Spectra Of Temperature Fluctuations Research Articles

Discussion of sound propagation through the turbulent Martian atmosphere and implications for inference of turbulence spectra.

Chide et al. [J. Acoust. Soc. Am. 155, 420-435 (2024)] provide a first attempt to infer the spectrum of temperature fluctuations on Mars from experimental data on the variances of travel-time and log-amplitude fluctuations recorded by the microphone on board the Perseverance rover. However, the theoretical formulations that were used to interpret the travel-time data have limitations. In addition to explaining those issues, this article also outlines approaches for predicting statistical characteristics of acoustic signals in the Martian atmosphere. In particular, the experimentally observed dependence of the travel-time variance on the propagation range can be attributed to ground-blocking of buoyantly produced turbulent velocity fluctuations and the non-Markov character of phase fluctuations.

The Study of Internal Gravity Waves in the Earth’s Atmosphere by Radio Occultations: A Review

Internal gravity waves (IGWs) in the middle atmosphere are the main source of mesoscale fluctuations of wind and temperature. The parameterization of IGWs and study of their climatology is necessary for the development of global atmospheric circulation models. In this review, we focus on the application of Radio Occultation (RO) observations for the retrieval of IGW parameters. (1) The simplest approach employs the retrieved temperature profiles. It is based on the fact that IGWs are highly anisotropic structures and can be accurately retrieved by RO. The basic assumption is that all the temperature fluctuations are caused by IGWs. The smoothed background temperature profile defines the the Brunt–Väisälä frequency, which, together with the temperature fluctuations, defines the IGW specific potential energy. Many studies have derived the distribution and climatology of potential energy, which is one of the most important characteristics of IGWs. (2) More detailed analysis of the temperature profiles is based on the derivation of the temperature fluctuation spectra. For saturated IGWs, the spectra must obey the power law with an exponent of −3. Such spectra are obtained by using Wave Optical (WO) processing. (3) More advanced analysis employs space–frequency analysis. It is based on phase-sensitive techniques like cross S- or wavelet transforms in order to identify propagating IGWs. (4) Another direction is the IGW parameter estimate from separate temperature profiles applying the stability condition in terms of the Richardson number. In this framework, a necessary condition is formulated that defines whether or not the temperature fluctuations can be related to IGW events. The temperature profile retrieval involves integral transforms and filtering that constitute the observation filter. (5) A simpler filter is implemented by the analysis of the RO amplitude fluctuation spectra, based on the diffraction theory in the framework of the phase screen and weak fluctuation approximations. The two spectral parameters, the external scale and the structural characteristic, define the specific potential energy. This approach allows the derivation of the spacial and seasonal distributions of IGW activity. We conclude that the success of IGW study by RO is stimulated by a large number of RO observations and advanced techniques based on Fourier and space–time analysis, physical equations describing IGWs, and diffraction theory.

Statistical Characteristics of Mesoscale Fluctuations of Wind Velocity, Temperature, and Gas Concentrations Obtained from Aircraft Measurements in the Troposphere of the Arctic Region

Abstract The results of airborne measurements and statistical characteristics of mesoscale fluctuations of wind velocity, temperature, and concentrations of gas constituents at different heights of a stably stratified troposphere are presented. The measurements were carried out in September 2022 in the Arctic region of Russia with the aircraft laboratory Tu-134 “Optik.” The obtained spectra and structure functions of the fluctuations are interpreted with the theoretical model of formation of the spectrum of mesoscale wind velocity and temperature fluctuations described in the paper. The presence at high wavenumbers of a steep section in the obtained horizontal wavenumber spectra of the fluctuations of wind velocity and greenhouse gas concentration with a slope close to −3 is discussed. The fluctuation spectra along different slanted tracks of the aircraft crossing the tropospheric layer between altitudes of 1 and 9 km are also obtained and analyzed with the theoretical model.

Development of correlation ECE system for electron temperature fluctuation measurement in LHD

Correlation-ECE (C-ECE) is a standard method for investigating turbulence driven transport. This method allows electron temperature fluctuations that contain information on turbulent transport and independent thermal noise. The turbulence feature is extracted from a correlation analysis from two close locations. The A C-ECE system is utilized on the large helical device (LHD) to measure emission within the frequency range of 74–79.6 GHz. This system employs the spectral decorrelation method and serves as a collective Thomson scattering diagnostic receiver in the LHD. The C-ECE receiver system is comprised of a filter bank system with 32 band-pass filters and a fast digitizer system operating at a sampling rate of 12.5 GHz in the intermediate frequency (IF) stage. This study presents initial experimental results on temperature fluctuation spectra in the LHD, obtained through the C-ECE system using a coherency-based analysis method. An MHD mode at 5 kHz is excited from the onset of neutral beam injection in a magnetic probe, and coherence spectra are obtained from two C-ECE receiver systems. The temperature fluctuation results are derived from the coherence spectrum after bias removal and indicate a level of approximately 3% in the frequency range of 0 to 400 kHz. Further investigations will be conducted to explore drift wave turbulence activities and reconstruct the radial profile of temperature fluctuation in the LHD using the C-ECE receiver systems.

Resolvent-based analysis of hypersonic turbulent boundary layers with/without wall cooling

The ability of the low-rank approximation of hypersonic turbulent boundary layers with/without wall cooling is examined with the linear resolvent operator in a compressible form. The freestream Mach number of the base flow is 5.86, and the friction Reynolds number is 420. The wall-to-recovery temperature ratio is set as 1.0 and 0.25, respectively, corresponding to an adiabatic wall condition and a cold-wall condition. Different from the resolvent analysis of incompressible turbulent boundary layers, the optimal response mode in the wave-parameter space exhibits a relatively subsonic and a relatively supersonic region [Bae et al., “Resolvent-based study of compressibility effects on supersonic turbulent boundary layers,” J. Fluid Mech. 883, A29 (2020)], divided by the freestream relative Mach number of unity. The features of energy distribution of the optimal response mode in space and scales are examined, and the energy spectra of streamwise velocity and temperature fluctuations, carried by the optimal response mode, are discussed with typical subsets of streamwise and spanwise wavelengths. This reveals the dynamics of the near-wall small-scale and outer larger-scale motions and the distinction in the relatively subsonic/supersonic region. Moreover, the coherent structures, including the velocity and temperature streaks, quasi-streamwise vortices, and large-scale/very-large-scale motions, are identified in the optimal response mode. Special attention is paid to the effects of wall cooling.

Fluctuations by atmospheric turbulence in aircraft flyover auralisation

Long-term exposure to aircraft noise causes significant health issues among residents near airports. Therefore, noise impact assessments and noise control at the source are important aspects of the design of new aircraft. The design process of low-noise aircraft can be supported with auralisation of virtual flyovers. In order to render plausible aircraft auralisations, multiple propagation phenomena have to be considered, such as geometrical spreading, air absorption, Doppler effect, and reflections from the ground. Additionally, measurements of aircraft flyover show clear patterns of amplitude and phase fluctuations by atmospheric turbulence. Aircraft flyover auralisations should incorporate these clearly audible features of sound propagation in real-world conditions to be perceived as plausible. We present new approaches of time-variant filtering techniques to account for phase and amplitude fluctuations as a function of atmospherical conditions characterised by the von Kármán turbulence spectrum of wind and temperature fluctuations. Compared to earlier approaches, the proposed model is closer to the physical mechanisms. The application of the filters leads to a reduction of unnatural flanging and to a higher naturalness of level fluctuations. As the proposed method has shown to increase plausibility of aircraft flyover auralisation, its application in perception-based evaluation of future aircraft concepts is forseen.

Contribution of Gravity Waves to Universal Vertical Wavenumber (∼m−3) Spectra Revealed by a Gravity‐Wave‐Permitting General Circulation Model

AbstractObservations with high vertical resolution have revealed that power spectra of horizontal wind and temperature fluctuations versus vertical wavenumber have a universal shape with a steep slope in a high range, approximately proportional to . Several theoretical models explaining this spectral slope were proposed under an assumption of gravity wave (GW) saturation. However, little evidence has been obtained to show that these universal spectra are fully composed of GWs. To confirm the validity of this assumption, two kinds of spectra are calculated using outputs from a GW‐permitting high‐top general circulation model. One is the spectra for GWs designated by fluctuations having total horizontal wavenumbers of 21–639. The other is the spectra of fluctuations unfiltered except extracting the linear trend in each vertical profile that were often analyzed in the observational studies. A comparison between the two shows that GWs dominate the observed spectra only in a higher part of the steep slope, whereas disturbances other than GWs significantly contribute to its lower part. Moreover, geographical distributions of the characteristic wavenumbers, slopes, and spectral densities of GW spectra are examined for several divided height regions of the whole middle atmosphere. It is shown that strong vertical shear below the zonal wind jets as well as wave saturation are responsible for the formation of the steep slopes of GW spectra.

Methodology for assessing atmospheric effects during baikal earthquakes

Strong earthquakes (M>5.0) recorded from 2020 to 2021 within the Baikal rift zone were studied. The «background» time intervals of the current period when tangible earthquakes were not observed are highlighted. Seismogravitational fluctuations in temperature and pressure were recorded. It was found that before the studied earthquakes harmonics with a period of 92-96 hours appear in the spectrum of temperature fluctuations at the isobaric level of 300 hPa. Such harmonics are absent in the corresponding background temperature series. The fact of the appearance of new harmonics can be used as a sign of an imminent earthquake in the Baikal region. As a result, a method for estimating atmospheric effects during strong earthquakes is proposed.

DNS Study of turbulent heat transfer in an elliptical pipe flow subjected to system rotation about the major axis

Turbulent heat transfer in an elliptical pipe flow subjected to spanwise system rotation about the major axis has been studied through direct numerical simulations (DNS). The influence of the Coriolis force on the turbulent heat convection has been analyzed through analyses of the first- and second-order statistical moments of the temperature field in both physical and spectral spaces. The mean temperature, turbulent heat fluxes, pre-multiplied spectra of temperature fluctuations, and coherent thermal structures of the rotating flows are compared against those of the non-rotating flow. It is observed that the secondary flow pattern is sensitive to the rotation number and has a significant impact on the transport process of thermal energy and on the value of the Nusselt number. Through a budget analysis of the vertical turbulent heat flux, it is revealed that the profiles of the budget terms are symmetrical about the minor axis and the turbulent production is the primary source term in a non-rotating flow. However, as soon as the system rotation is imposed, the profiles become asymmetrical and the Coriolis term starts to dominate the turbulent production process as the primary source for turbulent heat flux at a moderate rotation number. Examination of the coherent thermal structures within the flow further reveals that the Coriolis force acts to reduce the vertical turbulent heat flux on the pressure side of the pipe.

Seasonal change in heat flux at the water-bottom sediment boundary in a small lake

Heat exchange with bottom sediments is the main component of the thermal regime of ice-covered shallow lakes of the temperate zone, which explains the importance of its study and parameterization for inclusion in numerical models. Circulations arising in ice-covered lakes due to heat exchange with bottom sediments, and existing for several months, can make a significant contribution to the transport of dissolved and suspended particles along the water column. The aim of this work was to study the seasonal variability of the heat flux at the waterbottom boundary in a shallow lake during the under-ice period, including the period of spring under-ice convection. Based on the analysis of data from high-frequency (minute) long-term measurements of water temperature in the bottom area of a small lake in the temperate zone, a wide range of variability of the heat flux across the water-bottom boundary during the winter from minute to daily fluctuations was established. The role of the spring under-ice heating in the change in the heat flow at the water-bottom boundary is shown. It is shown that shallow areas of the lake bottom, falling into the zone of influence of spring subglacial convection, can accumulate heat already at the end of the ice period. The comparison of temperature fluctuations in the deep-water part of the lake and tin he area with depths close to the average is carried out. It is shown that the spectrum of temperature fluctuations has similar periods, however, in time, sharp temperature jumps in different areas of the lake do not coincide.

Mathematical Modelling of Climate Change and Variability in the Context of Outdoor Ergonomics

The current climate change, unlike previous ones, is caused by human activity and is characterized by an unprecedented rate of increase in the near-surface temperature and an increase in the frequency and intensity of hazardous weather and climate events. To survive, society must be prepared to implement adaptation strategies and measures to mitigate the negative effects of climate change. This requires, first of all, knowledge of how the climate will change in the future. To date, mathematical modelling remains the only method and effective tool that is used to predict the climate system’s evolution under the influence of natural and anthropogenic perturbations. It is important that mathematics and its methods and approaches have played a vital role in climate research for several decades. In this study, we examined some mathematical methods and approaches, primarily, mathematical modelling and sensitivity analysis, for studying the Earth’s climate system, taking into account the dependence of human health on environmental conditions. The essential features of stochastic climate models and their application for the exploration of climate variability are examined in detail. As an illustrative example, we looked at the application of a low-order energy balance model to study climate variability. The effects of variations in feedbacks and the climate system’s inertia on the power spectrum of global mean surface temperature fluctuations that characterized the distribution of temperature variance over frequencies were estimated using a sensitivity analysis approach. Our confidence in the obtained results was based on the satisfactory agreement between the theoretical power spectrum that was derived from the energy balance model and the power spectrum that was obtained from observations and coupled climate models, including historical runs of the CMIP5 models.

Spectra of Temperature Fluctuations in the Solar Wind

Turbulent cascade transferring the free energy contained within the large scale fluctuations of the magnetic field, velocity and density into the smaller ones is probably one of the most important mechanisms responsible for heating of the solar corona and solar wind, thus the turbulent behavior of these quantities is intensively studied. The temperature is also highly fluctuating quantity but its variations are studied only rarely. There are probably two reasons, first the temperature is tensor and, second, an experimental determination of temperature variations requires knowledge of the full velocity distribution with an appropriate time resolution but such measurements are scarce. To overcome this problem, the Bright Monitor of the Solar Wind (BMSW) on board Spektr-R used the Maxwellian approximation and provided the thermal velocity with a 32 ms resolution, investigating factors influencing the temperature power spectral density shape. We discuss the question whether the temperature spectra determined from Faraday cups are real or apparent and analyze mutual relations of power spectral densities of parameters like the density, parallel and perpendicular components of the velocity and magnetic field fluctuations. Finally, we compare their spectral slopes with the slopes of the thermal velocity in both inertial and kinetic ranges and their evolution in course of solar wind expansion.

Osnovnyye zakonomernosti vertikal'nogo turbulentnogo obmena v kvaziodnorodnykh i stratifitsirovannykh sloyakh Chernogo morya

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. For the upper mixed layer, the turbulent energy dissipation rate ɛ and the exchange coefficient were calculated using the velocity fluctuation spectra based on the Kolmogorov hypotheses on the turbulence spectrum inertial range. In the stratified layers, the turbulence coefficient and the dissipation rate were experimentally determined both from the spectra of the velocity horizontal fluctuations’ gradients and the vertical spectra of temperature fluctuations using the concept of the effective scale of turbulent spots. Depending on the features of the hydrological regime and the prevailing energy contributors to turbulence generation, five layers were identified and described (including their characteristic power dependences of the vertical turbulent diffusion coefficients K on the buoyancy frequency N) using the 1.5D-model of vertical turbulent exchange for the basin under study. For the stratified layers, the 1.5D-model results were comparatively analyzed with those of the other semi-empirical and theoretical models describing the most probable hydrophysical processes in each specific layer; the relations for the vertical turbulent exchange coefficient were obtained depending on the buoyancy frequency. Conclusions. Comparison of the experimental data collected under different hydrometeorological conditions with the simulations resulted from the known turbulence models for the sea upper layer showed that the best agreement between the simulation and measurement data was provided by a multiscale model taking into account three basic mechanisms of turbulence generation: current velocity shear, instability of wave motions, and wave breaking. The turbulent exchange coefficient dependencies on depth are conditioned by the affect of the turbulence dominant source at a given level. In the stratified layers, the exchange coefficient dependence on buoyancy frequency is determined by the hydrophysical processes in each layer; the relations obtained for individual layers indicate intensity of the contributions of vertical advection, internal wave breakings, turbulence diffusion and geothermal flux.

Basic Regularities of Vertical Turbulent Exchange in the Mixed and Stratified Layers of the Black Sea

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. For the upper mixed layer, the turbulent energy dissipation rate ɛ and the exchange coefficient were calculated using the velocity fluctuation spectra based on the Kolmogorov hypotheses on the turbulence spectrum inertial range. In the stratified layers, the turbulence coefficient and the dissipation rate were experimentally determined both from the spectra of the velocity horizontal fluctuations’ gradients and the vertical spectra of temperature fluctuations using the concept of the effective scale of turbulent patches. Depending on the features of the hydrological regime and the prevailing energy contributors to turbulence generation, five layers were identified and described (including their characteristic power dependences of the vertical turbulent diffusion coefficients K on the buoyancy frequency N) using the 1.5D-model of vertical turbulent exchange for the basin under study. For the stratified layers, the 1.5D-model results were comparatively analyzed with those of the other semi-empirical and theoretical models describing the most probable hydrophysical processes in each specific layer; the relations for the vertical turbulent exchange coefficient were obtained depending on the buoyancy frequency. Conclusions. Comparison of the experimental data collected under different hydrometeorological conditions with the simulations resulted from the known turbulence models for the sea upper layer showed that the best agreement between the simulation and measurement data was provided by a multiscale model taking into account three basic mechanisms of turbulence generation: current velocity shear, instability of wave motions, and wave breaking. The turbulent exchange coefficient dependencies on depth are conditioned by the effect of the turbulence dominant source at a given level. In the stratified layers, the exchange coefficient dependence on buoyancy frequency is determined by the hydrophysical processes in each layer; the relations obtained for individual layers indicate intensity of the contributions of vertical advection, internal wave breakings, turbulence diffusion and geothermal flux.

IR thermography study of flow structure and parameters in diffusion flames

The flame structure and flow modes have been investigated in the process of diffusion combustion of a number of liquid fuels, such as ethanol, benzine, kerosene and diesel fuel, by using the technique of infrared (IR) thermography in the narrow spectral range (2.5–2.7 μm). IR thermography provides useful information on the thermal behavior of turbulent diffusion flames, which is the thermal representation of turbulent processes in the hydrodynamic structure of flames. By analyzing IR images and spectra of flame temperature fluctuations, seven characteristic zones with different flow modes have been identified in the flames. To estimate flame flow parameters, the turbulent Reynolds number has been used thus taking account the amplitude and frequency of the temperature fluctuations determined by processing IR images of flames. The Reynolds number strongly increases during the diffusion combustion of kerosene, in contrast to benzine, diesel fuel and ethanol. This can be explained by a more complex chemical composition of kerosene and a multi-stage character of chemical reactions.

Experimental evidence of a phase transition in the multifractal spectra of turbulent temperature fluctuations at a forest canopy top

Ramp–cliff patterns visible in scalar turbulent time series have long been suspected to enhance the fine-scale intermittency of scalar fluctuations compared to longitudinal velocity fluctuations. Here, we use the wavelet transform modulus maxima method to perform a multifractal analysis of air temperature time series collected at a pine forest canopy top for different atmospheric stability regimes. We show that the multifractal spectra exhibit a phase transition as the signature of the presence of strong singularities corresponding to sharp temperature drops (respectively jumps) bordering the so-called ramp (respectively inverted ramp) cliff patterns commonly observed in unstable (respectively stable) atmospheric conditions and previously suspected to contaminate and possibly enhance the internal intermittency of (scalar) temperature fluctuations. Under unstable (respectively stable) atmospheric conditions, these ‘cliff’ singularities are indeed found to be hierarchically distributed on a ‘Cantor-like’ set surrounded by singularities of weaker strength typical of intermittent temperature fluctuations observed in homogeneous and isotropic turbulence. Under near-neutral conditions, no such a phase transition is observed in the temperature multifractal spectra, which is a strong indication that the statistical contribution of the ‘cliffs’ is not important enough to account for the stronger intermittency of temperature fluctuations when compared to corresponding longitudinal velocity fluctuations.

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.

Diagnostics of transient heat transfer regimes based on statistical and frequency analysis of temperature fluctuations

ABSTRACT The paper presents the results of experimental and theoretical studies of temperature fluctuations at the surface of heaters in different heat transfer regimes. Developing several methods of treatment for the temperature fluctuations, we succeed in the diagnosing the onset of transient boiling regimes. The proposed methods are based on the statistical analysis of histograms and amplitude-frequency analysis of the spectra of temperature fluctuations. In addition, the study demonstrates and compares how these techniques may be utilized to predict the transitions from the convective heat transfer to the nucleate boiling and the film boiling regimes.

The Inflationary Mechanism in Asymptotically Safe Gravity

According to the asymptotic safety conjecture, gravity is a renormalizable quantum field theory whose continuum limit is defined by an interacting fixed point of the renormalization group flow. In these proceedings, we review some implications of the existence of this nontrivial fixed point in cosmological contexts. Specifically, we discuss a toy model exemplifying how the departure from the fixed-point regime can explain the approximate scale-invariance of the power spectrum of temperature fluctuations in the cosmic microwave background.

High frequency temperature fluctuation measurements by Rayleigh scattering and constant-voltage cold-wire techniques

The thermal inertia of sensors drastically limits the measurement of the temperature fluctuations in the high-frequency range. This issue is often addressed using cold wire techniques with dedicated corrections. In this study, three methods are employed to compensate high-frequency attenuation, and the correction of the end losses, are evaluated for four wires with different aspect ratios and diameters. The fidelity of the corrected measurements is assessed by comparing the spectra of temperature fluctuations obtained with the cold wires operating in a constant voltage circuit, to those derived from optical measurements. The latter method is based on Rayleigh scattering and is in principle not affected by thermal inertia as it relies on molecular light scattering. Two flows presenting high levels of temperature fluctuations are considered. Namely, the wake of a heated cylinder, and a mixing layer between two jets in co-flow and at different temperatures. These two configurations allow exploring cold wire performances at high frequency, and show that precise measurements can be performed up to 10 kHz with a wire $$1\,\upmu \hbox {m}$$ in diameter.