Search NASA⌕ Search

SEARCH · Search NASA

Results for “atmospheric acoustics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

Some effects of the atmosphere and microphone placement on aircraft flyover noise measurements

The effects of varying atmospheric conditions on certification-type noise measurements were studied. Tests were made under various atmospheric conditions at two test sites, Fresno, California, and Yuma, Arizona, using the same test aircraft, noise, and weather measuring equipment, and operating personnel. Measurements were made to determine the effects of the atmosphere and of microphone placement on aircraft flyover noise. The measurements were obtained for characterization of not only the acoustic signature of the test aircraft, but also specific atmospheric characteristics. Data are presented in the form of charts and tables which indicate that for a wide range of weather conditions, at both site locations, noise data were repeatable for similar aircraft operating conditions. The placement of microphones at ground level and at 1.2 m over both spaded sand and concrete illustrate the effects of ground reflections and surface impedance on the noise measurements.

Hosier, R. N.↗

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. Furthermore, these results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

58 GEOSCIENCES↗

On sound generation by turbulent convection: A new look at old results

We have revisited the problem of acoustic wave generation by turbulent convection in stellar atmospheres. The theory of aerodynamically generated sound, originally developed by Lighthill and later modified by Stein to include the effects of stratification, has been used to estimate the acoustic wave energy flux generated in solar and stellar convection zones. We correct the earlier computations by incorporating an improved description of the spatial and temporal spectrum of the turbulent convection. We show the dependence of the resulting wave fluxes on the nature of the turbulence, and compute the wave energy spectra and wave energy fluxes generated in the Sun on the basis of a mixing-length model of the solar convection zone. In contrast to the previous results, we show that the acoustic energy generation does not depend very sensitively on the turbulent energy spectrum. However, typical total acoustic fluxes of order F(sub A) = 5 x 10(exp 7) ergs/sq cm/s with a peak of the acoustic frequency spectrum near omega = 100 mHz are found to be comparable to those previously calculated. The acoustic flux turns out to be strongly dependent on the solar model, scaling with the mixing-length parameter alpha as alpha(exp 3.8). The computed fluxes most likely constitute a lower limit on the acoustic energy produced in the solar convection zone if recent convection simulations suggesting the presence of shocks near the upper layers of the convection zone apply to the Sun.

Musielak, Z. E.↗

Evaluation of geophysical and anthropogenic sources of hydroacoustic noise in the Alaskan arctic

Quantifying the ocean soundscape is crucial for ocean-based seismoacoustic monitoring; it sets a baseline for the kinds and sizes of signals that can be detected above the background noise. As sea ice recedes, human activity in and around the Arctic Ocean is increasing, elevating sound levels and heightening the urgency of monitoring. Here, seven years of passive acoustic recordings from a National Oceanographic and Atmospheric Administration hydrophone in the Beaufort Sea are analyzed, focusing on frequencies between 1 and 125 Hz, a band of interest for detecting regional earthquakes and similar events. Sound is related to geophysical and anthropogenic sources, and seasonal and intraseasonal variations in the soundscape are examined. Sea ice emerges as a keystone feature of the Arctic Ocean acoustic environment, controlling or contributing to ambient sound levels at all frequencies studied. During low-ice months, sound levels are dominated by wind and sea surface waves, and in ice-covered months, wind-driven ice noise dominates. Seismic air gun surveys are prominent during low-ice periods, with sound levels decreasing with increasing distance and bathymetric complexity along the propagation path. The implications of this baseline soundscape for event detection in the Alaskan Arctic are discussed.

Niklasson, Siobhan [Los Alamos National Laboratory↗

Detection of the Large Surface Explosion Coupling Experiment by a Sparse Network of Balloon-Borne Infrasound Sensors

In recent years, high-altitude infrasound sensing has become more prolific, demonstrating an enormous value especially when utilized over regions inaccessible to traditional ground-based sensing. Similar to ground-based infrasound detectors, airborne sensors take advantage of the fact that impulsive atmospheric events such as explosions can generate low frequency acoustic waves, also known as infrasound. Due to negligible attenuation, infrasonic waves can travel over long distances, and provide important clues about their source. Here, we report infrasound detections of the Apollo detonation that was carried on 29 October 2020 as part of the Large Surface Explosion Coupling Experiment in Nevada, USA. Infrasound sensors attached to solar hot air balloons floating in the stratosphere detected the signals generated by the explosion at distances 170–210 km. Three distinct arrival phases seen in the signals are indicative of multipathing caused by the small-scale perturbations in the atmosphere. We also found that the local acoustic environment at these altitudes is more complex than previously thought.

47 OTHER INSTRUMENTATION↗

Magnetised quark nuggets in the atmosphere

A search for magnetised quark nuggets (MQN) is reported using acoustic signals from hydrophones placed in the Great Salt Lake (GSL) in the USA. No events satisfying the expected signature were seen. This observation allows limits to be set on the flux of MQNs penetrating the Earth’s atmosphere and depositing energy in the GSL. The expected signature of the events was ​derived from pressure pulses caused by high-explosive cords between the lake surface and bottom at various locations in the GSL. The limits obtained from this search are compared with those obtained from previous searches and are compared to models for the formation of MQNs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Acoustic waves from the 2023 April 20 SpaceX Starship rocket explosion travelling in the elevated ‘AtmoSOFAR’ channel

SUMMARY The ability to detect low-frequency sounds from distant energetic events depends on the temperature and wind structure of the atmosphere. Thus, from time to time surface-based acoustic detectors may not be able to capture sounds arriving from certain directions. However, the temperature minimum at the tropopause may create an acoustic duct called the ‘AtmoSOFAR’ channel that could transmit acoustic waves laterally—but perhaps not to the ground. If true, then elevated sensors such as those borne aloft by balloons would record the signatures even in regions where ground-based sensors cannot. This has been difficult to prove because high altitude acoustic sources are rare and balloon deployments are sporadic. This work describes the detection and characterization of powerful acoustic waves generated during the launch and terminal explosion of the SpaceX Starship rocket on 2023 April 20 using a pair of microbarometers on a stratospheric balloon. The signals travelled through the AtmoSOFAR channel, carrying information about the size and nature of their source. This channel also appears to leak some acoustic energy to the ground, in agreement with previous studies. The acoustic yield of the Starship terminal explosion was on the order of $10^3$ tons trinitrotoluene equivalent, which agrees with the estimated fuel load of the vehicle to about a factor of 2, but is two orders of magnitude larger than optical estimates. These results support an earlier study that claimed lateral transmission of sound from a smaller rocket through the AtmoSOFAR channel. The transmission of source information through the AtmoSOFAR channel motivates its use for monitoring other natural and anthropogenic events using balloon-borne sensors. This may become increasingly important as more and more private and government entities conduct spacecraft launches and reentries. It may also provide a means of monitoring clear air turbulence and other sound-generating atmospheric phenomena at a distance.

58 GEOSCIENCES↗

Wind and Temperature Consensus at Horn Point, HU-Beltsville, Piney Run (Maryland) in support of CoURAGE

The Maryland Department of the Environment (MDE) operates a ground-based atmospheric profiling network consisting of collocated radar wind profilers (RWP) and radio acoustic sounding systems (RASS) as part of its Ambient Air Monitoring Program. This network provides continuous observations of wind and temperature structure in the lower troposphere to support air quality forecasting, regulatory analysis, and atmospheric research. The network currently includes three fixed sites across Maryland: Horn Point (HP, lower eastern shore) [38.587525°,-76.141006°], Howard University-Beltsville (HUB, central Maryland) [39.055277°, -76.878632°], and Piney Run (PR, western Maryland) [39.705950°, -79.012000°] The network is designed to capture regional variability in atmospheric transport and boundary-layer processes. These systems measure vertical profiles of horizontal wind speed and direction using Doppler radar techniques, with observations typically spanning from ~100 m above ground level up to approximately 2.5–4 km. Measurements are derived from the Doppler shift of backscattered electromagnetic signals, enabling retrieval of wind vectors at multiple altitudes with high temporal resolution (e.g., 30-minute averages reported every 6 minutes). Each radar wind profiler is paired with a Radio Acoustic Sounding System (RASS) to provide profiles of virtual temperature in the lower atmosphere (~100–200 m AGL) by measuring the propagation speed of acoustic waves. Together, the RWP/RASS system yields a coupled data set of thermodynamic and kinematic atmospheric structure, including additional parameters such as vertical velocity, radial velocity, signal-to-noise ratio, and spectral width for advanced analysis. There are two types of files for each station: wind data (files with a "w" prefix) and virtual temperature RASS data (files with a "t" prefix). The wind data files are in the format wYYDDD.cns, where YY is the 2-digit year and DDD is the day of the year. The RASS virtual temperature data files are in the format tYYDDD.cns. Each record has the following header structure: Line 1 : Station Name RASS files Line 2 : RASS rev DeTect_2.0, WINDS files Line 2 : WINDS rev ATI 5.1 Line 3 : N latitude, W longitude, and site elevation (m) Line 4 : Date and begin time of consensus: yy mm dd hh mn ss plus # minutes to add to get UTC Line 5 : Consensus averaging time (minutes); number of beams; number of range gates Line 6 : Number of records required to make consensus (num) total number of records (tot) and the consensus window size (m/s) in the format: num:tot (window) RASS files Line 7 : no. of coded cells, no. of spec, pulse width (ns), and inter-pulse period (µs), WINDS files Line 7 : No. of coded cells, no. of spectra, pulse width (ns), and inter-pulse period (µs), each with a pair of values: first value is for oblique beams, second for vertical RASS files Line 8 : Full scale Doppler value (m/s) Delay to first gate (ns) Number of gates Spacing of gates (ns), WINDS files Line 8 : Full scale Doppler velocity (m/s), oblique and vertical Vertical correction applied to oblique beams? (0 = no, 1 = yes) Delay to first gate (ns), oblique and vertical Number of gates, oblique and vertical Spacing of gates (ns), oblique and vertical Line 9 : Azimuth and elevation (9s indicate vertical beam not used) RASS files Line 10, values : HT = Height above ground (km), T = Uncorrected virtual temperature consensus (deg C), Tc = Corrected virtual temperature consensus (deg C), W = Vertical wind consensus (9s indicate vertical beam not used, w-component, positive upward, m/s), CNT = Number of records that made consensus (for the 3 values in same order), SNR = Average signal to noise ratio (dB) of records in consensus (same order) WINDS files Line 10, values : HT = Height above ground (km), SPD = Wind speed (m/s), DIR = Wind direction (deg E of N from N), RAD = Radial velocities for each beam (m/s) in order given in azimuth and elevation line (positive toward radar; 9s indicate vertical beam not used, CNT = Number of records that made consensus, SNR = Average signal to noise ratio (dB) of records in consensus

{"wind speed and direction",temperature}↗

Isolating the Source Region of Infrasound Travel Time Variability Using Acoustic Sensors on High-Altitude Balloons

High-altitude balloons carrying infrasound sensor payloads can be leveraged toward monitoring efforts to provide some advantages over other sensing modalities. On 10 July 2020, three sets of controlled surface explosions generated infrasound waves detected by a high-altitude floating sensor. One of the signal arrivals, detected when the balloon was in the acoustic shadow zone, could not be predicted via propagation modeling using a model atmosphere. Considering that the balloon’s horizontal motion showed direct evidence of gravity waves, we examined their role in infrasound propagation. Implementation of gravity wave perturbations to the wind field explained the signal detection and aided in correctly predicting infrasound travel times. Our results show that the impact of gravity waves is negligible below 20 km altitude; however, their effect is important above that height. The results presented here demonstrate the utility of balloon-borne acoustic sensing toward constraining the source region of variability, as well as the relevance of complexities surrounding infrasound wave propagation at short ranges for elevated sensing platforms.

47 OTHER INSTRUMENTATION↗

Structure and Dynamics of the Quiet Solar Chromosphere

The grant supported research on the structure of the quiet, nonmagnetic chromosphere and on wave excitation and propagation in both the nonmagnetic chromosphere and the magnetic network. The work on the structure of the chromosphere culminated in the recognition that between two competing views of the solar chromosphere, older models by Avrett and collaborators (referred to as VAL) and the newer, dynamical model by Carlsson & Stein (referred to as CS), the clear decision is in favor of the older models, and this in spite of the evident lack of physics, which does not include wave motion and oscillations. The contrast between the static VAL models and the dynamical CS model can be stated most succinctly by comparing the temperature variation implied by the VAL models and the temperature fluctuations of the CS model, which are, respectively, of the order of 10% for the VAL model (at heights where hydrogen is 50% ionized) and a factor of 10 (at the upper boundary of their chromospheric model). The huge fluctuations of the CS model have never been observed, whereas the smaller temperature variations of the VAL models are consistent with ground-based and space-based observations. While it should be obvious which model describes the Sun and which one fails, the case is far from settled in the minds of solar physicists. Thus, much educational work remains to be done and, of course, more research to develop arguments that make the case more convincing. The research on waves and oscillations has been based on a unified theory of excitation of acoustic waves in the field-free atmosphere and of transverse and longitudinal waves in magnetic flux tubes located in the magnetic network by noting, first, that impulsive excitation of all these waves in gravitationally stratified media leads to oscillations at the respective cutoff frequencies and, second, that the observed oscillation frequencies in the nonmagnetic and magnetic parts of the chromosphere match corresponding cutoff frequencies in the upper solar photosphere. The dynamical simulations by Carlsson and Stein have been most instructive and of fundamental importance for understanding wave propagation in a stratified medium by their "flaws", the most important of which is an intensity excess at the H2v emission peak in the H line of Ca II, which is surprising since the observed intensity should have been an upper limit to the simulated intensity. The only plausible explanation for a predicted intensity that is higher than observed is that energy is spread horizontally in upward propagation in the Sun, but not in the plane-wave modeling of CS (as well as by almost everyone else). Investigations of the horizontal size of the region disturbed by the upward-propagating shock in the acoustic-wave propagation implies that the waves in H2v bright-point oscillations emanate from a point source with a diameter corresponding to the width of an intergranular lane, about 100 km, and reach a size of about 4000 km in the upper layers of the chromosphere. Linear, analytic modeling of waves emanating from a point source in a stratified atmosphere shows that the upward-expanding propagation channel does not have sharp boundaries and that the shape of the wave front depends on the order of the wave behind the initial pulse. Otherwise, the behavior of the linear waves resembles that of the nonlinear shock waves observed in the Sun. Research that needs to be done to firm up the conclusions reached above concerns the numerical simulations of nonlinear waves and oscillations in a three-dimensional stratified atmosphere with impulsive excitation, and observations linking directly the horizontal size of the disturbed area in upward propagation to individual waves.

Kalkofen, Wolfgang↗

Ionospheric Signature of Surface Mine Blasts from Global Positioning System Measurements

Sources such as atmospheric or buried explosions and shallow earthquakes are known to produce infrasonic pressure waves in the atmosphere. Because of the coupling between neutral particles and electrons at ionospheric altitudes, these acoustic and gravity waves induce variations of the ionospheric electron density. The Global Positioning System (GPS) provides a way of directly measuring the total electron content in the ionosphere and, therefore, of detecting such perturbations in the upper atmosphere. In July and August 1996, three large surface mine blasts (1.5 Kt each) were detonated at the Black Thunder coal mine in eastern Wyoming. As part of a seismic and acoustic monitoring- experiment, we deployed five dual-frequency GPS receivers at distances ranging from 50 to 200 km from the mine and were able to detect the ionospheric perturbation caused by the blasts. The perturbation starts 10 to 15 min after the blast, lasts for about 30 min, and propagates with an apparent horizontal velocity of 1200 meters per second. Its amplitude reaches 3 x 10 (exp 14) el per square meters in the 7-3 min period band, a value close to the ionospheric perturbation caused by the M = 6.7 Northridge earthquake. The small signal-to-noise ratio of the perturbation can be improved by slant-stacking the electron content time-series recorded by the different GPS receivers taking into account the horizontal propagation of the perturbation. The energy of the perturbation is concentrated in the 200 to 300 second period band, a result consistent with previous observations and numerical model predictions. The 300 second band probably corresponds to gravity modes and shorter periods to acoustic modes, respectively. Using a 1-D stratified velocity model of the atmosphere we show that linear acoustic ray tracing fits arrival times at all GPS receivers. We interpret the perturbation as a direct acoustic wave caused by the explosion itself. This study shows that even relatively small subsurface events can produce ionospheric perturbations that are above the detection threshold of the GPS technique. By sensing derivative signals, which can be detected over a relatively broad region, it appears that GPS might be particularly useful for source characterization within the first acoustic quiet zone where infrasound would probably be ineffective. This suggests that dual-frequency GPS monitoring could contribute to Comprehensive Nuclear Test Ban Treaty verification.

Calais, Eric↗

Acoustic Travel-Time Tomography for Wind Energy

New remote sensing technologies for direct observation of the atmospheric flow in the proximity of operating wind turbines are necessary for the advancement of wind turbine design, wind plant control, and the validation of high-fidelity numerical models; fundamental goals of the DOE Wind Energy Technology Office's (WETO's) A2e program. Modern remote sensing technologies for commercial and research applications rely on the backscatter of light or sound waves, which limits spatial and temporal resolution and cannot produce reliable flow estimates near solid bodies or reflective surfaces. Acoustic tomography (AT) is an innovative sensing technology based on fundamental thermodynamic properties of the atmosphere and an inverse algorithm that can reconstruct both velocity and temperature fields within a network of acoustic transducers. AT relies on the direct travel path of acoustic signals between speakers and microphones in the network and can achieve much higher resolutions than conventional backscatter technologies. For wind energy R&D applications, AT represents an extremely economical option over other remote sensing technologies, integrating mature and commonly available acoustic and signal processing hardware. This report is intended as an update on the development of the AT array on the NREL Flatirons Campus (FC) and includes a brief review of the instrumentation, the calibration of equipment, signal processing, and resulting flow field estimates. Designs for future AT systems and applications are detailed in this report, including summaries of new capabilities, engineering and theoretical challenges, and anticipated costs help to outline future directions for AT technology R\&D. The potential for application of AT to utility-scale turbines is also discussed. Investing in the development of the proposed instrument will establish AT as a transformational RS technique that represents a significant advance in measurement instrumentation, enabling new fundamental insights into the structure of the atmospheric boundary layer and supporting applications for wind energy, pollution transport, and resource characterization. AT is also an extremely economical option over other RS instruments, integrating mature and commonly available acoustic and signal processing hardware.

17 WIND ENERGY↗

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Kopasakis, George↗

Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Atmospheric Turbulence Modeling↗

Stage-by-Stage and Parallel Flow Path Compressor Modeling for a Variable Cycle Engine, NASA Advanced Air Vehicles Program - Commercial Supersonic Technology Project - AeroServoElasticity

This paper covers the development of stage-by-stage and parallel flow path compressor modeling approaches for a Variable Cycle Engine. The stage-by-stage compressor modeling approach is an extension of a technique for lumped volume dynamics and performance characteristic modeling. It was developed to improve the accuracy of axial compressor dynamics over lumped volume dynamics modeling. The stage-by-stage compressor model presented here is formulated into a parallel flow path model that includes both axial and rotational dynamics. This is done to enable the study of compressor and propulsion system dynamic performance under flow distortion conditions. The approaches utilized here are generic and should be applicable for the modeling of any axial flow compressor design accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

Compressor Modeling Modeling↗

Sonic-boom propagation through a stratified atmosphere.

Theoretical approach to the problem of predicting the sonic-boom signature due to a maneuvering aircraft, with outline of the resulting calculation method. This method includes the effects of a variable, stratified atmosphere, and is based on geometric-acoustic principles. A nonlinear distortion is used to account for the weak shock field. The analytical results are compared with experimental data and excellent agreement was found, particularly with regard to signature length.

Hayes, W. D.↗

Prediction of thermal acoustic oscillations (TAOs) in the CLAES solid CO2/neon system

Results are presented of a study initiated to investigate the possibility that the existence of thermal acoustic oscillations (TAOs) in the Cryogenic Limb Atmospheric Etalon Spectrometer (CLAES) neon plumbing system ground configuration could be the cause of higher-than-predicted heat rates measured during thermal ground testing. Tests were conducted between warm boundary temperatures ranging from 40 to 100 K, which simulated the actual test conditions of the CLAES CO2/neon system. TAOs were observed between 6 and 106 Torr, which agreed with the analytical predictions, and verified the possible existence of TAOs in the CLAES system during ground testing. The presence of TAOs was eventually confirmed in the CLAES system during a subsequent thermal test and were determined to have caused the higher heat rates measured during the prior thermal test.

Spradley, I. E.↗

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

New calculations of the acoustic wave energy fluxes generated in the solar convective zone have been performed. The treatment of convective turbulence in the sun and solar-like stars, in particular, the precise nature of the turbulent power spectrum has been recognized as one of the most important issues in the wave generation problem. Several different functional forms for spatial and temporal spectra have been considered in the literature and differences between the energy fluxes obtained for different forms often exceed two orders of magnitude. The basic criterion for choosing the appropriate spectrum was the maximal efficiency of the wave generation. We have used a different approach based on physical and empirical arguments as well as on some results from numerical simulation of turbulent convection.

Musielak, Z. E.↗