Phase Speed Changes Research Articles

Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model.

An equivalent circuit model has been developed to model a one-dimensional waveguide with many side-branch Helmholtz resonators. This waveguide constitutes a phononic crystal that has been shown to have decreased phase speed below the resonance frequency of an individual resonator. This decreased phase speed can be exploited to achieve super-resolution using broadband time reversal focusing techniques. It is shown that the equivalent circuit model is capable of quantifying this change in phase speed of the crystal and also the small-scale wave-resonator interactions within the crystal. The equivalent circuit model enables the parameterization of the physical variables and the optimization of the focusing bandwidth by balancing the combination of increasing resolution and decreasing amplitude near the resonance frequency. It is shown that the quality factor-in this case, the quality factor determined by the geometric shape of each resonator-controls the range of frequencies that are strongly affected by the Helmholtz resonators.

Wind-induced changes to surface gravity wave shape in deep to intermediate water

Abstract

Experimental study on surface wave modifications by different ice covers

A laboratory experimental study conducted in a freshwater wave flume installed in a refrigerated room characterized the modifications of wave propagation along on-site manufactured ice covers. Monochromatic surface waves of various amplitudes and frequencies were generated and propagated through three types of ice covers: sheet ice, broken ice floes, and grease ice. This study characterized the spatial evolutions of wave height attenuation and phase speed changes. Wave phase speed increased significantly in sheet ice relative to open water values while no significant changes in phase speed were present with other ice covers. The modifications by sheet ice are consistent with thin plate model predictions based on the elasticity of ice, using measured mechanical properties of sheet ice. Attenuation was strongest for shorter waves in sheet ice followed by grease ice and ice floes. Attenuation under grease ice is shown to be related to the surface wave orbital velocity, similar to dissipation by bottom friction and swell dissipation. The attenuation coefficient of grease ice normalized by wavenumber is proportional to wave steepness with a coefficient varying with ice properties. This laboratory experimental study examined and characterized wave dispersion and attenuation under these different ice properties and wave characteristics, which could be useful in understanding and modeling wave-ice interaction processes in open waters.

On wave propagation in a rotating random micropolar generalized thermoelastic medium

This article examines the problem of wave propagation in a rotating random micropolar generalized thermoelastic medium. The entire frame of reference is assumed to be rotating with a uniform angular velocity where is a unit vector representing the direction of the axis of rotation. The smooth perturbation technique amenable to stochastic differential equations has been employed. The generalized dispersion equation has been derived and analyzed. The effects due to random variations of micropolar elastic and generalized thermal parameters have been observed. The effect of rotation on wave propagation is discussed. Change of phase speed occurs on account of random fluctuations of inhomogeneities of the medium. Attenuation coefficients for both random and nonrandom media have been computed both theoretically and numerically. Some illustrative graphs have been drawn to demonstrate the effects of rotation and generalized thermoelastic parameters on wave propagation in the micropolar medium.

Nonlinear Evolution Equations of Co-propagating Waves over Finite Depth Fluid

Using Zakharov integral equation approach, a pair of coupled non-linear evolution equations are derived for two co-propagating weakly nonlinear gravity wave packets over finite depth fluid. Equations obtained here are not valid for resonant or quasi-resonant three-wave interactions and also inapplicable for shallow water. The two evolution equations are then employed to perform modulational instability analysis of a pair of co-propagating uniform Stokes wavetrains. It is found that the relative change in phase speed of one uniform wavetrain increases with the increase in wave steepness of the other wavetrain, but it decreases with the increase in the depth of the medium. It is also observed that the growth rate of instability of one uniform wavetrain increases with the increase in wave steepness of the second wavetrain and also with the decrease in the depth of the medium.

Changes in the MJO under greenhouse gas-induced warming in CMIP5 models.

This study investigates changes to the Madden-Julian Oscillation (MJO) in response to greenhouse-gas induced warming during the 21st century. Changes in the MJO's amplitude, phase speed, and zonal scale are examined in five Coupled Model Intercomparison Project Phase 5 (CMIP5) models that demonstrate superior MJO characteristics. Under warming, the CMIP5 models exhibit a robust increase in the spectral power of planetary-scale, intraseasonal, eastward-propagating (MJO) precipitation anomalies (~10.9 %K-1). The amplification of MJO variability is accompanied by an increase of the spectral power of the corresponding westward traveling waves at a similar rate. This suggests that enhanced MJO variability in a warmer climate is likely caused by enhanced background tropical precipitation variability, not by changes in the MJO's stability. All models examined show an increase in the MJO's phase speed (1.8 - 4.5 %K-1) and a decrease in the MJO's zonal wavenumber (1.0 - 3.8 %K-1). Using a linear moisture mode framework, this study tests the theory-predicted phase speed changes against the simulated phase speed changes. It is found that the MJO's acceleration in a warmer climate is a result of enhanced horizontal moisture advection by the steepening of the mean meridional moisture gradient and the decrease in zonal wavenumber, which is partially offset by the lengthening of the convective moisture adjustment timescale and the increase in gross dry stability. While the ability of the linear moisture mode framework to explain MJO phase speed changes is model dependent, the theory can accurately predict the phase speed changes in the model ensemble.

On wave propagation in a random conducting magneto-non-simple thermo-viscoelastic medium

• The waves in a random magneto-non-simple thermo-visco-elastic medium is studied. • The couple dispersion equation for longitudinal and transverse waves is analyzed. • The effect of thermal field to attenuate longitudinal waves is discussed. • Effect of magnetic conductivity is studied both theoretically and numerically. • Effect of visco-elasticity is discussed both analytically and numerically. The paper examines the problem of wave propagation in a random conducting magneto- non-simple thermo-viscoelastic medium. The medium has been assumed to be weakly conducting and weakly thermal. The thermomechanical coupling parameter and the conductivity are random functions, proportional to ε, with non-zero mean values, ε measuring the smallness of the scale of random fluctuation of inhomogeneities of the medium. The smooth perturbation technique enunciated by Keller (1964) has been employed to analyze the appropriate dispersion equation in non-simple thermoelastic medium. The longitudinal and transverse waves were discussed by using a particular form of thermomechanical coupling parameter representing the corresponding auto-correlation function. The effect of magnetic conductivity has been investigated. The phenomena of attenuation of waves and change of phase speed were discussed numerically in details.

On waves in a random micropolar conducting magneto-thermo-viscoelastic medium

ABSTRACTEffects of random inhomogeneity on wave propagation in the interacting micropolar conducting magneto-generalized thermo-viscoelastic medium are studied. The couple stress theory relevant to micropolar solids is employed. The analysis is carried out under the smooth perturbation technique amenable to stochastic linear differential equations up to the second perturbation. The perturbing field has been assumed to be weakly conducting and weakly thermal. The generalized thermoelasticity has been used. Six different types of waves have been observed to propagate in the medium. The dispersion equations have been derived. Effects due to random variations of micropolar-elastic, conducting-electromagnetic and generalized thermo-visco-parameters have been computed. Effects of random heterogeneity of the conducting magnetic field are readily available up to first order perturbation. However effects of the generalized thermal field are discernible only in the domain of second order perturbation. Change of phase speed occurs on account of randomness. Attenuation coefficients for types of waves have been computed. A special type of generalized theromomechanical auto- and cross-correlation functions has been used to approximately measure effects of random variations of parameters. Uncoupled problem has been formulated for future investigations.

Characterization of Moist Processes Associated With Changes in the Propagation of the MJO With Increasing CO2.

The processes that lead to changes in the propagation and maintenance of the Madden‐Julian Oscillation (MJO) as a response to increasing CO2 are examined by analyzing moist static energy budget of the MJO in a series of NASA GISS model simulations. It is found changes in MJO propagation is dominated by several key processes. Horizontal moisture advection, a key process for MJO propagation, is found to enhance predominantly due to an increase in the mean horizontal moisture gradients. The terms that determine the strength of the advecting wind anomalies, the MJO horizontal scale and the dry static stability, are found to exhibit opposing trends that largely cancel out. Furthermore, reduced sensitivity of precipitation to changes in column moisture, i.e., a lengthening in the convective moisture adjustment time scale, also opposes enhanced propagation. The dispersion relationship of Adames and Kim, which accounts for all these processes, predicts an acceleration of the MJO at a rate of ∼3.5% K−1, which is consistent with the actual phase speed changes in the simulation. For the processes that contribute to MJO maintenance, it is found that damping by vertical MSE advection is reduced due to the increasing vertical moisture gradient. This weaker damping is nearly canceled by weaker maintenance by cloud‐radiative feedbacks, yielding the growth rate from the linear moisture mode theory nearly unchanged with the warming. Furthermore, the estimated growth rates are found to be a small, negative values, suggesting that the MJO in the simulation is a weakly damped mode.

On wave propagation in a random micropolar generalized thermoelastic medium

AbstractThis paper endeavours to study aspects of wave propagation in a random generalized-thermal micropolar elastic medium. The smooth perturbation technique conformable to stochastic differential equations has been employed. Six different types of waves propagate in the random medium. The dispersion equations have been derived. The effects due to random variations of micropolar elastic and generalized thermal parameters have been computed. Randomness causes change of phase speed and attenuation of waves. Attenuation coefficients for high frequency waves have been computed. Second moment properties have been briefly discussed with application to wave propagation in the random micropolar elastic medium. Integrals involving correlation functions have been transformed to radial forms. A special type of generalized thermo-mechanical auto-correlation functions has been used to approximately compute effects of random variations of parameters. Uncoupled problem has been briefly outlined.

On wave propagation in a random micropolar thermoelastic medium, second moments, and associated Green’s tensor

The couple stress theory developed by Eringen comprises granular materials as also composite fibrous materials. As such, micropolar materials present an inclusive model of composite materials. This article endeavors to study aspects of wave propagation in a random weakly thermal micropolar elastic medium. The smooth perturbation technique has been employed. The classical thermoelasticity has been used. Six different types of waves have been observed to propagate in the random interacting medium. Dispersion equations have been derived. The effects due to random variations of micropolar elastic and thermal parameters have been observed. Change of phase speed occurs on account of randomness. Attenuation coefficients for high-frequency waves have been computed. Second moment properties have been discussed with application to wave propagation in the random micropolar elastic medium. 36 + 1 components of the associated Green’s tensor have been computed. Integrals involving correlation functions have been transformed to radial forms. A special type of correlation function has been used to approximately measure effects of random variations of parameters.

Understanding Midlatitude Jet Variability and Change Using Rossby Wave Chromatography: Methodology

Abstract Rossby wave chromatography (RWC) is implemented in a linearized barotropic model as a tool to diagnose and understand the interaction between the midlatitude jet and the eddies. Given the background zonal-mean flow and the space–time structure of the baroclinic wave activity source, RWC calculates the space–time structure of the upper-tropospheric eddy momentum fluxes. Using the convergence of the vertical Eliassen–Palm (E–P) flux in the upper troposphere as the wave source, RWC reproduces the main features of a GCM’s mean state and response to external forcing. When coupled to the zonal-mean zonal wind and a simple model of wave activity source phase speed changes, RWC also simulates the temporal evolution of the GCM’s internally generated zonal-mean zonal wind anomalies. Because the full space–time structure of the baroclinic wave activity source is decoupled from the background flow, RWC can be used to isolate and quantify the dynamical mechanisms responsible for 1) the poleward shift of the midlatitude jet and 2) the feedbacks between the eddy momentum fluxes and the background flow in general.

Understanding Midlatitude Jet Variability and Change Using Rossby Wave Chromatography: Wave–Mean Flow Interaction

Abstract Rossby wave chromatography (RWC) is implemented in a linearized barotropic model as a tool to understand the interaction between the midlatitude jet and the eddy momentum fluxes (uυ) in an idealized GCM. Given the background zonal-mean flow and the space–time structure of the baroclinic wave activity source, RWC calculates the space–time structure of the upper-tropospheric uυ. RWC allows a clean separation of the effects of phase speed changes and index of refraction changes (i.e., changes in background flow) on uυ. It is found that uυ reinforces imposed zonal-mean zonal wind (u) anomalies that are collocated with the centers of action of the first empirical orthogonal function (EOF1) of the GCM. Critical-level dynamics are essential for the positive feedback when u is equatorward of the mean jet, and “reflecting level” dynamics are essential for the positive feedback when u is poleward of the jet. The eddy momentum flux caused by changes in the phase speeds of the wave sources, on the other hand, are associated with a negative feedback. When the imposed u is out of phase with EOF1, the eddies tend to shift the imposed u poleward (equatorward) for anomalies that are equatorward (poleward) of the poleward center of action of EOF1. Critical (reflecting)-level dynamics is most important for the poleward shift in the subtropics (midlatitudes). Because there are no baroclinic feedbacks in these experiments, these results suggest that barotropic feedbacks alone can account for the structure of the u variability in the midlatitudes.

Downward transfer of momentum by wind-driven waves

A model for the downward transfer of wind momentum is derived for growing waves. It is shown that waves, which grow due to an uneven pressure distribution on the water surface or a wave-coherent surface shear stress have horizontal velocities out of phase with the surface elevation. Further, if the waves grow in the x-direction, while the motion is perhaps time-periodic at any fixed point, the Reynolds stresses associated with the organized motion are positive. This is in agreement with several field and laboratory measurements which were previously unexplained, and the new theory successfully links measured wave growth rates and measured sub-surface Reynolds stresses. Wave coherent air pressure (and/or surface shear stress) is shown to change the speed of wave propagation as well as inducing growth or decay. From air pressure variations that are in phase with the surface elevation, the influence on the waves is simply a phase speed increase. For pressure variations out of phase with surface elevation, both growth (or decay) and phase speed changes occur. The theory is initially developed for long waves, after which the velocity potential and dispersion relation for linear waves in arbitrary depth are given. The model enables a sounder model for the transfer to storm surges or currents of momentum from breaking waves in that it does not rely entirely on ad-hoc turbulent diffusion. Future models of atmosphere-ocean exchanges should also acknowledge that momentum is transferred partly by the organized wave motion, while other species, like heat and gasses, may rely totally on turbulent diffusion. The fact that growing wind waves do in fact not generally obey the dispersion relation for free waves may need to be considered in future wind wave development models.

MAGNETOSEISMOLOGICAL DETERMINATION OF MAGNETIC FIELD AND PLASMA DENSITY HEIGHT VARIATION IN A SOLAR SPICULE

The variation of magnetic field strength and plasma density along a solar spicule is determined by the use of magnetoseismology. From Solar Optical Telescope observations of a kink wave propagating along a spicule, by estimating the spatial change in phase speed and velocity amplitude, a novel approach is demonstrated to determine the chromospheric height variation of both magnetic field and plasma density. Furthermore, the magnetoseismological estimate of the plasma density gradient is combined with electron density estimates from spectroscopy to determine the changing degree of ionization of hydrogen along a spicule.

Structure of AGCM-Simulated Convectively Coupled Kelvin Waves and Sensitivity to Convective Parameterization

Abstract A study of the convectively coupled Kelvin wave (CCKW) properties from a series of atmospheric general circulation model experiments over observed sea surface temperatures is presented. The simulations are performed with two different convection schemes (a mass flux scheme and a moisture convergence scheme) using a range of convective triggers, which inhibit convection in different ways. Increasing the strength of the convective trigger leads to significantly slower and more intense CCKW activity in both convection schemes. With the most stringent trigger in the mass flux scheme, the waves have realistic speed and variance and also exhibit clear shallow-to-deep-to-stratiform phase tilts in the vertical, as in observations. While adding a moisture trigger results in vertical phase tilts in the mass flux scheme, the moisture convergence scheme CCKWs show no such phase tilts even with a stringent convective trigger. The changes in phase speed in the simulations are interpreted using the concept of “gross moist stability” (GMS). Inhibition of convection results in a more unstable tropical atmosphere in the time mean, and convection is shallower on average as well. Both of these effects lead to a smaller GMS, which leads to slower propagation of the waves, as expected from theoretical studies. Effects such as changes in radiative heating, atmospheric humidity, and vertical velocity following the wave have a relatively small effect on the GMS as compared with the time mean state determined by the convection scheme.

Experimental Study of Sound Propagation Through Bubbly Water: Comparison With Optical Measurements

The study of the acoustical properties of bubbly flows remains a challenge for scientists. Classical theoretical results provide the expression of a complex effective wave number characterizing sound propagation through such a medium. Theoretical attenuation and phase-speed changes of sound can be obtained from this effective wave number and are specifically observable around characteristic frequencies related to the size of the bubbles. With the aim to contribute to the ongoing research, this paper presents experimental work conducted in a large laboratory tank, to study sound propagation through bubbly water. An original bubble generation technique and the characterization of the generated bubbles by both acoustical and optical methods are reported. In the experiments of this work, air bubbles are injected, using a high-pressure washer, into a large water-filled tank through which sound signals are propagated. The characteristic frequencies and the bubble sizes are determined from the measurements of the sound attenuation and the sound phase speed. These measurements are complemented by concurrent acquisitions of acoustic signals and optical images. A comparative study is conducted between the bubble size distributions deduced from the optical and those deduced from the acoustical measurements.

Characteristics of Baroclinic Wave Packets during Strong and Weak Stratospheric Polar Vortex Events

Abstract This study tested a numerical and theoretical prediction that the stratosphere and troposphere are coupled through the effect of stratospheric vertical wind shear on baroclinic waves. Wavelengths, phase speeds, and background quasigeostrophic potential vorticity gradients were analyzed over the Pacific and Atlantic during strong and weak stratospheric polar vortex events and interpreted in terms of the counterpropagating Rossby wave perspective on baroclinic instability. Effects of zonal variations in the background flow were included in the analysis of phase speeds. Observed changes in wave packet average wavelength and phase speed support the vertical shear hypothesis for stratosphere–troposphere coupling; however, changes in the intrinsic phase speed contradict the hypothesis. This inconsistency was resolved by considering the change in zonal wind speed in the lower stratosphere, which accounts for most of the change in phase speeds during strong and weak vortex events. Changes in the average wavelengths and meridional wave activity flux are also consistent with this modified hypothesis involving the stratospheric zonal wind. The results demonstrate that a simple mechanism for stratosphere–troposphere coupling can be found in the observational record.

Variability of Intraseasonal Kelvin Waves in the Equatorial Pacific Ocean

Abstract Previous observational work has demonstrated that the phase speed of oceanic equatorial Kelvin waves forced by the Madden–Julian oscillation (MJO) appears to vary substantially. Processes that are responsible for systematic changes in the phase speed of these waves are examined using an ocean general circulation model. The model was integrated for 26 yr with daily wind stress derived from the NCEP–NCAR reanalysis. The model is able to reproduce observed systematic changes of Kelvin wave phase speed reasonably well, providing a tool for the analysis of their dynamics. The relative importance of the upper ocean background state and atmospheric forcing for phase speed changes is determined based on a series of model experiments with various surface forcings. Systematic changes in phase speed are evident in all model experiments that have different slowly varying basic states, showing that variations of the upper ocean background state are not the primary cause of the changes. The model experiments that include and exclude intraseasonal components of wind stress in the eastern Pacific demonstrate that wind stress changes to the east of the date line can significantly alter the speed of Kelvin waves initially generated over the western Pacific, which often results in a phase propagation faster than the free wave speed. These faster waves contribute to the systematic changes of phase speed evident in observations. Similar results are also obtained using a linear stratified model, eliminating nonlinearity as a possible cause of the phase speed changes.

On the propagation of hydromagnetic waves in a plasma of thermal and suprathermal components

The propagation of MHD waves is studied when two ideal fluids, thermal and suprathermal gases, coupled by magnetic field are moving with the steady flow velocity. The fluids move independently in a direction perpendicular to the magnetic field but gets coupled along the field. Due to the presence of flow in suprathermal and thermal fluids there appears forward and backward waves. All the forward and backward modes propagate in such a way that their rate of change of phase speed with the thermal Mach number is same. It is also found that besides the usual hydromagnetic modes there appears a suprathermal mode which propagates with faster speed. Surface waves are also examined on an interface formed with composite plasma (suprathermal and thermal gases) on one side and the other is a non-magnetized plasma. In this case, the modes obtained are two or three depending on whether the sound velocity in thermal gas is equal to or greater than the sound velocity in suprathermal gas. The results lead to the conclusion that the interaction of thermal and suprathermal components may lead to the occurrence of an additional mode called suprathermal mode whose phase velocity is higher than all the other modes.