system. This paper has been cited in early works on focusing schlieren as one of the first implementations of such a system, but has not been widely cited in the bulk of the literature on the focusing schlieren method (aside from a more recent M.S. thesis), perhaps due to the difficulty of accessing the paper or that no translation was available. The purpose of this translation is to provide an English version of the article for researchers interested in this work of Dr. Hartmann, and in particular the description of his focusing schlieren system and its application.
Julius Hartmann↗
A Lagrangian mean theory of wave, mean-flow interaction with applications to nonacceleration and its breakdown
A review is given of new Lagrangian mean theory of wave transport. Attention is focused on the so-called 'nonacceleration' theorem, and it is shown that such a theorem arises naturally in the Lagrangian mean framework. Also discussed is a simple example of the Stokes drift, a concept which is central to nonacceleration. The Lagrangian mean theory substantially simplifies and unifies the understanding of wave driving in cases where nonacceleration is violated because of wave transience and dissipation. Moreover, the theory has given new insights in one particular case, that of Rossby gravity wave, mean-flow interaction. These insights have successfully explained some hitherto unresolved paradoxes in the theory of the quasi-biennial oscillation of zonal wind in the equatorial stratosphere. Some brief remarks are also made concerning some of the outstanding difficulties of the theory in need of future investigation.
Dunkerton, T.↗
The role of Ekman flow and planetary waves in the oceanic cross-equatorial heat transport
A numerical model is used to mechanistically simulate the oceans' seasonal cross-equatorial heat transport. The basic process of Ekman pumping and drift is able to account for a large amount of the cross-equatorial flux. Increased easterly wind stress in the winter hemisphere causes Ekman surface drift poleward, while decreased easterly stress allows a reduction in the poleward drift in the summer hemisphere. The addition of planetary and gravity waves to this model does not alter the net cross-equatorial flow, although the planetary waves are clearly seen. On comparison with Oort and Vonder Haar (1976), this adiabatic advective redistribution of heat is seen to be plausible up to 10-20 deg N, beyond which other dynamics and thermodynamics are indicated.
Schopf, P. S.↗
Kelvin wave packets and flow acceleration - A comparison of modeling and observations
Atmospheric Kelvin waves, as revealed by temperatures obtained from the recent Limb Infrared Monitor of the Stratosphere (LIMS) experiment, commonly occur in packets. A simple two-dimensional gravity-wave model is used to study the upward propagation of these packets through different zonal mean wind profiles derived from the LIMS data. The observed prevalence of high frequency waves in the lower mesosphere and low frequency waves in the lower stratosphere can be exlained by dispersion of energy associated with the range of frequencies comprising a packet. Dominant wave frequencies at upper and lower levels are more distinctly separated if the packet propagates through a layer of westerly winds. Due to dispersion and shear effects, a packet of short temporal length at low levels will have a considerably extended impact on a layer of westerly winds at higher levels. Observed and modeled westerly accelerations resulting from packet absorption occur in the same layer, and are similar in magnitude and duration. These results support the theory that Kelvin waves are responsible for the westerly phase of the semiannual oscillation.
Coy, L.↗
Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow
The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.
Baysal, Oktay↗
Finite-difference theory for sound propagation in a lined duct with uniform flow using the wave envelope concept
Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.
Baumeister, K. J.↗
Sound generated by instability waves of supersonic flows. I Two-dimensional mixing layers. II - Axisymmetric jets
An investigation is conducted of the phenomenon of sound generation by spatially growing instability waves in high-speed flows. It is pointed out that this process of noise generation is most effective when the flow is supersonic relative to the ambient speed of sound. The inner and outer asymptotic expansions corresponding to an excited instability wave in a two-dimensional mixing layer and its associated acoustic fields are constructed in terms of the inner and outer spatial variables. In matching the solutions, the intermediate matching principle of Van Dyke and Cole is followed. The validity of the theory is tested by applying it to an axisymmetric supersonic jet and comparing the calculated results with experimental measurements. Very favorable agreements are found both in the calculated instability-wave amplitude distribution (the inner solution) and the near pressure field level contours (the outer solution) in each case.
Tam, C. K. W.↗
Two-dimensional Unsteady Flow in a Traveling Wave Plasma Accelerator
Two-dimensional unsteady flow in traveling wave plasma accelerator studied using small perturbation theory
PLASMA ACCELERATOR↗
Direct calculations of waves in fluid flows using high-order compact difference scheme
The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expression for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations. The numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the Courant-Friedrichs-Lewy (CFL) limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about six - eight grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 - 300 time steps. Three numerical examples of waves in compressible flow are included: (1) sound propagation in a duct with linear shear, (2) linear wave growth in a compressible free shear layer, and (3) vortex pairing in a compressible free shear layer perturbed at two frequencies.
Yu, Sheng-Tao↗
Direct calculations of waves in fluid flows using a high-order compact difference scheme
The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expressions for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations, and the numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the CFL limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about 6 to 8 grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 to 300 time steps. Three numerical examples of waves in compressible flow are included.
Yu, Sheng-Tao↗
Experimental feasibility of investigating acoustic waves in Couette flow with entropy and pressure gradients
The feasibility is discussed for an experimental program for studying the behavior of acoustic wave propagation in the presence of strong gradients of pressure, temperature, and flow. Theory suggests that gradients effects can be experimentally observed as resonant frequency shifts and mode shape changes in a waveguide. A convenient experimental geometry for such experiments is the annular region between two co-rotating cylinders. Radial temperature gradients in a spinning annulus can be generated by differentially heating the two cylinders via electromagnetic induction. Radial pressure gradients can be controlled by varying the cylinder spin rates. Present technology appears adequate to construct an apparatus to allow independent control of temperature and pressure gradients. A complicating feature of a more advanced experiment, involving flow gradients, is the requirement for independently controlled cylinder spin rates. Also, the boundary condition at annulus terminations must be such that flow gradients are minimally disturbed. The design and construction of an advanced apparatus to include flow gradients will require additional technology development.
Parrott, Tony L.↗
Taylor-Goertler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations
The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.
Hall, Philip↗
Solitary Rossby waves in zonal shear flows and their interactions
Interactions of long-wave solitons propagating in shear flows are described by a coupled pair of Korteweg-de Vries equations. The basic equation of motion for the analysis is the quasi-geostrophic forecast equation, and the interaction of two wave modes is studied. The solution for mode 1-mode 2 interaction of solitary waves in an asymmetric shear flow of a barotropic atmosphere with divergence is constructed. Streamline patterns for certain flows are obtained. An unsteady solitary wave solution for a modified Korteweg-de Vries equation is derived.
Redekopp, L. G.↗