Equatorial Zonal Jet Formation through the Barotropic Instability of Low-Frequency Mixed Rossby–Gravity Waves, Equilibration by Inertial Instability, and Transition to Superrotation

2009 ◽  
Vol 66 (9) ◽  
pp. 2600-2619 ◽  
Author(s):  
Mark D. Fruman ◽  
Bach Lien Hua ◽  
Richard Schopp
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Horizontal Velocity ◽  
Barotropic Instability ◽  
Velocity Amplitude ◽  
Zonal Scale ◽  
Zonal Jets ◽  
Initial Wave ◽  
Inertial Instability ◽  
Long Time

Abstract Depth-dependent barotropic instability of short mixed Rossby–gravity (MRG) waves is proposed as a mechanism for the formation of equatorial zonal jets. High-resolution primitive equation simulations show that a single MRG wave of very short zonal wavelength and small to moderate amplitude is unstable and leads to the development of a largely barotropic, zonally symmetric flow, featuring a westward jet at the equator and extra-equatorial jets alternating in direction with latitude. At higher but still moderate amplitude, westward flow still prevails at the equator at depths of maximum horizontal velocity amplitude in the initial wave, but the long-term equilibrated state can also feature eastward “superrotating” jets at the equator near the depths of zero horizontal velocity in the initial wave. The formation of the superrotating jets in the simulations is found to be sensitive to the inclusion of the nontraditional Coriolis force in the equations of motion. A linear theory is used to demonstrate the existence of exponentially growing horizontally nondivergent perturbations with a dominant zonally symmetric zonal velocity component. An argument for the sense and positioning of the jets relative to the equator is given in terms of inertial instability and the meridional mixing of planetary vorticity by the small zonal-scale components of the linearly unstable modes. In the long time evolution of the flow, if the amplitude of the westward equatorial jet becomes too great, zonally symmetric inertial instability limits the growth of the jets, and inertial adjustment leads to the homogenization of potential vorticity in latitude and depth around the equator.

Transient Wave Propagation in a Symmetrically Layered Elastic Plate

1974 ◽  
Vol 41 (3) ◽  
pp. 684-690 ◽  
Author(s):  
D. C. Viano ◽  
J. Miklowitz
Keyword(s):  
Near Field ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Short Wave ◽  
Frequency Equation ◽  
Layered Plate ◽  
Transient Wave ◽  
Long Time ◽  
Transient Wave Propagation ◽  
Front Running

The response of a symmetrically layered plate subjected to symmetric step normal line face loads is determined. The solution, which is based on the equations of motion from linear elasticity, is obtained in the form of an infinite series of integrals with each term being the contribution from a branch of the underlying frequency equation. Through numerical analysis several of the lower branches of the frequency equation, which depend on layered plate ratios (four material and one thickness) are evaluated and used to write the transient response in the near field. Integrations based on the first five branches show the dominance of the lowest mode in the solution. Applying arguments of stationary phase to the spectrum, yields low frequency-long wave and high frequency-short wave approximations for use in obtaining the far field-long time disturbance. The former governs a front running “head of the pulse” for the layered plate, and the latter, later arriving Rayleigh and Stoneley waves.

scholarly journals Electromagnetic power of lightning superbolts from Earth to space

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
J.-F. Ripoll ◽  
T. Farges ◽  
D. M. Malaspina ◽  
G. S. Cunningham ◽  
E. H. Lay ◽  
...  
Keyword(s):  
Low Frequency ◽  
Optical Emission ◽  
High Energy ◽  
Very Low Frequency ◽  
Electromagnetic Power ◽  
Power Spectral ◽  
High Energy Tail ◽  
Van Allen Probes ◽  
Long Time ◽  
Low Frequency Waves

AbstractLightning superbolts are the most powerful and rare lightning events with intense optical emission, first identified from space. Superbolt events occurred in 2010-2018 could be localized by extracting the high energy tail of the lightning stroke signals measured by the very low frequency ground stations of the World-Wide Lightning Location Network. Here, we report electromagnetic observations of superbolts from space using Van Allen Probes satellite measurements, and ground measurements, and with two events measured both from ground and space. From burst-triggered measurements, we compute electric and magnetic power spectral density for very low frequency waves driven by superbolts, both on Earth and transmitted into space, demonstrating that superbolts transmit 10-1000 times more powerful very low frequency waves into space than typical strokes and revealing that their extreme nature is observed in space. We find several properties of superbolts that notably differ from most lightning flashes; a more symmetric first ground-wave peak due to a longer rise time, larger peak current, weaker decay of electromagnetic power density in space with distance, and a power mostly confined in the very low frequency range. Their signal is absent in space during day times and is received with a long-time delay on the Van Allen Probes. These results have implications for our understanding of lightning and superbolts, for ionosphere-magnetosphere wave transmission, wave propagation in space, and remote sensing of extreme events.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

2016 ◽  
Vol 32 (3) ◽  
pp. 297-311
Author(s):  
T.-Y. Zhao ◽  
H.-Q. Yuan ◽  
B.-B. Li ◽  
Z.-J. Li ◽  
L.-M. Liu
Keyword(s):  
Thermal Shock ◽  
High Frequency ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Cantilever Plate ◽  
Analysis Method ◽  
Multiple Frequency ◽  
Width Direction ◽  
Blade Tip ◽  
High Frequency Vibrations

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Multirate Integration for Multibody Dynamic Analysis With Decomposed Subsystems

1999 ◽  
Author(s):  
Sung-Soo Kim ◽  
Jeffrey S. Freeman
Keyword(s):  
Dynamic Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Inertia Force ◽  
Integration Scheme ◽  
Integration Algorithm ◽  
Multibody Dynamic ◽  
Higher Order Derivative ◽  
Derivative Information

Abstract This paper details a constant stepsize, multirate integration scheme which has been proposed for multibody dynamic analysis. An Adams-Bashforth Moulton integration algorithm has been implemented, using the Nordsieck form to store internal integrator information, for multirate integration. A multibody system has been decomposed into several subsystems, treating inertia coupling effects of subsystem equations of motion as the inertia forces. To each subsystem, different rate Nordsieck form of Adams integrator has been applied to solve subsystem equations of motion. Higher order derivative information from the integrator provides approximation of inertia force computation in the decomposed subsystem equations of motion. To show the effectiveness of the scheme, simulations of a vehicle multibody system that consists of high frequency suspension motion and low frequency chassis motion have been carried out with different tire excitation forces. Efficiency of the proposed scheme has been also investigated.

Interaction of Point Defects in Ice

1978 ◽  
Vol 21 (85) ◽  
pp. 115-122
Author(s):  
J. H. Bilgram ◽  
H. Gränicher
Keyword(s):  
Experimental Data ◽  
Dielectric Properties ◽  
Temperature Dependence ◽  
Point Defects ◽  
Low Frequency ◽  
Defect Concentration ◽  
Dielectric Measurements ◽  
Long Time ◽  
Nmr Techniques ◽  
Bjerrum Defect

AbstractThe interaction of point detects in ice has been neglected for a long time. Experimental data obtained from dielectric measurements on HF-doped crystals stimulated a new evaluation of the possibility of an interaction between Bjerrum defects and ions. In a previous paper it has been shown that this leads us to assume the existence of aggregates of Bjerrum defects and ions. In this paper these aggregates and Bjerrum defects are used to explain the dielectric properties of ice, especially the temperature dependence of the product of the high and low frequency conductivity σ0σ∞.The interaction of Bjerrum defects and impurity molecules leads to a dependence of the concentration of frenkel pairs on Bjerrum-defect concentration. At HF concentrations above the native Bjerrum-defect concentration the formation of a Frenkel pair is enhanced. This leads to the fast out-diffusion which has been studied in highly doped crystals by means of NMR techniques.

Prognostic relevance of anamnestic and diagnostic parameters in low-frequency hearing impairment

2006 ◽  
Vol 120 (8) ◽  
pp. 613-618 ◽  
Author(s):  
W Maier ◽  
J Schipper
Keyword(s):  
Prognostic Factor ◽  
Hearing Impairment ◽  
Hearing Threshold ◽  
Low Frequency ◽  
Prognostic Indicators ◽  
Infusion Therapy ◽  
Prognostic Relevance ◽  
Long Time ◽  
Dehydration Therapy

Low-frequency hearing impairment (LFHI) is mainly attributed to endolymphatic hydrops and has a great variety of possible outcomes. At present, no conservative therapeutic regimen has proven to be ‘gold-standard’, and information about the prognostic indicators of LFHI is scarce.In a retrospective investigation, we evaluated the records of 90 patients who had been treated with infusions improving blood perfusion. In patients lacking complete remission, dehydration infusion therapy was added. We also undertook audiometric follow up. We calculated the outcomes after infusion therapy, dehydration therapy and after long-time hearing follow up, and we determined the prognostic relevance of several parameters of anamnesis and clinical examination to outcomes, for both therapeutic interventions and long-time hearing.The prognosis of LFHI was significantly correlated to certain anamnestic and clinical parameters; a short duration of the disease, lack of vertigo and female gender implied a better outcome. The pretherapeutic hearing threshold was an important prognostic factor; the outcome was significantly worse in patients with distinct hearing impairment in low or high frequencies, compared with that in patients with little hearing loss. Whereas vertigo was a negative prognostic factor, the results of quantitative vestibular testing were irrelevant to the outcome. The glycerol test failed to predict the effectiveness of dehydration therapy and lacked any value in predicting prognosis.These results allow the clinician to focus the anamnesis and diagnostic examination on prognostically relevant parameters, thus enabling a better estimation of the long-term disease course and improved counselling of patients. Furthermore, these results help to distinguish valuable from irrelevant diagnostic procedures.

scholarly journals CONSTRUCTING HYPERBOLIC SYSTEMS IN THE ASHTEKAR FORMULATION OF GENERAL RELATIVITY

2000 ◽  
Vol 09 (01) ◽  
pp. 13-34 ◽  
Author(s):  
GEN YONEDA ◽  
HISA-AKI SHINKAI
Keyword(s):  
General Relativity ◽  
Hyperbolic System ◽  
Hyperbolic Systems ◽  
Equations Of Motion ◽  
Well Posedness ◽  
Symmetric Hyperbolic System ◽  
The Cauchy Problem ◽  
Long Time ◽  
Vacuum Spacetime ◽  
Gauge Conditions

Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We, here, present three kinds of hyperbolic systems in the Ashtekar formulation of general relativity for Lorentzian vacuum spacetime. We exhibit several (I) weakly hyperbolic, (II) diagonalizable hyperbolic, and (III) symmetric hyperbolic systems, with each their eigenvalues. We demonstrate that Ashtekar's original equations form a weakly hyperbolic system. We discuss how gauge conditions and reality conditions are constrained during each step toward constructing a symmetric hyperbolic system.

scholarly journals Low-frequency unsteadiness in the wake of a normal flat plate

1998 ◽  
Vol 370 ◽  
pp. 101-147 ◽  
Author(s):  
F. M. NAJJAR ◽  
S. BALACHANDAR
Keyword(s):  
Shear Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Low Frequency ◽  
Separated Flow ◽  
Phase Mismatch ◽  
Streamwise Vortices ◽  
Long Time ◽  
Drag And Lift ◽  
High Degree

The separated flow past a zero-thickness flat plate held normal to a free stream at Re=250 has been investigated through numerical experiments. The long-time signatures of the drag and lift coefficients clearly capture a low-frequency unsteadiness with a period of approximately 10 times the primary shedding period. The amplitude and frequency of drag and lift variations during the shedding process are strongly modulated by the low frequency. A physical interpretation of the low-frequency behaviour is that the flow gradually varies between two different regimes: a regime H of high mean drag and a regime L of low mean drag. It is observed that in regime H the shear layer rolls up closer to the plate to form coherent spanwise vortices, while in regime L the shear layer extends farther downstream and the rolled-up Kármán vortices are less coherent. In the high-drag regime three-dimensionality is characterized by coherent Kármán vortices and reasonably well-organized streamwise vortices connecting the Kármán vortices. With a non-dimensional spanwise wavelength of about 1.2, the three-dimensionality in this regime is reminiscent of mode-B three-dimensionality. It is observed that the high degree of spanwise coherence that exists in regime H breaks down in regime L. Based on detailed numerical flow visualization we conjecture that the formation of streamwise and spanwise vortices is not in perfect synchronization and that the low-frequency unsteadiness is the result of this imbalance (or phase mismatch).

Use of seismoscope records to determine ML and peak velocities

1984 ◽  
Vol 74 (1) ◽  
pp. 315-324
Author(s):  
David M. Boore
Keyword(s):  
Lower Bound ◽  
San Francisco ◽  
Peak Velocity ◽  
Response Spectrum ◽  
Single Point ◽  
Empirical Relation ◽  
Low Frequency ◽  
Simulation Method ◽  
Horizontal Velocity ◽  
Earthquake Moment

Abstract More information about ground motion can be extracted from seismoscope records than a single point on a response spectrum. To demonstrate this, the relation between seismoscope response and Wood-Anderson instrument output and peak horizontal ground velocity has been studied by simulating the various responses for a range of distances and magnitudes. The simulations show that the relation used by Jennings and Kanamori (1979) to convert from peak seismoscope readings to the peak response of a Wood-Anderson instrument has a distance- and magnitude-dependent systematic error. The error is negligible, however, for modern seismoscopes at distances of a few tens of kilometers. At several hundred kilometers, the relation underestimates the Wood-Anderson response by as much as a factor of two. The spread in Jennings and Kanamori's estimate of ML for the 1906 San Francisco earthquake, recorded on seismoscopes having relatively low natural frequencies (0.26 and 0.5 Hz), is reduced by the results in this paper—the upper value, from a seismoscope in Carson City, Nevada, at 290 km from the fault, going from ML = 7.2 to ML = 7.0 and the lower value, from Yountville, California (R ≈ 60 km), going from about 6.3 to 6.4. About 0.3 units of the remaining spread may be due to local geologic site conditions. If the 0.3 units is distributed equally between the Yountville and Carson City recordings, the estimates of ML for the San Francisco earthquake then become 6.5 and 6.8, somewhat lower than Jennings and Kanamori's final estimates of 634 to 7. Although the error in using the relation of Jennings and Kanamori to estimate Wood-Anderson response was at most a factor of 1.6 for the 1906 earthquake, the error can be substantially larger for smaller earthquakes recorded on similar low frequency seismoscopes. The relation between Wood-Anderson and seismoscope response used by Jennings and Kanamori can be combined with an empirical relation between peak horizontal velocity and Wood-Anderson response to predict peak velocity from seismocope recordings. The simulations show that this relation (vmax = 8.1Awa, where vmax is the peak horizontal velocity in centimeters/second and Awa is one-half the range of the Wood-Anderson motion in meters) forms a lower bound for estimates of peak velocity from seismoscope recordings. The relation is good for stations within about 100 km of earthquakes with moment magnitudes of about 4.5 to 6.5, and it underestimates peak velocity by factors up to 2 or 3 for larger earthquakes at distances within 100 km. An application of the simulation method to the 1976 Guatemala earthquake (moment magnitude = 7.6) results in 37 cm/sec as a lower bound to vmax, with 66 cm/sec as a more likely value, from the seismocope recording in Guatemala City (approximately 25 km from the Motagua fault).

Sign in / Sign up

Export Citation Format

Share Document