Internal gravity waves generated by oscillations of a sphere

1987 ◽  
Vol 183 ◽  
pp. 439-450 ◽  
Author(s):  
J. C. Appleby ◽  
D. G. Crighton
Keyword(s):  
Gravity Waves ◽  
Separation Of Variables ◽  
Near Field ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Spherical Body ◽  
The Body ◽  
Wave Radiation ◽  
Far Field ◽  
Field Solution

We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.

scholarly journals Investigation on Wireless Link for Medical Telemetry Including Impedance Matching of Implanted Antennas

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1431
Author(s):  
Ilkyu Kim ◽  
Sun-Gyu Lee ◽  
Yong-Hyun Nam ◽  
Jeong-Hae Lee
Keyword(s):  
Real Time ◽  
Human Body ◽  
Near Field ◽  
Impedance Matching ◽  
The Body ◽  
Field Pattern ◽  
Communication Link ◽  
Far Field ◽  
Antenna Coupling ◽  
Medical Telemetry

The development of biomedical devices benefits patients by offering real-time healthcare. In particular, pacemakers have gained a great deal of attention because they offer opportunities for monitoring the patient’s vitals and biological statics in real time. One of the important factors in realizing real-time body-centric sensing is to establish a robust wireless communication link among the medical devices. In this paper, radio transmission and the optimal characteristics for impedance matching the medical telemetry of an implant are investigated. For radio transmission, an integral coupling formula based on 3D vector far-field patterns was firstly applied to compute the antenna coupling between two antennas placed inside and outside of the body. The formula provides the capability for computing the antenna coupling in the near-field and far-field region. In order to include the effects of human implantation, the far-field pattern was characterized taking into account a sphere enclosing an antenna made of human tissue. Furthermore, the characteristics of impedance matching inside the human body were studied by means of inherent wave impedances of electrical and magnetic dipoles. Here, we demonstrate that the implantation of a magnetic dipole is advantageous because it provides similar impedance characteristics to those of the human body.

Simultaneous Noise and Performance Measurements for High-Speed Jet Noise Reduction Technologies

2009 ◽  
Author(s):  
Dean Long ◽  
Steven Martens
Keyword(s):  
Noise Reduction ◽  
High Speed ◽  
Near Field ◽  
Jet Noise ◽  
Source Distribution ◽  
Test Facility ◽  
Wave Radiation ◽  
Far Field ◽  
Shock Cell ◽  
Field Noise

Model scale tests are conducted to assess the Noise/Performance trade for high speed jet noise reduction technologies. It is demonstrated that measuring the near field acoustic signature with a microphone array can be used to assess the far field noise using a procedure known as acoustic holography. The near field noise measurement is mathematically propagated producing an estimate of the noise level at the new location. Outward propagation produces an estimate of the far field noise. Propagation toward the jet axis produces the source distribution. Tests are conducted on convergent/divergent nozzles with three different area ratios, and several different chevron geometries. Noise is characterized by two independent processes: Shock cell noise radiating in the forward quadrant is produced when the nozzle is operated at non-ideally expanded conditions. Mach wave radiation propagates into the aft quadrant when the exhaust temperature is elevated. These results show good agreement with actual far field measurements from tests in the GE Cell 41 Acoustic Test Facility. Simultaneous performance measurement shows the change in thrust coefficient for different test conditions and configurations. Chevrons attached to the nozzle exit can reduce the noise by several dB at the expense of a minimal thrust loss.

Nonlinear internal gravity waves in a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 497-512 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Main Effect ◽  
Local Wave ◽  
The Mean ◽  
The Waves ◽  
Circulation Theorem

The interaction between internal gravity waves in a rotating frame and the mean flow is discussed for the case when the properties of the mean flow vary slowly on a scale determined by the local wave structure. The principle of conservation of wave action is established. It is shown that the main effect of the waves on the Lagrangian mean velocity is due to an appropriate ‘radiation stress’ tensor. A circulation theorem and a potential-vorticity equation are derived for the mean velocity.

Static-dynamic strain response to the 2016 M6.2 Hutubi earthquake (eastern Tien Shan, NW China) recorded in a borehole strainmeter network

2020 ◽  
Author(s):  
Zheng Gong ◽  
Yan Jing ◽  
Haibing Li
Keyword(s):  
Epicentral Distance ◽  
Near Field ◽  
Tien Shan ◽  
Dynamic Strain ◽  
Wave Radiation ◽  
Far Field ◽  
High Angle ◽  
Static Strain ◽  
Fault Parameters ◽  
Strain Responses

&lt;p&gt;Strain caused by earthquakes give rise to many earthquake-related hydrological changes. Mechanisms responsible for them are different from place to place, depending on whether the trigger is the static strain or dynamic strain. Theoretic calculation indicates that the great difference in dependence on epicentral distance is robust enough to discriminate them, however, few studies based on direct strain measurements have tested this hypothesis. The 2016 M6.2 Hutubi Earthquake is a reverse event occurred in the northern Chinese Tien Shan, and the coseismic strain responses have been recorded by nine 4-component RZB borehole strainmeters at the distance from near field to far field. The nearest four stations have recorded resolvable static strain responses, and all stations have perfectly recorded the dynamic strain waves. Our result shows that the difference in the dependence on distance is truly reliable to differentiate static strains from dynamic strains, the static strain is of the same magnitude with the dynamic strain in the near field, and as the distance increase to intermediate and far field, the static strain are a few magnitude smaller. Yet the ratio between them is a complex index relating to the rupturing process itself, the tectonic background, and the seismic wave radiation pattern. Furthermore, the calibrated static strain were also used to relocate the fault plane through a grid-search method, and the result shows that the seismogenic fault is surprisingly a high-angle backthrust fault. The determined fault parameters are 279&amp;#176;/70&amp;#176;/87&amp;#176;, which are also consistent with the aftershock distribution. It indicates that the high-angle backthrust in the Chinese Tien Shan are capable of breaking individually. Considering the high vertical displacement, and their abundance inside the Tien Shan orogenic belt, the high-angle backthrust faults may had also played a significant role in building the modern ultra-high relief in Tien Shan.&lt;/p&gt;

The radiation and scattering of surface waves by a vertical circular cylinder in a channel

1992 ◽  
Vol 338 (1650) ◽  
pp. 325-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Gravity Waves ◽  
The Body ◽  
Far Field ◽  
Algebraic Equations ◽  
Surface Gravity Waves ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Correct Form ◽  
Body Boundary

In this paper we consider the problems of the radiation and scattering of surface gravity waves by a vertical circular cylinder placed on the centreline of a channel of width 2 d and depth H , and either extending from the bottom through the free surface or truncated so as to fill only part of the depth. These problems are solved, for arbitrary incident wavenumber k , by constructing appropriate multipoles for cylinders placed symmetrically in channels and then using the body boundary condition to derive a set of infinite systems of linear algebraic equations. For the general problems considered here, this method is superior to the more usual approach of using a set of image cylinders to model the channel walls, in particular the occurrence of modes other than the fundamental when kd > is accurately modelled and the correct form predicted for the far-field.

Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

2015 ◽  
Vol 772 ◽  
pp. 80-106 ◽  
Author(s):  
Norihiko Sugimoto ◽  
K. Ishioka ◽  
H. Kobayashi ◽  
Y. Shimomura
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Water System ◽  
Local Maximum ◽  
Vortex Pair ◽  
Wave Radiation ◽  
Earth’S Rotation ◽  
Far Field ◽  
Earth's Rotation

Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$-plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$, there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$. Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$. To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

scholarly journals Internal Wave Radiation through Surface Mixed Layer Turbulence

2019 ◽  
Vol 49 (7) ◽  
pp. 1827-1844
Author(s):  
Lars Czeschel ◽  
Carsten Eden
Keyword(s):  
Internal Wave ◽  
Mixed Layer ◽  
Gravity Waves ◽  
Transition Layer ◽  
Wave Spectrum ◽  
Internal Gravity Waves ◽  
Heat Fluxes ◽  
Wave Radiation ◽  
Substantial Part ◽  
Surface Mixed Layer

AbstractIn a series of large-eddy simulations with different forcing, we study the generation of internal gravity waves at the base of the surface mixed layer. If turbulent eddies act as obstacles and undulate the base of the mixed layer, horizontal velocities associated with inertial oscillations and Ekman dynamics can move the obstacles relative to the stratified interior, exciting internal gravity waves similar to lee waves. We find strong evidence that the “obstacle mechanism” is able to excite large parts of the internal wave spectrum, including near inertial waves. The high-frequency part of the excited wave spectrum is filtered by the increased stratification in the transition layer between the mixed layer and lower stratified interior, but a substantial part of the wave spectrum is able to overcome this barrier, hence contributing to interior mixing. The magnitude of the downward-radiated energy below the transition layer depends on the source of turbulence, but we show that the obstacle mechanism, especially under destabilizing heat fluxes, has the potential to contribute considerably to the internal wave energy in the interior ocean.

Simultaneous Noise and Performance Measurements for High Speed Jet Noise Reduction Technologies: Part II—Near Field Array Calibration

2011 ◽  
Author(s):  
Dean Long ◽  
Steve Martens
Keyword(s):  
Noise Reduction ◽  
High Speed ◽  
Near Field ◽  
Jet Noise ◽  
Source Distribution ◽  
Wave Radiation ◽  
Far Field ◽  
Performance Measurements ◽  
Shock Cell ◽  
Field Noise

Part I of this paper describes a methodology for assessing the far field jet noise from high speed exhaust nozzles using a microphone array in the near field of the exhaust plume. The near field noise measurement is mathematically propagated producing an estimate of the noise level at the new location. Outward propagation produces an estimate of the far field noise. Propagation toward the jet axis produces the source distribution. Part II described here provides a direct validation of this process using a generic CD nozzle in a facility where both the near field and the far field are measured simultaneously. Comparison of these data sets show good agreement over the typical operating range for this type of nozzle. The far field noise is characterized by two independent processes: Shock cell noise radiating in the forward quadrant is produced when the nozzle is operated at non-ideally expanded conditions. Mach wave radiation propagates into the aft quadrant when the exhaust temperature is elevated. Subsequent tests in an acoustically treated nozzle thrust stand demonstrate the value of the near field array allowing immediate feedback on the noise/performance tradeoff for high speed jet noise reduction technologies.

scholarly journals Numerical modelling of tsunami wave run-up and breaking within a two-dimensional atmosphere–ocean two-layer model

2014 ◽  
Vol 2 (5) ◽  
pp. 3397-3421
Author(s):  
S. P. Kshevetskii ◽  
I. S. Vereshchagina
Keyword(s):  
Gravity Waves ◽  
Turbulent Mixing ◽  
Tsunami Wave ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Fluid Mixing ◽  
Stratified Medium ◽  
Layer Model ◽  
Two Layer Model ◽  
Run Up

Abstract. A numerical model of propagation of internal gravity waves in a stratified medium is applied to the problem of tsunami wave run-up onto a shore. In the model, the ocean and the atmosphere is considered as a united continuum whose the density varies with height with a saltus at a water–air boundary. Correct conditions of join at a water–air interlayer are automatically ensured because the solution is searched for as a generalised one. The density stratification in the ocean and in the atmosphere is supposed to be an exponential one, but in the ocean, a scale of stratification of density is large and the density varies slightly. The wave running to a shore is taken as a long solitary wave. The wave evolution is simulated with consideration of time-varying vertical wave structure. Inshore, the wave breaks down, and intensive turbulent mixing develops in water thickness. The effect of breakdown depends on shape of the bottom. If slope of the bottom is small, and inshore the depth grows slowly with distance from a shore, then mixing happens only in the upper stratum of the fluid, thanks to formation of a dead region near the bottom. If the bottom slope inshore is significant, then the depth of fluid mixing is dipped up to 50 metres. The developed model shows the depth of mixing effects strongly depends on shape of a bottom, and the model may be useful for investigation of influences of strong gales and hurricanes on coastline and beaches and investigation of dependence of stability of coastline and beaches on bottom shape.

Nonlinear internal gravity waves in a slowly varying medium

1972 ◽  
Vol 54 (2) ◽  
pp. 193-207 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Incompressible Fluid ◽  
Gravity Waves ◽  
Time Scale ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Transport Equations ◽  
Inviscid Incompressible Fluid ◽  
Local Wave ◽  
The Waves

Nonlinear internal gravity waves in an inviscid incompressible fluid are discussed for the case when the properties of the medium vary slowly on a scale determined by the local wave structure. A two-time-scale technique is used to obtain transport equations which describe the slowly varying modulations of the waves. Various solutions of these transport equations are discussed.

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