Spontaneous imbalance in the non-hydrostatic Boussinesq equations

2018 ◽  
Vol 847 ◽  
pp. 614-643 ◽  
Author(s):  
Hossein A. Kafiabad ◽  
Peter Bartello
Keyword(s):  
Energy Spectrum ◽  
Total Energy ◽  
Time Evolution ◽  
Time Scales ◽  
Frequency Analysis ◽  
High Frequency ◽  
Large Scale ◽  
Boussinesq Equations ◽  
High Frequencies ◽  
High Frequency Waves

Whereas high-frequency waves are valid solutions to the Boussinesq equations in certain limits, their amplitudes are generally observed to be small in large-scale atmospheric and oceanic data. Traditionally, this has led to the development of balance models, reducing the dynamics to only the slow subset. Their solutions, however, can spontaneously generate imbalance in the context of the full equations. To quantify this, we calculate how much energy is transferred from the balanced to the unbalanced part of a turbulent rotating stratified flow that has been initialised to remove high frequencies. We lay out an approach to derive the time evolution of the balanced modes in which their interactions with unbalanced modes are taken into account. This enables us to calculate the budget of balanced (and unbalanced) energy. Our results show that imbalance generation occurs at scales where the Froude and Rossby numbers are still small and the energy spectrum is steep. We find that the scale at which maximum imbalance is generated depends on the peak of the energy spectrum and is invariant to the strength of rotation over the range examined. The unbalanced energy, after being transferred from the balanced component of the flow at larger scales, is cascaded forward and forms a shallow energy spectrum. The steep balanced subrange of the energy spectrum and the shallow subrange cross and form a kink in the total energy spectrum consistent with observed atmospheric and oceanic data. A frequency analysis at different wavenumbers shows that the separation of time scales breaks down at wavenumbers larger than those of maximum imbalance generation, but smaller than the kink of the energy spectrum. Below these scales, there is a single turbulent distribution of frequencies.

Transient Vibrations of Two-Dimensional Beam Frames at Mid- and High-Frequencies

2019 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Frequency Analysis ◽  
High Frequency ◽  
Transfer Functions ◽  
Flexible Structures ◽  
Frame Structure ◽  
Inverse Laplace Transform ◽  
Two Dimensional ◽  
Beam Structure ◽  
Element Analysis ◽  
High Frequencies

Abstract Transient vibrations of flexible structures at mid- and high-frequencies have important applications in aerospace, civil, auto and ship engineering. In this paper, a new method is developed for the determination of the transient vibration solutions of two-dimensional beam frames in mid- and high-frequency regions. In the development, the governing equations of a beam frame structure are formulated by an augmented Distributed Transfer Function Method (DTFM), without the need for discretization and approximation. The augmented DTFM differs from the traditional DTFM in that it does not contain the singularities of subsystem transfer functions, which is crucially important in a mid- or high-frequency analysis. The proposed method delivers exact eigensolutions of a beam structure from low- to high-frequencies without numerical instability. With the platform provided by the augmented DTFM, the transient response of a beam structure can be conveniently estimated by either modal expansion or the residue formula for inverse Laplace transform. A highlight of the augmented DTFM lies in that detailed information at mid- and high-frequencies, such as local displacement, slope, bending moment and shear force at any point, can be obtained, which otherwise may be difficult with conventional methods for mid- and high-frequency analysis. The proposed method is illustrated on several examples and is computationally efficient and stable from low- to high-frequency regions. In the numerical simulation, the augmented DTFM is shown to produce more accurate results than traditional finite element analysis (FEA). The proposed method is extensible to three-dimensional beam structures.

Cable Fault Recognition Based on the Wavelet Energy Spectrum of Mode Components

2013 ◽  
Vol 427-429 ◽  
pp. 834-837
Author(s):  
Mei Wang ◽  
Jing Wu
Keyword(s):  
Energy Spectrum ◽  
High Frequency ◽  
Transient Current ◽  
Power Cable ◽  
Two Phase ◽  
High Frequencies ◽  
Wavelet Energy ◽  
Fault Recognition ◽  
Frequency Components ◽  
Independent Mode

When a fault appeared in a power cable transmission line, the transient current with high frequencies would be produced in the system. Three independent mode components could be obtained by applying the phase mode transformation to the transient current. For different types of the faults, the three independent mode components have different features. Based on wavelet energy spectrum of mode components, a method for cable fault recognition is developed in this paper. First, the fault current is decomposed by using Karenbaue transformation matrix. Then, wavelet transformation is uses to obtain the coefficients of the high frequency components which reflect the original signal high frequency energy. Finally, based on the wavelet energy spectrum method and the detailed coefficient manipulation, the equivalent norms of the mode components are obtained. Compared with the traditional fault recognition method, the new method depends less on zero mode component in two-phase short to ground state, and it can recognize the fault class in the cases of different fault positions, different fault path resistances and different inception angles.

scholarly journals LONG-PERIOD VARIABILITY OF LARGE-SCALE CIRCULATION SYSTEM AND MESOSCALE VORTICES AS SELF-ORGANIZATION PHENOMENON

2019 ◽  
Vol 47 (3) ◽  
pp. 206-219
Author(s):  
A. B. Fedotov
Keyword(s):  
Numerical Model ◽  
Total Energy ◽  
Time Scales ◽  
Temporal Variability ◽  
Large Scale ◽  
Center Of Mass ◽  
Self Organization ◽  
Circulation System ◽  
Large Scale Circulation ◽  
Long Period

Within the framework of the numerical model of a two-layer ocean with the depth of layers corresponding to the average ocean conditions, the evolution of large-scale circulation under the action of an external stationary vorticity flow under constant dissipation parameters is studied, the time scales of long-period oscillations of the energy of flows are analyzed. The temporal variability of the enstrophy spectrum of the system of flows is considered, the connection of oscillations of the total energy of large-scale circulation with oscillations of the position of the center of mass of the enstrophy spectrum of the system is revealed.

scholarly journals Tropical temperature variability and Kelvin wave activity in the UTLS from GPS RO measurements

2016 ◽  
Author(s):  
Barbara Scherllin-Pirscher ◽  
William J. Randel ◽  
Joowan Kim
Keyword(s):  
High Frequency ◽  
Large Scale ◽  
Wave Activity ◽  
Kelvin Waves ◽  
Temperature Variability ◽  
Kelvin Wave ◽  
Quasi Biennial Oscillation ◽  
Tropical Tropopause ◽  
Tropopause Region ◽  
High Frequency Waves

Abstract. Tropical temperature variability over 10–30 km and associated Kelvin wave activity is investigated using GPS radio occultation (RO) data from January 2002 to December 2014. RO data are a powerful tool to quantify tropical temperature oscillations with short vertical wavelengths due to their high vertical resolution and high accuracy and precision. Gridded temperatures from GPS RO show strongest variability in the tropical tropopause region (on average 3 K2). Large-scale zonal variability is dominated by transient high-frequency waves (2 K2) and about half of high-frequency variance is explained by eastward traveling Kelvin waves with periods of 7 to 30 days (1 K2). Quasi-stationary waves associated with the annual cycle and inter-annual variability contribute about a third (1 K2) to total resolved zonal variance. High-frequency waves, including Kelvin waves, are highly transient in time. Above 20 km, Kelvin waves are strongly modulated by the quasi-biennial oscillation (QBO) in stratospheric zonal winds, with enhanced wave activity during the westerly shear phase of the QBO. In the tropical tropopause region, however, peaks of Kelvin wave activity are irregularly distributed in time. Several peaks coincide with maxima of zonal variance in tropospheric deep convection, but other episodes are not evidently related. Further investigations of convective forcing and atmospheric background conditions are needed to better understand variability near the tropopause.

scholarly journals Diffusion of inertia-gravity waves by geostrophic turbulence

2019 ◽  
Vol 869 ◽  
Author(s):  
Hossein A. Kafiabad ◽  
Miles A. C. Savva ◽  
Jacques Vanneste
Keyword(s):  
Energy Spectrum ◽  
Gravity Waves ◽  
Wave Energy ◽  
Large Scale ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Constant Frequency ◽  
Geostrophic Turbulence ◽  
Wave Energy Spectrum ◽  
Inertia Gravity Waves

The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumber diffusion results in a $k^{-2}$ wave energy spectrum consistent with as-yet-unexplained features of observed atmospheric and oceanic spectra.

scholarly journals Optimize BJT for Small Dimensions and High-Frequency Analysis

10.29007/8jx4 ◽  
2018 ◽  
Author(s):  
Bhargavi Patel ◽  
Ketan Patel
Keyword(s):  
Frequency Analysis ◽  
High Frequency ◽  
High Frequencies ◽  
Bipolar Junction Transistor ◽  
As Doping ◽  
Parameter Variations ◽  
Junction Transistor

In this paper, we have designed Bipolar junction transistor (BJT) structure for small dimensions that are (given by SCL Chandigarh) and high-frequency analysis. The material used is pure Si material no compounds such as SiGe, SiC is used. This transistor is examined by various effect of parameter variations such as doping, height, length through simulations. In this paper, we have optimized the small BJT at higher beta (β) 96.50 dB, and high- frequencies ft 8.64 GHz and fmax 21.51 GHz using pure Si material.

A New Approach to Transient Vibration Analysis of Two-Dimensional Beam Structures at Medium and High Frequencies

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Bingen Yang ◽  
Yichi Zhang
Keyword(s):  
Frequency Analysis ◽  
High Frequency ◽  
Vibration Analysis ◽  
Local Information ◽  
Two Dimensional ◽  
Transient Vibration ◽  
Beam Structures ◽  
High Frequencies ◽  
Analysis Tools ◽  
Internal Forces

Abstract Transient analysis of medium-frequency (mid-frequency) and high-frequency vibrations plays an important role in the research and development of complex structures in aerospace, automobile, civil, mechanical, and ship engineering. Low-frequency analysis tools, like the finite element methods, do not work well for mid- and high-frequency problems because they require a huge number of degrees-of-freedom and consequently costly computation, and are sensitive to material properties and boundary conditions. High-frequency analysis tools, such as the statistical energy analysis (SEA) and its variations, are unsuitable for midfrequency problems because they describe the vibrational behaviors of multibody structures in a global manner and cannot provide detailed local information about displacements and internal forces. In this paper, a new method, which is called the augmented distributed transfer function method (DTFM), is proposed for transient vibration analysis of two-dimensional beam structures at medium and high frequencies. Without the need for discretization and numerical integration, the augmented DTFM consistently delivers analytical transient solutions from low to high-frequency regions. A unique feature of the proposed method is that it can provide local information about system response, such as the displacements and internal forces of a structure, at any point and in any frequency region. Additionally, the proposed method provides a platform for model reduction, by which, a balance of efficiency and accuracy in mid- and high-frequency analyses can be achieved. The proposed method is demonstrated in numerical examples.

scholarly journals Complexity Changes in the US and China’s Stock Markets: Differences, Causes, and Wider Social Implications

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 75
Author(s):  
Jianbo Gao ◽  
Yunfei Hou ◽  
Fangli Fan ◽  
Feiyan Liu
Keyword(s):  
Stock Market ◽  
Time Scales ◽  
Stock Markets ◽  
High Frequency ◽  
Large Scale ◽  
Low Frequency ◽  
Stock Index ◽  
Chinese Market ◽  
Index Data ◽  
The Us

How different are the emerging and the well-developed stock markets in terms of efficiency? To gain insights into this question, we compared an important emerging market, the Chinese stock market, and the largest and the most developed market, the US stock market. Specifically, we computed the Lempel–Ziv complexity (LZ) and the permutation entropy (PE) from two composite stock indices, the Shanghai stock exchange composite index (SSE) and the Dow Jones industrial average (DJIA), for both low-frequency (daily) and high-frequency (minute-to-minute)stock index data. We found that the US market is basically fully random and consistent with efficient market hypothesis (EMH), irrespective of whether low- or high-frequency stock index data are used. The Chinese market is also largely consistent with the EMH when low-frequency data are used. However, a completely different picture emerges when the high-frequency stock index data are used, irrespective of whether the LZ or PE is computed. In particular, the PE decreases substantially in two significant time windows, each encompassing a rapid market rise and then a few gigantic stock crashes. To gain further insights into the causes of the difference in the complexity changes in the two markets, we computed the Hurst parameter H from the high-frequency stock index data of the two markets and examined their temporal variations. We found that in stark contrast with the US market, whose H is always close to 1/2, which indicates fully random behavior, for the Chinese market, H deviates from 1/2 significantly for time scales up to about 10 min within a day, and varies systemically similar to the PE for time scales from about 10 min to a day. This opens the door for large-scale collective behavior to occur in the Chinese market, including herding behavior and large-scale manipulation as a result of inside information.

Response of the North Atlantic circulation to the small-scale surface wind perturbations

2020 ◽  
Author(s):  
Shenjie Zhou ◽  
Xiaoming Zhai ◽  
Ian Renfrew
Keyword(s):  
Ocean Circulation ◽  
High Frequency ◽  
General Circulation ◽  
Large Scale ◽  
Sea Surface ◽  
Small Scale ◽  
Local Response ◽  
High Frequencies ◽  
Wind Variability

<p>High-frequency and small-scale processes in the atmosphere have an important influence on the evolution of the underlying ocean. They can not only introduce variability to the coupled systems but also have long-term ramification effects on the sea surface temperature, thermocline structure and large-scale ocean general circulation via nonlinear interactions.</p><p>Comparisons between the newly-released ECMWF fifth-generation global climate reanalyses (ERA5) wind product and satellite/in-situ observations show that the latest reanalyses winds still considerably underestimate wind variability at high-frequencies and small-scales. A novel approach, Cellular Automata (CA), is used here to stochastically perturb the ERA5 wind field. CA, originally introduced into the weather forecast model to mimic the near-grid-scale variability associated with convective cloud clustering, generates spatially and temporally coherent perturbation patterns. Results show that the CA-perturbed ERA5 wind field enjoys an improved wavenumber spectrum, especially over high wavenumber bands (scales <400 km), when compared to the QuikSCAT measurements. In addition, including CA patterns also brings the level of wind variability at high-frequencies (>1 cpd) closer to in-situ mooring measurements. The local response of the upper ocean properties is investigated by a Multi-Column K-Profile Parameterization (MC_KPP) ocean mixed layer model over Atlantic section. It is found that overall the sea surface temperature (SST) decreases and oceanic boundary layer (OBL) deepens to respond to the enhanced surface turbulent heat loss and shear instability generated at the base of surface OBL caused by the small-scale wind perturbations. In particular, SST tends to decrease the most over the summer hemisphere by up to 1°C locally and 0.1°C averaging across the basin, in correlation with shallower background OBL and smaller OBL heat capacity. </p><p>The ocean states under the forcing of stochastic wind perturbation as expressed by the local response are found rectified by a non-negilible magnitude. We argued that although the missed small-scale and high-frequency wind variability may be represented differently than our approach, our results highlighted the fact that these variabilities should take a singificant part in driving the current generation of coupled climate model. Furhtermore, the temproal and spatial variabilities of the local signals can pose significant influence on the large-scale ocean circulation in terms of their pathways, strengths and variabilities. The dynamical response of the ocean circulation is to be further understood with an eddy-resolving Massachusette Institute of Technology General Circulation Model (MITgcm).</p>

scholarly journals Flatness-Based High Frequency Control of a Hydraulic Actuator

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Florian Kock ◽  
Cornelius Ferrari
Keyword(s):  
High Frequency ◽  
Control Algorithm ◽  
Large Scale ◽  
Feedforward Control ◽  
Frequency Control ◽  
Hydraulic Actuator ◽  
Free Piston ◽  
High Frequencies ◽  
Control Concept ◽  
Feedforward Controller

This paper presents the design and implementation of a nonlinear feedforward control algorithm for a hydraulic actuator driven by a multistage servo valve. Combined with a conventional feedback control algorithm, high frequencies can be achieved even for large-scale strokes. In addition to the desired trajectory, the feedforward controller accepts the predicted dynamic load on the hydraulic actuator as an input. The performance of the control concept as well as the advantages of the load input are verified in simulations and experiments. Being exemplarily used for realizing a crankshaft-less test stand for free piston engines, the control algorithm is potentially suitable for further applications using hydraulic actuators in high frequency domain.

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