Growth Rate Of Surface Waves Research Articles

A description on plasma background effect in growth rate of THz waves in a metallic cylindrical waveguide, including a dielectric tube and two current sources

The propagation of slow waves in a dielectric tube surrounded by a long cylindrical metallic waveguide is investigated. The dielectric tube located in a background region of plasma under two different states A and B. In the A-state the dielectric tube hollow filled with the plasma and in the B-state the outer surface of dielectric tube has been covered by the plasma layer. There are two relativistic electron beams with opposite velocities injected in the waveguide as the energy sources. Using the fluid theory for the plasmas, the Cherenkov instability in the mentioned waveguide will be analyzed. The dispersion relations of E-mode waves for the states A, B have been obtained. The time growth rate of surface waves are compared with each other for two cases A and B. The effect of plasma region on time growth rate of the waves, will be investigated. In all cases it will be shown, while an electron beam is responsible for instability, another electron beam plays a stabilizing role.

Ion-driven instabilities of surface dust ion-acoustic waves in bounded plasma devices

The growth rates of the dust ion-acoustic surface wave in the plasma slab device containing ion streaming passing through the stationary electrons and dusty grains at the speed of wave phase velocity are derived and numerically analyzed. We have found that the growth rates for the resonant symmetric and antisymmetric waves are similar to the case of semi-bounded plasma when we have a thick slab. However, in the case of the symmetric wave, the growth rate moves towards the bulk wave as the slab thickness reduces. In the case of the antisymmetric wave, the growth rate increases fast as the slab thickness decreases. The growth rates of surface waves in a plasma slab are compared with those of semi-bounded and bulk waves.

Quasi-linear approximation for description of turbulent boundary layer and wind wave growth

This study describes an approximate quasi-linear model for the description of the turbulent boundary layer over steep surface waves. The model assumes that wave-induced disturbances of the atmospheric turbulent boundary layer could be reasonably described in a linear approximation with the momentum flux from wind to waves retained as the only nonlinear effect in the model. For the case of periodic long-crested waves, the model has been verified with a set of the original laboratory and numerical experiments. The laboratory experimental study of the airflow over the steep waves was performed by means of the PIV technique. The numerical study was performed with direct numerical simulation (DNS) of the turbulent airflow over waved surface at Re=15,000 for quasi-homogeneous waves, wave trains and parasitic capillaries riding on the crest of a steep waves. Examples are given of the application of the quasi-linear approximation to describe the turbulent boundary layer over waves with the continuous spectrum under the assumption of random phases of harmonics. In the latter case the quasi-linear model provides the growth rate of surface waves in the inertial interval of the surface wave spectrum proportional to w7/3 in agreement with predictions in [1].

Temporal characteristics of electrostatic surface waves in a cold complex plasma containing collision-dominated ion flow

The influence of electron-ion collision frequency and dust charge on the growth rate of two-stream instability of the electrostatic surface wave propagating at the interface of semi-infinite complex plasma whose constituents are electrons, negatively charged dust, and streaming ions. It is found that the surface wave can be unstable if the multiplication of wave number and ion flow velocity is greater than the total plasma frequency of electrons and dusts. The analytical solution of the growth rate is derived as a function of collision frequency, dust charge, and ion-to-electron density ratio. It is found that the growth rate is inversely proportional to the collision rate, but it is enhanced as the number of electrons residing on the dust grain surface is increased. The growth rate of surface wave is compared to that of the bulk wave.

Ion streaming instability of dust-acoustic surface waves in a semi-infinite Lorentzian complex plasma

The growth rate of the dust-acoustic surface wave in the semi-infinite complex plasma with an ion streaming passing through the plasma at rest is analytically derived. We have adopted the Lorentzian distribution for electrons to investigate the nonthermal property of a plasma on the growth rate. We find that the growth rate of the surface wave increases as the wave number increases, and it is always larger than that of the bulk wave, especially in the realm of large wave numbers. The nonthermal effect of Lorentzian electrons in the high-energy tail is found to enhance the growth rate. It is also found that the density and speed of streaming ion would increase the growth rate. The growth rate of the surface wave is compared to that of the bulk wave for various physical parameters.

Wind-wave amplification mechanisms: possible models for steep wave events in finite depth

Abstract. We extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth h are obtained.

Theoretical Analysis of Surface Waves on Liquid Jets in Crossflows with Deformation

Liquid jets in cross air flows are widely used and play an important role in propulsion systems, such as ramjet combustors. Surface waves on the liquid jets in gaseous crossflows have been observed in numerous experiments. Especially for lower gas Webber number, liquid jets breaks up due to the surface waves. However compared with injecting into gas coaxial flow, liquid jet will be deformed in crossflow due to the transverse aerodynamic force. Deformation of jet is investigated by analyzing stress force equilibrium of the cross-section. Though linear instability analysis, dispersion relation and growth rate of surface waves of liquid jet with deformation were derived. According to the present theoretical analysis, the cross-section shape can be deformed to stable ellipse only if the gas velocity was lower than 9m/s for 1mm diameter jet. The maximum growth rate of disturbances takes place at wave number 0.7 approximately, and it will decrease with increasing the jet diameter. The range of instable wave number will expand and the most instable wave number will grow for the deformed jets.

Quasi-linear model of interaction of surface waves with strong and hurricane winds

A quasi-linear model for determining the aerodynamic drag coefficient of the sea surface and the growth rate of surface waves under a hurricane wind is proposed. The model explains the reduction (stabilization) in the drag coefficient during hurricane winds. This model is based on the solution of the Reynolds equations in curvilinear coordinates with the use of the approximation of the eddy viscosity, which takes into account the presence of the viscous sublayer. The profile of the mean wind velocity is found with consideration for nonlinear wave stresses (wave momentum flux), whereas wave disturbances induced in air by waves on the water surface are determined in the context of linear equations. The model is verified by comparing the calculation results with experimental data for a wide range of wind velocities. The growth rate and drag coefficient for hurricane winds are calculated both with and without consideration for the shortwave portion of the windwave spectrum. On the basis of calculations with the quasi-linear model, a simple parametrization is proposed for the drag coefficient and the growth rate of surface waves during hurricane winds. This model is convenient for use in models of forecasting winds and waves.

Momentum flux budget analysis of wind‐driven air‐water interfaces

Accurate knowledge of the air‐sea momentum flux plays a critical role in ocean‐atmosphere modeling. In this study we investigate the momentum flux budget at an air‐water interface in the presence of wind‐driven gravity‐capillary waves. At the air‐sea interface the total momentum flux (wind stress) partitions into viscous and wave‐induced stress; the latter transfers momentum into surface waves. We estimate the wave growth rate (momentum transfer rate into waves) to close the momentum flux budget, using previous laboratory measurements of total and viscous stress, as well as surface wave spectra. The wave‐induced stress is computed via a parameterized wave growth rate, which is proportional to the turbulent stress divided by the wave‐phase speed squared. The constant of proportionality is then determined under two different assumptions. The first assumption (nonsheltering assumption) is that the turbulent stress is equal to the total wind stress. In the second assumption (sheltering assumption) the wave growth rate is determined by the local turbulent stress, which is a reduced turbulent stress due to the presence of longer waves. Both assumptions yield simple closed form expressions for the stress‐partitioning ratio (ratio between the total stress and the viscous stress). With the sheltering assumption the growth rate agrees with previous theoretical and empirical estimates. Without sheltering, the growth rate is significantly lower than previous estimates. Therefore our results indicate that the growth rate of surface waves is determined by the local, reduced turbulent stress rather than the total wind stress.