Frequency Spectra Of Fluctuations Research Articles

Voltage fluctuations and probe frequency jitter in electric force microscopy of a conductor.

Electric force microscopy probes the statistics of electric field fluctuations from a sample surface, both through measurement of the noncontact friction exerted on the oscillating charged probe and by determination of the power spectrum of stochastic probe frequency fluctuations, referred to as "jitter." Here we calculate the frequency jitter power spectrum determined over a conducting sample of finite thickness, whose response is characterized by a dielectric function that is wavevector-dependent. These calculations complement previous predictions of the coefficient of noncontact friction in an electric force microscopy measurement for the same model, and also previous predictions of the jitter power spectrum for a dielectric continuum. The inclusion both of a finite sample thickness and a wavevector-dependent dielectric response can significantly enhance the magnitude of the predicted jitter spectrum for a conductor, relative to a simpler model of an infinitely thick dielectric continuum. These calculations provide a baseline prediction of the jitter power spectrum generated by the dynamics of conduction electrons in a metal sample.

On wall pressure fluctuations in conical shock wave/turbulent boundary layer interaction

The structure and the frequency spectra of wall pressure fluctuations beneath a planar turbulent boundary layer interacting with a conical shock wave at Mach number $M_\infty =2.05$ and Reynolds number $\textit {Re}_\theta \approx 630$ (based on the upstream boundary layer momentum thickness) are examined to elucidate the effects of pressure gradient and flow separation on the characteristics of the wall pressure fluctuations, by exploiting a direct numerical simulation database. Upstream of the interaction, in the zero pressure gradient region, wall pressure statistics compare well with canonical compressible boundary layers in terms of fluctuation intensities and frequency spectra. Across the main interaction zone (APG1), the root-mean-square of wall pressure fluctuations becomes very large (corresponding to approximately 173.3 dB), with maximum increase approximately 12.7 dB from the incoming level. In the second adverse pressure gradient zone (APG2), the root-mean-square of wall pressure fluctuations attains a second peak (corresponding to $164.7$ dB), with an increase of 8.4 dB from the upstream level. Both the APG1 and APG2 regions feature a substantial fraction of flow reversal events, which are, however, scattered and interspersed with regions of attached flow. The wall pressure power spectral density exhibits a broadband and energetic low-frequency component associated with the global unsteadiness of the separation bubble/conical shock system. Analysis of the two-point correlations and wavenumber/frequency spectra of wall pressure fluctuations further suggests that the typical eddies become more elongated along the spanwise direction, as the flow in the separated region tends to escape the centreline, and the convection velocity is significantly reduced.

Estimation of wavenumber–frequency spectra of wall pressure due to turbulent flow over a flat plate using large-eddy simulation

The wavenumber–frequency spectra (WFS) of turbulent wall pressure fluctuations are used to design underwater acoustic systems, and a method is presented to determine them for flat plate flow using large-eddy simulations (LES). First, the Reynolds averaged Navier–Stokes (RANS) analysis is carried out for flow over the plate using k–ω shear-stress transport model. Flow parameters are extracted from the output of this analysis and used to impose boundary conditions for large-eddy simulations using a smaller domain with finer mesh. Mesh convergence studies are done to establish the adequacy of the proposed meshing scheme for estimating the turbulent boundary layer wall pressures. The stream-wise velocity profiles, turbulence intensities, and power spectra obtained using LES are compared with other computational and experimental results. The time history of fluctuating pressure on the wall at various stream-wise locations is used to estimate the WFS. Estimations are made of the convective ridge as well as sub-convective and low wavenumber portions of the spectrum. The computations are performed at momentum thickness-based Reynolds numbers (Rθ) of 5761, 7988, and 7709. The effect of downstream distance on the WFS is studied by computing it at three downstream locations and shown that the downstream distance has little effect on the WFS once the flow has become fully turbulent. The use of a desktop workstation for the estimation of WFS has not been reported earlier. The results show that the WFS of turbulent pressure due to flow over more complex geometries can be estimated using a similar method.

Effects of magnetic geometry on dynamics of current-convective turbulence in tokamak divertor plasma

The current-convective instability is one of the physical mechanisms that can drive fluctuating transport of plasma in the tokamak divertor. The impact of the tokamak magnetic geometry on spatial and temporal properties of saturated turbulence, driven by the instability, is investigated. The analysis is performed by employing the basic model of the instability [A. A. Stepanenko and S. I. Krasheninnikov, Phys. Plasmas 25, 012305 (2018)] extended to include contributions from the interchange drive. Turbulence simulations are carried out in BOUT++ under DIII-D-like conditions. The dependencies of amplitudes, spatial and frequency spectra of saturated plasma fluctuations on the curvature radius, and connection and shear lengths of magnetic field lines are found. It is demonstrated that taking the finite curvature of the magnetic field into account leads to a large increase in the turbulence amplitude, whereas the shear and connection lengths mainly affect the temporal dynamics of fluctuations and their spatial localization. In all cases shown, the turbulence frequency and wave-number spectra demonstrate better agreement with the experimentally observed ones, compared to the results of previous simulations based on the basic model of the current-convective instability.

Parabolic resolvent modes for streaky structures in transitional and turbulent boundary layers

Resolvent analysis is a powerful tool in fluid mechanics, both for laminar and turbulent flows. Depending on application, computational cost is still a limiting factor. We develop a parabolic method for the calculation of low-frequency resolvent modes, associated with streaky structures, which can enable more than an order of magnitude speed up compared to usual global calculations. The method is applied to both laminar and turbulent boundary layers, unveiling physical mechanisms such as those associated with streak growth due to free-stream turbulence, in the laminar case, and the double peak in the frequency spectrum of velocity fluctuations, in a turbulent boundary layer.

Influence of swirling flow parameters on frequency response of a simplified draft-tube in presence of cavitation

This paper focuses on investigating the influence of swirling flow parameters on frequency response of a simplified draft-tube under different cavitation numbers by using experimental approaches. The experiments are conducted for three swirl configurations featuring different swirl intensities conforming with the flow field in the draft-tube during high-load operation of a hydro-turbine. For this purpose, three stationary-blades swirl generators are used to generate axisymmetric swirling flows in a Venturi-tube with a diffuser resembling the draft-tube cone of a hydraulic turbine; and for each swirl configuration, the experiments are conducted over a wide range of cavitation numbers and flowrate values. Experiments include transient pressure measurements at different locations and high-speed visualization of cavitating flow in the Venturi. The results of transient pressure measurements are analyzed to identify the frequency spectrum of pressure fluctuations in the draft-tube. The first natural frequency of the draft-tube is identified for a wide range of operating conditions; and several correlations are established for its relationship with the flow parameters (cavitation number and swirl number). It is observed that the operating flowrate does not affect the natural frequency of the draft-tube. An unstable mode of cavitating flow is highlighted and a transition from stable to unstable modes is identified. Investigating the transition mechanism from the stable to the unstable modes of cavity led to identifying an excitation force for the onset of cavitation instability in the draft-tube. High-speed visualization of cavitation in the draft-tube is performed to capture the mean cavity volume and its fluctuations in time domain. The 1st natural frequency of the draft-tube is further predicted by analyzing the fluctuations of cavity volume. Furthermore, a 1D hydroacoustic model is also used to predict the local wave speed and the 1st natural frequency of the draft-tube. The obtained values of natural frequency from cavity visualization and 1D modelling are compared with the results of pressure measurements at the end.

Boundary-Layer Instabilities over a Cone–Cylinder–Flare Model at Mach 6

Computations are performed to investigate the convective and global boundary-layer instabilities over a sharp cone–cylinder–flare model at zero-degree angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University. The geometry consists of a nominally sharp 5 deg half-angle cone, followed by a cylindrical segment, and then a 10 deg flare. Additionally, flare half angles equal to 8 and 12 deg and nosetip radii equal to 0.1, 1, and 5 mm are studied. An axisymmetric separation bubble is generated as a result of the laminar shock–boundary-layer interaction in the cylinder–flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundary-layer edge and the reattachment shock. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations and the harmonic linearized Navier–Stokes equations. The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves capture the distinct lobes within the disturbance amplification spectra measured with PCB® and Kulite sensors. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 deg.

On the wavenumber–frequency spectrum of the wall pressure fluctuations in turbulent channel flow

Direct numerical simulations (DNS) of turbulent channel flows up to${Re}_{\tau} \approx 1000$are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber–frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber–frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

A study on the solar coronal dynamics during the post-maxima phase of the solar cycle 24 using S-band radio signals from the Indian Mars Orbiter Mission

ABSTRACT Radio signals from India’s Mars Orbiter Mission (MOM) have been used to study turbulence in the solar plasma during the post-maximum phase of solar cycle 24. S-band (2.29 GHz) radio carrier downlink signals from MOM were received at the Indian Deep Space Network, Bangalore, and frequency residuals were spectrally analysed to obtain coronal turbulence spectra at heliocentric distances ranging between 4 and 20 R⊙, corresponding to coronal regions where the solar wind is primarily accelerated. The frequency fluctuation spectrum relates to the turbulence regime in the near-Sun region. The turbulence power spectrum (the temporal spectrum of frequency fluctuations) at smaller heliocentric distances (<10 R⊙) reveals flattening in lower-frequency regions, with a spectral index αf ∼ 0.3−0.5, which corresponds to the solar wind acceleration region. For larger heliocentric distances (>10 R⊙), the curve steepens with a spectral index αf ∼ 0.7−0.8, a value close to 2/3 and indicative of a developed Kolmogorov-type turbulence spectrum. The findings are consistent with earlier results. Plausible explanations to support the theory of coronal heating by magnetohydrodynamic waves and the acceleration of the solar wind are presented. An insight into the feeble maximum of solar cycle 24 is discussed.

Effects of confinement on absolute and convective instabilities for momentum-driven countercurrent shear layers

We present results from the first experimental realization of a two-dimensional confined countercurrent shear layer driven by momentum flows, without the use of suction. Distinct peaks are observed in the frequency spectrum of velocity fluctuations, suggesting the presence of global instabilities. The variation of these frequencies with injected mass flow rate is predicted reasonably well by a spatiotemporal linear stability analysis of local velocity profiles, which checks for the presence of absolute instability, and suggests that confinement destabilizes the shear layer over a broad range of ratio of shear layer thickness to channel width.

New, improved analysis of correlation ECE data to accurately determine turbulent electron temperature spectra and magnitudes (invited).

Turbulent electron temperature fluctuation measurement using a correlation electron cyclotron emission (CECE) radiometer has become an important diagnostic for studying energy transport in fusion plasmas, and its use is widespread in tokamaks (DIII-D, ASDEX Upgrade, Alcator C-Mod, Tore Supra, EAST, TCV, HL-2A, etc.). The CECE diagnostic typically performs correlation analysis between two closely spaced (within the turbulent correlation length) ECE channels that are dominated by uncorrelated thermal noise emission. This allows electron temperature fluctuations embedded in the thermal noise to be revealed and fluctuation level and spectra determined. We have demonstrated a new, improved CECE coherency-based analysis for calculating the temperature fluctuation frequency spectrum and level, which has been verified both numerically through the simulation of synthetic ECE radiometer data and through analysis of experimental data from the CECE system on DIII-D. The new formulation places coherency-based analysis on a firm foundational footing and corrects some currently published methodologies. This new method accurately accounts for bias error in the coherence function and correctly calculates noise levels for a fixed data record length. It provides excellent accuracy in determining temperature fluctuation level (e.g., <10% error) even for a small realization number in the ensemble average. The method also has a smaller uncertainty (i.e., error bar) in the power spectrum when compared to the more standard cross-power method when evaluated at low coherency. Direct calculation of system noise level using correlation between randomized intermediate frequency signals is recommended.

Numerical Investigation of the Transient Flow and Frequency Characteristic in a Centrifugal Pump with Splitter Blades

To analyze the internal flow characteristics of each subchannel in a low-specific-speed centrifugal pump with splitter blades, the time histories and frequency spectra of pressure fluctuations and the distributions of the corresponding flow states in one impeller channel were investigated through the numerical analysis. Performance experiments and particle image velocimetry (PIV) tests were carried out to verify the results of the numerical calculations. The results suggested that the simulation analysis agreed well with the test results. The time histories and frequency spectra of pressure fluctuations depending on its location (close to or away from the volute tongue) present different changes. The predominant frequency of each monitor point equals to five or ten times shaft frequency. The jet-wake flow pattern at each subchannel separated by splitter blade in one impeller channel is not circumferentially uniform. For the channel away from volute tongue, the magnitude of turbulence kinetic energy in pressure side subchannel is well larger than that in suction side subchannel. With the increase in flow rate, the region close to the elbow of the volute outlet emerges a large-scale vortex.

Study on the Influence of Compressibility on Pressure Fluctuation Characteristics of Pump Turbine

In order to study the characteristics of pressure distribution and the influence of compressibility factors on pressure fluctuation of pump turbine under the condition of turbine. Based on RNG k-ԑ model, aiming at a pump turbine model, this paper uses UG NX10.0 software to build a three-dimensional model, and uses ICEM-CFD software to devide the mesh. Using ANSYS-CFX software, the unsteady simulation calculation of the whole flow passage under the opening of 10 mm movable guide vane is carried out, and the frequency spectrum of pressure fluctuation is obtained by using the fast Fourier transform. After analysis, the dynamic and static interference between the movable guide vane and the runner, as well as between the runner and the draft tube, has an impact on the pressure fluctuation in the front of the runner behind the guide vane and in the draft tube. There is a secondary peak at 9fn. Considering the compressibility, the amplitude of the fluctuation decreases, but the flow is more complex and the pressure fluctuation is more chaotic.

Origins of the suppression of fibril formation in grafted methylcellulose solutions

We utilize coarse-grained molecular-dynamics simulations to probe the influence of grafting on the conformation and aggregation of methylcellulose chains in water, inspired by the recent experiments on solutions of methylcellulose (MC) chains grafted with polyethylene glycol (PEG) that showed inhibition of methylcellulose fibril formation at high PEG-grafting densities [S. Morozova et al., Macromolecules (Washington, DC, U. S.) 51, 9413 (2018)]. These simulations reveal three features of the grafted system that should frustrate fibril assembly. First, multichain simulations indicate that the distance between the centers of mass of the chains increases at high grafting densities, suggesting that the ability to form collapsed structures is disrupted. Second, single-chain simulations using grafted MC show that the formation of the precursor toroidal structure responsible for fibril formation is hampered at high grafting densities. Third, the frequency spectrum of conformational fluctuations indicates that low-frequency modes dominate at higher grafting densities, suggesting a larger decorrelation time in conformational fluctuations. Together, these results provide a macromolecular basis for the suppression in fibril formation in grafted methylcellulose solutions for grafting densities exceeding approximately 10%.

Quantitative comparisons of electron-scale turbulence measurements in NSTX via synthetic diagnostics for high-k scattering

Two synthetic diagnostics are implemented for the high-k scattering system in NSTX (Smith et al 2008 Rev. Sci. Instrum. 79 123501) allowing direct comparisons between the synthetic and experimentally detected frequency and wavenumber spectra of electron-scale turbulence fluctuations. Synthetic diagnostics are formulated in real-space and in wavenumber space, and are deployed in realistic electron-scale simulations carried out with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545). A highly unstable electron temperature gradient (ETG) mode regime in a modest-β NSTX NBI-heated H-mode discharge is chosen for the analysis. Mapping the measured wavenumbers to field aligned coordinates shows that the high-k system is sensitive to fluctuations that are closer to the spectral peak in the density fluctuation wavenumber spectrum (streamers) than originally predicted. The analyses of synthetic spectra show that the frequency response of the detected fluctuations is dominated by Doppler shift and is insensitive to the turbulence drive. The shape of the high-k density fluctuation wavenumber spectrum is sensitive to the ETG turbulence drive conditions, and can be reproduced in a sensitivity scan of the most pertinent turbulent drive terms in the simulation.

Frequency Spectrum of Chemical Fluctuation: A Probe of Reaction Mechanism and Dynamics

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

Frequency spectrum of chemical fluctuation: Aprobe of reaction mechanism and dynamics.

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

Aeroacoustic simulation of the high-lift airfoil using hybrid reynolds averaged Navier-Stokes/high-order implicit large eddy simulation method

A hybrid RANS/HILES method (HRILES) is developed by combining the RANS-SST model and high order implicit large eddy simulation method (HILES) and employed with the Ffowcs Williams-Hawkings (FW-H) equation to predict the slat noise of 30P30N high-lift airfoil. Comparison has been made between the HRILES method and the traditional DDES based on the full-turbulence model SST by simulating the single cylinder case with &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$Re_{{d}}=4.3\times10^4$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20190777_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20190777_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. The HRILES method is able to predict the transition phenomenon and the small-scale separation bubble in the sub-critical wake region while the DDES can't and get a better mean wall pressure distribution than DDES. The amplitude and frequency spectrum of the far-field sound pressure level are in good agreement with the experimental data. In the simulation of 30P30N high-lift airfoil, the famous IDDES model is also used for comparison, both results are compared with experimental measurements. The computational mesh is provided by Japan Aerospace Exploration Agency (JAXA) in the Workshop on Benchmark problems for Airframe Noise Computations (BANC). The HRILES method obtains quantitative agreement with experimental data in terms of mean wall pressure coefficient, frequency spectrum of pressure fluctuations on the slat surface, and the mean flow statistics in the slat cusp shear layer. The IDDES model slightly underestimate the suction effect on the upper surface of the slat, and delays the instabilities in the slat cusp shear layer. The near-field noise spectra are compared with measurements obtained in JAXA low-speed Wind Tunnel. Narrow band peaks present are well recovered by both methods, while IDDES model overestimate the broadband noise. Far-field noise directivity results of every components, filtered in the band [256Hz–10KHz], are compared with each other, and the slat cove is confirmed to dominate the sound noise levels. The slat and flap noises show a typical dipole distribution, while the main wing noise's directivity is not apparent. Computational results show that the HRILES method, as one kind of generalized Hybrid RANS/LES method, HRILES can smoothly switch between the SST model and the HILES method. HRILES has the high-resolution simulation capability of the HILES in the LES region, and can reduce the requirements of the HILES method on the near-wall grid distribution by using the SST model in the inner boundary layer. As a result, the HRILES method has advantages in simulations at high reynolds numbers and aeroacoustic problems. Further research will be carried out in the applications at higher reynolds number flows with complex geometry in the future.

Advances in turbulence measurements using new Correlation ECE and nT-phase diagnostics at ASDEX Upgrade

Guided by predictions from nonlinear gyrokinetic simulations, two new turbulence diagnostics were designed and installed at ASDEX Upgrade (AUG) to probe the fundamentals of ion-scale turbulent electron heat transport. The first, a 30-channel correlation ECE (CECE) radiometer (105-128 GHz, 2nd harmonic X-mode), introduces a novel channel comb arrangement. This allows measurements of high radial resolution profiles (0:5 &lt; r/a &lt; 0:8) of low-k (k⍬⍴s &lt; 0:3) temperature fluctuation amplitudes, frequency spectra and radial correlation length profiles in unprecedented detail. The second diagnostic is formed by the addition of two W-band and one V-band X-mode reflectometers on the same line of sight as the CECE to enable measurements of the phase angle between turbulent density and temperature fluctuations. Historically, the radial alignment between reflectometer and radiometer has been a challenge due to the requirement that alignment is achieved within a radial correlation length (&lt; 5 10 mm). This challenge is significantly alleviated by using the CECE channel comb arrangement and the maximal coherence between reflectometer and radiometer can be unambiguously captured. Measurements of these quantities have been made in an AUG L-mode plasma, at the same radial location and have provided simultaneous quantitative constraints on realistic gyrokinetic simulations [Physics of Plasmas 25, 055903 (2018)] using the gyrokinetic code GENE. Here we present diagnostic detail for this study.

Effect of the Magnetopause and Bow Shock on Characteristics of Plasma Turbulence in the Earth’s Magnetosheath

The magnetosheath is a natural laboratory for the study of plasma turbulence. The magnetopause and the bow shock prevent freely development of turbulence and modify turbulent cascade. In this paper, the effect of the magnetosheath boundaries on the forms of frequency spectra of ion flux fluctuations is analyzed based on statistics. In addition, variance in the spectrum characteristics are considered, such as spectral slope at the magnetohydrodynamic (MHD) and kinetic scales, as well as the frequency of transition between these scales when the satellite crosses the magnetosheath. The analysis is based on measurement of the ion flux by the Fast Solar Wind Monitor (BMSW) onboard the Spektr-R satellite with a time resolution of 31 ms. It is shown that the probability of observing spectra of the particular type greatly varies upon crossing of the magnetosheath: standard spectra with two slopes and a distinct breakpoint are observed in most cases in all parts of the magnetosheath, and the probability of their observation is slightly higher upon the approach to the magnetopause; spectra with a peak in the region of transition between the scales (MHD and kinetic) are more often observed closer to the bow shock, and spectra with a plateau in the region of transition between the scales are usually observed closer to the magnetopause. It is revealed that the spectra at the MHD scales immediately behind the bow shock are described by a power function with index –1.3 on average, which noticeably differs from the index of –5/3 predicted by the classical theories. The spectra at the kinetic scales immediately behind the shock wave become steeper than in the solar wind and slightly flatten on the approach to the magnetopause.