Nonlinear Effects in Resonantly Driven Surface Waves on Fluids

1972 ◽  
Vol 50 (19) ◽  
pp. 2235-2243
Author(s):  
F. L. Curzon ◽  
G. N. Ionides
Keyword(s):  
Surface Waves ◽  
Electric Fields ◽  
Driving Force ◽  
Wave Amplitude ◽  
Nonlinear Effects ◽  
Microwave Resonator ◽  
Electrode Geometry ◽  
Fluid Surface ◽  
Electric Stress ◽  
Time Periodic

The results presented in this paper show that fluid surface waves, resonantly driven by spatially nonuniform, time periodic electric fields, exhibit nonlinear effects when the wave amplitude ξ exceeds a significant fraction of the distance D between the driver electrode and the fluid surface. The phase difference between the surface wave and the driving force, as well as the dependence of wave amplitude on the electric stress are computed and compared with experimental results. For ξ/D exceeding ~0.7 (dependent on electrode geometry) the surface waves excited are unstable (also confirmed experimentally). The experiments are performed on surface waves on mercury contained in a cylindrical microwave resonator. Shifts in the microwave resonant frequency (caused by the surface waves) monitor the displacement of the fluid surface.

Investigation of Hydrodynamic Surface Waves with a Cylindrical Microwave Resonator. IV. Application of a Strong Electrostatic Field

1971 ◽  
Vol 49 (4) ◽  
pp. 458-466 ◽  
Author(s):  
F. L. Curzon ◽  
G. N. Ionides
Keyword(s):  
Electric Field ◽  
Surface Waves ◽  
Electrostatic Field ◽  
Oscillation Frequency ◽  
Wave Amplitude ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Microwave Resonator ◽  
Uniform Field ◽  
Static Electric Field

The reduction of the oscillation frequency of surface waves caused by a static electric field normal to the surface has been investigated with a microwave resonator. The stationary deformation of the surface caused by the spatially non-uniform field has been used to verify that the detectable wave amplitude is of the order of 5 × 10−3 cm, which is much smaller than other scale lengths (> 1 cm) of the system. The results can therefore justifiably be compared with the predictions of the linearized equations of motion. The experimental results agree well with the theory, which takes into account the spatial non-uniformity of the electrostatic field.

An investigation of hydrodynamic surface waves with a cylindrical microwave resonator. I. Theory of method

1968 ◽  
Vol 46 (18) ◽  
pp. 2001-2007 ◽  
Author(s):  
F. L. Curzon ◽  
R. L. Pike
Keyword(s):  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Surface Mode ◽  
Microwave Resonator ◽  
Cylindrical Resonator ◽  
Resonant Frequencies ◽  
Fluid Surface

In the first of this series of papers, we show that shifts in the resonant frequencies of a microwave resonator produced by boundary distortions can be used to study surface waves on conducting fluids.Surface waves can easily be studied under conditions where linearity requirements are satisfied. In addition, it is shown that a resonator of rectangular cross section acts as an analogue Fourier analyzer, so that a surface mode of a particular geometry can be observed, even when several modes are present simultaneously on the fluid surface. General results for a cylindrical resonator are first derived for TE and TM electromagnetic modes, and detailed calculations are then presented for resonators of rectangular and circular cross sections, since these are the most important practical examples.

scholarly journals Extremal periodic wave profiles

2007 ◽  
Vol 7 (1) ◽  
pp. 33-40 ◽  
Author(s):  
E. van Groesen ◽  
Keyword(s):  
Surface Waves ◽  
Periodic Wave ◽  
Feasible Region ◽  
Cnoidal Wave ◽  
Fluid Surface ◽  
Energy Integrals ◽  
Wave Profiles ◽  
Energy Plane ◽  
Crest Height

Abstract. As a contribution to deterministic investigations into extreme fluid surface waves, in this paper wave profiles of prescribed period that have maximal crest height will be investigated. As constraints the values of the momentum and energy integrals are used in a simplified description with the KdV model. The result is that at the boundary of the feasible region in the momentum-energy plane, the only possible profiles are the well known cnoidal wave profiles. Inside the feasible region the extremal profiles of maximal crest height are "cornered" cnoidal profiles: cnoidal profiles of larger period, cut-off and periodically continued with the prescribed period so that at the maximal crest height a corner results.

Particle Compaction with Alternating Electric Fields: The Effects of Electrode Geometry

1986 ◽  
Vol 73 ◽  
Author(s):  
Alan J. Hurd
Keyword(s):  
Electric Fields ◽  
Colloidal Particles ◽  
Dielectric Material ◽  
Double Layers ◽  
Electrode Geometry ◽  
Dipole Interactions ◽  
Alternating Electric Fields ◽  
Alternating Electric Field ◽  
Dc Bias ◽  
Induced Dipoles

ABSTRACTA technique for inducing ordered, close-packed arrangements of various symmetries among colloidal particles is discussed. An external alternating electric field applied to the colloid induces dipole interactions of variable strength by polarizing either the dielectric material of the particles or their electrostatic double layers. Ordering in various symmetries can be obtained by switching the field rapidly between pairs of electrodes, thereby changing the orientation of the induced dipoles. A small dc bias serves to deposit and compact the aligned particles.

Technique for Reducing the Effects of Nonlinear Terms on Electric Field Measurements of Electric Field Sensor Arrays on Aircraft Platforms

2015 ◽  
Vol 32 (5) ◽  
pp. 993-1003 ◽  
Author(s):  
D. M. Mach
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Electric Fields ◽  
Sensor Arrays ◽  
Field Measurements ◽  
Nonlinear Effects ◽  
Electric Field Sensor ◽  
Cloud Properties ◽  
Field Sensor ◽  
Nonlinear Components

AbstractA generalized technique has been developed that reduces the contributions of nonlinear effects that occur during measurements of natural electric fields around thunderstorms by an array of field mills on an aircraft. The nonlinear effects can be due to nearby charge emitted by the aircraft as it acquires and sheds charge, but the nonlinear effects are not limited to such sources. The generalized technique uses the multiple independent measurements of the external electric field obtained during flight to determine and remove nonlinear contaminations in the external vector electric field. To demonstrate the technique, a simulated case with nonlinear contaminations was created and then corrected for the nonlinear components. In addition, data from two different field programs utilizing two different aircraft and field mill configurations, each containing observable and different nonlinear effects, were also corrected for the significant nonlinear effects found in the field mill outputs. The expanded independent measurements in this new technique allow for the determination and correction of components in the field mill outputs from almost any measurable source. Alternate utilization of the technique can include removing effects in the aircraft charging such as aircraft altitude, cloud properties, engine power settings, or aircraft flap deployment. This technique provides a way to make more precise measurements of the true external electric field for scientific studies of cloud electrification.

scholarly journals Nonperturbative Kinetic Description of Electron-Hole Excitations in Graphene in a Time Dependent Electric Field of Arbitrary Polarization

Particles ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 208-230 ◽  
Author(s):  
Stanislav A. Smolyansky ◽  
Anatolii D. Panferov ◽  
David B. Blaschke ◽  
Narine T. Gevorgyan
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Kinetic Equations ◽  
Nonlinear Effects ◽  
Two Dimensions ◽  
Time Dependent ◽  
Polarization Current ◽  
Kinetic Description ◽  
Orthogonal Direction ◽  
Electron Hole

On the basis of the well-known kinetic description of e − e + vacuum pair creation in strong electromagnetic fields in D = 3 + 1 QED we construct a nonperturbative kinetic approach to electron-hole excitations in graphene under the action of strong, time-dependent electric fields. We start from the simplest model of low-energy excitations around the Dirac points in the Brillouin zone. The corresponding kinetic equations are analyzed by nonperturbative analytical and numerical methods that allow to avoid difficulties characteristic for the perturbation theory. We consider different models for external fields acting in both, one and two dimensions. In the latter case we discuss the nonlinear interaction of the orthogonal currents in graphene which plays the role of an active nonlinear medium. In particular, this allows to govern the current in one direction by means of the electric field acting in the orthogonal direction. Investigating the polarization current we detected the existence of high frequency damped oscillations in a constant external electric field. When the electric field is abruptly turned off residual inertial oscillations of the polarization current are obtained. Further nonlinear effects are discussed.

On the sound field generated by membrane surface waves on a wedge-shaped boundary

1987 ◽  
Vol 411 (1840) ◽  
pp. 239-250 ◽  
Keyword(s):  
Exact Solution ◽  
Surface Wave ◽  
Surface Waves ◽  
Wave Amplitude ◽  
Membrane Surface ◽  
Sound Field ◽  
Acute Angle ◽  
Rigid Surface ◽  
Arbitrary Angle ◽  
Method Of Solution

A semi-infinite membrane, joined to a rigid surface at an arbitrary angle, supports incident unattenuated surface waves. A compressible fluid is contained within the two semi-infinite boundaries and the resultant reflected surface-wave amplitude and the scattered acoustic field is sought. A method of solution is presented for wedge angles(2 p + 1) π/2 q , p and q integers, and the exact solution is obtained for an acute angle of ¼π.

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