scholarly journals The route to dissipation in strongly stratified and rotating flows

2013 ◽  
Vol 720 ◽  
pp. 66-103 ◽  
Author(s):  
Enrico Deusebio ◽  
A. Vallgren ◽  
E. Lindborg
Keyword(s):  
Energy Transfer ◽  
Energy Flux ◽  
Rotation Rate ◽  
Energy Cascade ◽  
Small Scale ◽  
Linear Wave ◽  
Frequency Spectra ◽  
Large Rotation ◽  
Time Frequency ◽  
Triad Interactions

AbstractWe investigate the route to dissipation in strongly stratified and rotating systems through high-resolution numerical simulations of the Boussinesq equations (BQs) and the primitive equations (PEs) in a triply periodic domain forced at large scales. By applying geostrophic scaling to the BQs and using the same horizontal length scale in defining the Rossby and the Froude numbers, $\mathit{Ro}$ and $\mathit{Fr}$, we show that the PEs can be obtained from the BQs by taking the limit ${\mathit{Fr}}^{2} / {\mathit{Ro}}^{2} \rightarrow 0$. When ${\mathit{Fr}}^{2} / {\mathit{Ro}}^{2} $ is small the difference between the results from the BQ and the PE simulations is shown to be small. For large rotation rates, quasi-geostrophic dynamics are recovered with a forward enstrophy cascade and an inverse energy cascade. As the rotation rate is reduced, a fraction of the energy starts to cascade towards smaller scales, leading to a shallowing of the horizontal spectra from ${ k}_{h}^{- 3} $ to ${ k}_{h}^{- 5/ 3} $ at the small-scale end. The vertical spectra show a similar transition as the horizontal spectra and we find that Charney isotropy is approximately valid also at larger wavenumbers than the transition wavenumber. The high resolutions employed allow us to capture both ranges within the same simulation. At the transition scale, kinetic energy in the rotational and in the horizontally divergent modes attain comparable values. The divergent energy is several orders of magnitude larger than the quasi-geostrophic divergent energy given by the $\Omega $-equation. The amount of energy cascading downscale is mainly controlled by the rotation rate, with a weaker dependence on the stratification. A larger degree of stratification favours a downscale energy cascade. For intermediate degrees of rotation and stratification, a constant energy flux and a constant enstrophy flux coexist within the same range of scales. In this range, the enstrophy flux is a result of triad interactions involving three geostrophic modes, while the energy flux is a result of triad interactions involving at least one ageostrophic mode, with a dominant contribution from interactions involving two ageostrophic and one geostrophic mode. Dividing the ageostrophic motions into two classes depending on the sign of the linear wave frequency, we show that the energy transfer is for the largest part supported by interactions within the same class, ruling out the wave–wave–vortex resonant triad interaction as a mean of the downscale energy transfer. The role of inertia-gravity waves is studied through analyses of time-frequency spectra of single Fourier modes. At large scales, distinct peaks at frequencies predicted for linear waves are observed, whereas at small scales no clear wave activity is observed. Triad interactions show a behaviour which is consistent with turbulent dynamics, with a large exchange of energy in triads with one small and two large comparable wavenumbers. The exchange of energy is mainly between the modes with two comparable wavenumbers.

scholarly journals PIV Measurements in the Atmospheric Boundary Layer within and above a Mature Corn Canopy. Part I: Statistics and Energy Flux

2007 ◽  
Vol 64 (8) ◽  
pp. 2805-2824 ◽  
Author(s):  
R. van Hout ◽  
W. Zhu ◽  
L. Luznik ◽  
J. Katz ◽  
J. Kleissl ◽  
...  
Keyword(s):  
Time Series ◽  
Energy Flux ◽  
Striking Similarity ◽  
Small Scale ◽  
Mean Flow ◽  
Local Isotropy ◽  
Frequency Spectra ◽  
Piv Measurements ◽  
Kolmogorov Length Scale ◽  
Corn Canopy

Particle image velocimetry (PIV) measurements just within and above a mature corn canopy have been performed to clarify the small-scale spatial structure of the turbulence. The smallest resolved scales are about 15 times the Kolmogorov length scale (η ≈ 0.4 mm), the Taylor microscales are about 100η, and the Taylor scale Reynolds numbers range between Rλ = 2000 and 3000. The vertical profiles of mean flow and turbulence parameters match those found in previous studies. Frequency spectra, obtained using the data as time series, are combined with instantaneous spatial spectra to resolve more than five orders of magnitude of length scales. They display an inertial range spanning three decades. However, the small-scale turbulence in the dissipation range exhibits anisotropy at all measurement heights, in spite of apparent agreement with conditions for reaching local isotropy, following a high-Reynolds-number wind tunnel study. Directly calculated subgrid-scale (SGS) energy flux, determined by spatially filtering the PIV data, increases significantly with decreasing filter size, providing support for the existence of a spectral shortcut that bypasses the cascading process and injects energy directly into small scales. The highest measured SGS flux is about 40% of the estimated energy cascading rate as determined from a −5/3 fit to the spectra. Terms appearing in the turbulent kinetic energy budget that can be calculated from the PIV data are in agreement with previous results. Evidence of a very strong correlation between dissipation rate and out-of-plane component of the vorticity is demonstrated by a striking similarity between their time series.

Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation

2009 ◽  
Vol 619 ◽  
pp. 1-44 ◽  
Author(s):  
Z. XIAO ◽  
M. WAN ◽  
S. CHEN ◽  
G. L. EYINK
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Physical Mechanism ◽  
Energy Cascade ◽  
Small Scale ◽  
Local Energy ◽  
Two Dimensional ◽  
Turbulent Stress ◽  
Inverse Energy Cascade ◽  
The Mean

We report an investigation of inverse energy cascade in steady-state two-dimensional turbulence by direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation, with small-scale forcing and large-scale damping. We employed several types of damping and dissipation mechanisms in simulations up to 20482 resolution. For all these simulations we obtained a wavenumber range for which the mean spectral energy flux is a negative constant and the energy spectrum scales as k−5/3, consistent with the predictions of Kraichnan (Phys. Fluids, vol. 439, 1967, p. 1417). To gain further insight, we investigated the energy cascade in physical space, employing a local energy flux defined by smooth filtering. We found that the inverse energy cascade is scale local, but that the strongly local contribution vanishes identically, as argued by Kraichnan (J. Fluid Mech., vol. 47, 1971, p. 525). The mean flux across a length scale ℓ was shown to be due mainly to interactions with modes two to eight times smaller. A major part of our investigation was devoted to identifying the physical mechanism of the two-dimensional inverse energy cascade. One popular idea is that inverse energy cascade proceeds via merger of like-sign vortices. We made a quantitative study employing a precise topological criterion of merger events. Our statistical analysis showed that vortex mergers play a negligible direct role in producing mean inverse energy flux in our simulations. Instead, we obtained with the help of other works considerable evidence in favour of a ‘vortex thinning’ mechanism, according to which the large-scale strains do negative work against turbulent stress as they stretch out the isolines of small-scale vorticity. In particular, we studied a multi-scale gradient (MSG) expansion developed by Eyink (J. Fluid Mech., vol. 549, 2006a, p. 159) for the turbulent stress, whose contributions to inverse cascade can all be explained by ‘thinning’. The MSG expansion up to second order in space gradients was found to predict well the magnitude, spatial structure and scale distribution of the local energy flux. The majority of mean flux was found to be due to the relative rotation of strain matrices at different length scales, a first-order effect of ‘thinning’. The remainder arose from two second-order effects, differential strain rotation and vorticity gradient stretching. Our findings give strong support to vortex thinning as the fundamental mechanism of two-dimensional inverse energy cascade.

Small-scale structure and energy transfer in homogeneous turbulence

2018 ◽  
Vol 854 ◽  
pp. 505-543 ◽  
Author(s):  
Douglas W. Carter ◽  
Filippo Coletti
Keyword(s):  
Energy Transfer ◽  
Large Scale ◽  
Probability Distributions ◽  
Physical Space ◽  
Energy Cascade ◽  
Homogeneous Turbulence ◽  
Small Scale ◽  
Mean Flow ◽  
Number Range ◽  
Wide Range

We use high-resolution velocity measurements in a jet-stirred zero-mean-flow facility to investigate the topology and energy transfer properties of homogeneous turbulence over the Reynolds number range $Re_{\unicode[STIX]{x1D706}}\approx 300$–500. The probability distributions of the enstrophy and strain-rate fields show long tails associated with the most intense events, while the weaker events behave as random variables. The high-enstrophy and high-strain structures are shaped as tube-like and sheet-like objects, respectively, the latter often wrapped around the former. Both types of structures have thickness that scales in Kolmogorov units, and display self-similar topology over a wide range of scales. The small-scale turbulence activity is found to be strongly correlated with the large-scale activity, suggesting that the phenomenon of amplitude modulation (previously observed in advection-dominated shear flows) is not limited to specific production mechanisms. Observing the significant variations in spatially averaged enstrophy, we heuristically define hyperactive and sleeping states of the flow: these also correspond to, respectively, high and low levels of large-scale velocity gradients. Moreover, the hyperactive and sleeping states contribute very differently to the inter-scale energy flux, characterized via the nonlinear transfer term in the Kármán–Howarth–Monin equation. While the energy cascades to smaller scales along the jet-axis direction, a weaker but sizable inverse transfer is observed along the transverse direction; a behaviour so far only observed in spatially developing flows. The hyperactive states are characterized by very intense energy transfers, while the sleeping states account for weaker fluxes, largely directed from small to large scales. This implies that the form of energy cascade depends on the presence (or absence) of intense turbulent structures. These results are at odds with the classic concept of the energy cascade between adjacent scales, but are compatible with the view of a cascade in physical space.

scholarly journals Deep Learning Approach for Vibration Signals Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3929
Author(s):  
Han-Yun Chen ◽  
Ching-Hung Lee
Keyword(s):  
Surface Roughness ◽  
Tool Wear ◽  
Parameters Optimization ◽  
Frequency Spectra ◽  
Vibration Signals ◽  
Bearing Faults ◽  
Time Frequency ◽  
And Performance ◽  
The One ◽  
Short Time

This study discusses convolutional neural networks (CNNs) for vibration signals analysis, including applications in machining surface roughness estimation, bearing faults diagnosis, and tool wear detection. The one-dimensional CNNs (1DCNN) and two-dimensional CNNs (2DCNN) are applied for regression and classification applications using different types of inputs, e.g., raw signals, and time-frequency spectra images by short time Fourier transform. In the application of regression and the estimation of machining surface roughness, the 1DCNN is utilized and the corresponding CNN structure (hyper parameters) optimization is proposed by using uniform experimental design (UED), neural network, multiple regression, and particle swarm optimization. It demonstrates the effectiveness of the proposed approach to obtain a structure with better performance. In applications of classification, bearing faults and tool wear classification are carried out by vibration signals analysis and CNN. Finally, the experimental results are shown to demonstrate the effectiveness and performance of our approach.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

scholarly journals Modeling of Non-WSSUS Double-Rayleigh Fading Channels for Vehicular Communications

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Carlos A. Gutiérrez ◽  
J. J. Jaime-Rodríguez ◽  
J. M. Luna-Rivera ◽  
Daniel U. Campos-Delgado ◽  
Javier Vázquez Castillo
Keyword(s):  
Fading Channels ◽  
Communication Systems ◽  
Rayleigh Fading ◽  
Channel Model ◽  
Closed Form Solution ◽  
Multipath Fading ◽  
Rayleigh Distribution ◽  
Rayleigh Fading Channels ◽  
Small Scale ◽  
Time Frequency

This paper deals with the modeling of nonstationary time-frequency (TF) dispersive multipath fading channels for vehicle-to-vehicle (V2V) communication systems. As a main contribution, the paper presents a novel geometry-based statistical channel model that facilitates the analysis of the nonstationarities of V2V fading channels arising at a small-scale level due to the time-varying nature of the propagation delays. This new geometrical channel model has been formulated following the principles of plane wave propagation (PWP) and assuming that the transmitted signal reaches the receiver antenna through double interactions with multiple interfering objects (IOs) randomly located in the propagation area. As a consequence of such interactions, the first-order statistics of the channel model’s envelope are shown to follow a worse-than-Rayleigh distribution; specifically, they follow a double-Rayleigh distribution. General expressions are derived for the envelope and phase distributions, four-dimensional (4D) TF correlation function (TF-CF), and TF-dependent delay and Doppler profiles of the proposed channel model. Such expressions are valid regardless of the underlying geometry of the propagation area. Furthermore, a closed-form solution of the 4D TF-CF is presented for the particular case of the geometrical two-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of small-scale nonstationary V2V double-Rayleigh fading channels.

Novel Method for Detecting Weak AE Signals Based on the Similarity of Time-Frequency Spectra

Geophysics ◽  
2021 ◽  
pp. 1-62
Author(s):  
Wencheng Yang ◽  
Xiao Li ◽  
Yibo Wang ◽  
Yue Zheng ◽  
Peng Guo
Keyword(s):  
Mathematical Morphology ◽  
Signal To Noise Ratio ◽  
Critical Role ◽  
Real Data ◽  
Monitoring Method ◽  
Frequency Spectra ◽  
Arrival Times ◽  
Time Frequency ◽  
Fracturing Process ◽  
Ae Signals

As a key monitoring method, the acoustic emission (AE) technique has played a critical role in characterizing the fracturing process of laboratory rock mechanics experiments. However, this method is limited by low signal-to-noise ratio (SNR) because of a large amount of noise in the measurement and environment and inaccurate AE location. Furthermore, it is difficult to distinguish two or more hits because their arrival times are very close when AE signals are mixed with the strong background noise. Thus, we propose a new method for detecting weak AE signals using the mathematical morphology character correlation of the time-frequency spectrum. The character in all hits of an AE event can be extracted from time-frequency spectra based on the theory of mathematical morphology. Through synthetic and real data experiments, we determined that this method accurately identifies weak AE signals. Compared with conventional methods, the proposed approach can detect AE signals with a lower SNR.

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