Linear and Non-Linear Dynamics of Inertial Waves in a Rotating Cylinder with Antiparallel Inclined Ends

This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius.Three different regimes are found:inertial wave attractor,global oscillations(the cavity’s resonant modes)and regime of symmetric reflection of wave beams.In linear wave regimes,a steady single vortex elongated along the rotation axis is generated.The location of the wave’s interaction with the sloping ends determines the vortex position and the vorticity sign.In non-linear regimes several pairs of the triadic resonance subharmonics are detected simultaneously.The instability of triadic resonance is accompanied by the periodic generation of mean vortices drifting in the azimuthal direction.Moreover,the appearance frequency of the vortices is consistent with the low-frequency subharmonic of the triadic resonance.The experimental results shed light on the mechanisms of the inertial wave interaction with zonal flow and may be useful for the development of new methods of mixing.

Flow structures, nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures,nonlinear inertial waves and energy transfer in a rotating fluid sphere,using a Galerkin spectral method based on helical-wave decomposition(HWD).Numerical simulations of flows in a sphere are performed with different system rotation rates,where a large-scale forcing is employed.For the case without system rotation,the intense vortex structures are tube-like.When a weak rotation is introduced,small-scale structures are reduced and vortex tubes tend to align with the rotation axis.As the rotation rate increases,a large-scale anticyclonic vortex structure is formed near the rotation axis.The structure is shown to be led by certain geostrophic modes.When the rotation rate further increases,a cyclone and an anticyclone emerge from the top and bottom of the boundary,respectively,where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow.Based on HWD,effects of spherical confinement on rotating turbulence are systematically studied.It is found that the forward cascade becomes weaker as the rotation increases.When the rotation rate becomes larger than some critical value,dual energy cascades emerge,with an inverse cascade at large scales and a forward cascade at small scales.Finally,the flow behavior near the boundary is studied,where the average boundary layer thickness gets smaller when system rotation increases.The flow behavior in the boundary layer is closely related to the interior flow structures,which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.

Observations of near-inertial waves induced by parametric subharmonic instability

Near-inertial waves(NIWs), which can be generated by wind or the parametric subharmonic instability(PSI) of internal tides, are common in the South China Sea(SCS). Moored current observations from the northern SCS have revealed that the PSI of semidiurnal(D_2) internal tides is another source of NIWs. The objective of this study was to examine the energy variance in the PSI of D_2 tides. The PSI of D_2 internal tides generated NIWs and waves with frequencies around the difference frequency of D_2 and f. The observed NIWs induced by PSI could be distinguished clearly from those elicited by typhoon Krosa. Shortly after Krosa entered the SCS, NIWs began to intensify on the surface and they propagated downward over subsequent days. The near-inertial currents were damped quickly and they became relatively weak before the waves were reinforced beneath the mixed layer when wind stress was relatively weak. Rotation spectra indicated an energy peak at exactly the difference frequency D_2–f of the NIWs and D_2, indicating nonlinear wave-wave interaction among D_2, f, and D_2–f. Depth-time maps of band-pass fi ltered velocities of D_2 –f showed the waves amplifi ed when the NIWs were reinforced, and they intensifi ed at depths with strong D_2 tides. The energies of the NIWs and D_2 –f had high correlation with the D_2 tides. The PSI transferred energy of low-mode D_2 internal tides to high-mode NIWs and D_2–f waves. For the entire observational period, PSI reinforcement was observed only when mesoscale eddies emerged and when D_2 was in spring tide, revealing a close connection between mesoscale eddies and NIWs. Mesoscale eddies could increase the energy in the f-band by enhancing the PSI of D_2 internal tides. Thus, this represents another mechanism linking the energy of mesoscale eddies to that of NIWs.

Inertial Waves Occurring in a Liquid Metal Column due to Pulsed Excitation by a Rotating Magnetic Field

We present an experimental study concerning the flow inside a liquid metal column exposed to a pulsed rotating magnetic field.This paper is aimed at highly resolved,quantitative velocity measurements in the eutectic GalnSn alloy.A novel ultrasound Doppler system was used two measure two-dimensional velocity fields of the secondary flow in the radial-meridional plane.It employs an array of 25 transducer elements allowing a fast electronic traversing with concurrently high spatial and temporal resolution.The measurements revealed transient flow regimes showing distinct inertial oscillations and coherent vortex structures.The results demonstrate that the arising flow structure depends sensitively on the frequency of the RMF pulses.A maximum intensity of a periodic meridional flow can be observed,if the corresponding pulse frequency fp relates to the eigenperiod of the respective inertial mode in a developed regime.The electromagnetic stirring method that uses a modulated RMF offers considerable potential to enhance the stirring efficiency and to optimize the properties of castings by a well-aimed flow control during solidification.

Some Possible Solutions of Nonlinear Internal Inertial Gravity Wave Equations in the Atmosphere

In this paper, the nonlinear internal inerntial gravity wave equation is derived by the analysis method of phase plane and is solved by integration method. The results showed that this nonlinear equation not only has ordinary solitary wave solution but also has another extra-ordinary solutions, and the form of solution is related to stratification stability, wave velocity and direction of wave motion.

A parameterization scheme of vertical mixing due to inertial internal wave breaking in the ocean general circulation model

Based on the theoretical spectral model of inertial internal wave breaking （fine structure） proposed previ- ously, in which the effects of the horizontal Coriolis frequency component f-tilde on a potential isopycnal are taken into account, a parameterization scheme of vertical mixing in the stably stratified interior be- low the surface mixed layer in the ocean general circulation model （OGCM） is put forward preliminarily in this paper. Besides turbulence, the impact of sub-mesoscale oceanic processes （including inertial internal wave breaking product） on oceanic interior mixing is emphasized. We suggest that adding the inertial inter- hal wave breaking mixing scheme （F-scheme for short） put forward in this paper to the turbulence mixing scheme of Canuto et al. （T-scheme for short） in the OGCM, except the region from 15°S to 15°N. The numeri- cal results ofF-scheme by usingWOA09 data and an OGCM （LICOM, LASG/IAP climate system ocean model） over the global ocean are given. A notable improvement in the simulation of salinity and temperature over the global ocean is attained by using T-scheme adding F-scheme, especially in the mid- and high-latitude regions in the simulation of the intermediate water and deep water. We conjecture that the inertial internal wave breaking mixing and inertial forcing of wind might be one of important mechanisms maintaining the ventilation process. The modeling strength of the Atlantic meridional overturning circulation （AMOC） by using T-scheme adding F-scheme may be more reasonable than that by using T-scheme alone, though the physical processes need to be further studied, and the overflow parameterization needs to be incorporated. A shortcoming in F-scheme is that in this paper the error of simulated salinity and temperature by using T-scheme adding F-scheme is larger than that by using T-scheme alone in the subsurface layer.

An Alternative Method to Study Wave Scattering by Semi-infinite Inertial Surfaces

A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.

Is the small-scale turbulence an exclusive breaking product of oceanic internal waves

On the basis of the theoretical research results by the author and the literature published up to date, the analysis and the justification presented in this paper show that the breaking products of oceanic internal waves are not only turbulence, but also the fine-scale near-inertial internal waves （the oceanic reversible finestructure） for inertial waves and the internal solitary waves for internal tides respectively. It was found that the oceanic reversible finestructure may be induced by the effect of the horizontal component f （f = 2Ωcosφ） of the rotation vector on inertial waves. And a new instability of the theoretical shear and strain spectra due to the effect of f occurs at critical vertical wavenumber β c ≈ 0.1 cpm. It happens when the levels of shear and strain of the reversible finestructure are higher than those of inertial waves, which is induced by the effect of f along an ＂iso-potential-pycnal＂ of internal wave. If all breaking products of internal waves are taken into account, the average kinetic energy dissipation rate is an order of magnitude larger than the values of turbulence observed by microstructure measurements. The author’s theoretical research results are basically in agreement with those observed in IWEX, DRIFTER and PATCHEX experiments. An important impersonal fact is that on the mean temporal scale of thermohaline circulation these breaking products of internal waves exist simultaneously with turbulence. Because inertial waves are generated by winds at the surface, and internal tides are generated by strong tide-topography interactions, the analysis and justification in this paper support in principle the abyssal recipes Ⅱ：energetics of tidal and wind mixing by Munk Wunsch in 1998, in despite of the results of microstructure measurements for the turbulent kinetic energy dissipation rate and the diapycnal turbulent eddy diffusivity.

Acceleration of solar wind particles due to inertial Alfvén waves

Gaining an understanding of the effects and dynamics of the solar wind is crucial for the study of space weather,Earth's magnetosphere,spacecraft protection,the dynamics of the Solar System,and various other subjects.Observations show that Alfvén waves effectively transfer energy to resonant particles.This study demonstrates how inertial Alfvén waves deliver their energy to resonant plasma particles in different solar environments under certain conditions.The analysis shows that inertial Alfvén waves experience more rapid damping with increasing parallel wavenumber,ambient magnetic field strength,and particle number density,coupled with a decrease in temperature.The rate of energy transfer to resonant particles intensifies with higher temperatures and reduced parallel wavenumber and particle number density.Particles with higher initial velocities actively participate in Landau damping,especially in regions with a stronger ambient magnetic field.

Dynamic and Numerical Study of Waves in the Tibetan Plateau Vortex

In terms of its dynamics, The Tibetan Plateau Vortex （TPV） is assumed to be a vortex in the botmdary layer forced by diabatic heating and friction. In order to analyze the basic characteristics of waves in the vortex, the governing equations for the vortex were established in column coordinates with the balance of gradient wind. Based on this, the type of mixed waves and their dispersion characteristics were deduced by solving the linear model. Two numerical simulations with triple-nested domains--one idealized large-eddy simulation and one of a TPV that took place on 14 August 2006---were also carried out. The aim of the simulations was to validate the mixed wave deduced from the governing equations. The high-resolution model output data were analyzed and the results showed that the tangential flow field of the TPV in the form of center heating was cyclonic and convergent in the lower levels and anticyclonic and divergent in the upper levels. The simulations also showed that the vorticity of the vortex is uneven and might have shear flow along the radial direction. The changing vorticity causes the formation and spreading of vortex Rossby （VR） waves, and divergence will cause changes to the n^otion of the excitation and evolution of inertial gravity （IG） waves. Therefore, the vortex may contain what we call mixed ：inertial gravity-vortex Rossby （IG-VR） waves. It is suggested that some strongly developed TPVs should be studied in the future, because of their effects on weather in downstream areas.

Inertial gravity wave parameters for the lower stratosphere from radiosonde data over China

Characterization of gravity wave （GW） parameters for the stratosphere is critical for global atmospheric circulation models. These parameters are mainly determined from measurements. Here, we investigate variation in inertial GW activity with season and latitude in the lower stratosphere （18-25 km） over China, using radiosonde data with a high vertical resolution over a 2-year period. Eight radiosonde stations were selected across China, with a latitudinal range of 22°-49°N. Analyses show that the GW energy in the lower stratosphere over China has obvious seasonal variation and a meridional distribution, similar to other regions of the globe. The GW energy is highest in winter, and lowest in summer; it decreases with increasing latitude. Velocity perturbations with longitude and latitude are almost the same, indicating that GW energy is horizontally isotropic. Typically, 85% of the vertical wavelength distribution is concentrated between elevations of 1 and 3 km, with a mean value of 2 kin; it is almost constant with latitude. Over 80% of all the horizontal wavelengths occur in the range 100-800 km, with a mean value of 450 km; they show a weak decrease with increasing latitude, yielding a difference of about 40 km over the 22°-49°N range. The ratio of horizontal wavelength over vertical wavelength is about 200：1, which implies that inertial GWs in the lower stratosphere propagate along nearly horizontal planes. Ratios of their intrinsic frequency to the Coriolis parameter decrease with increasing latitude; most values are between 1 and 2, with a mean value of 1.5. Study of the propagation directions of GW energy shows that upward fractions account for over 60% at all stations. In contrast, the horizontal propagation direction is significantly anisotropic, and is mainly along prevailing wind directions; this anisotropy weakens with increasing latitude.

DEVELOPMENT OF INTERNAL INERTIAL GRAVITY WAVES IN THE ATMOSPHERE WITH HETEROGENEOUS STRATIFICATION

In this paper,by the WKB method the relation between the energy increase of internal inertial gravity waves and heterogeneous atmospheric stratification is derived,and a new generalized wave action is defined and its conservation is proved.

An elastic electrode model for wave propagation analysis in piezoelectric layered structures of film bulk acoustic resonators

Wave propagation in a piezoelectric layered structure of a film bulk acoustic resonator （FBAR/ is studied. The accurate results of dispersion relation are calculated using the proposed elastic electrode model for both electroded and unelectroded layered plates. The differences of calculated cut-off frequencies between the current elastic electrode model and the simplified inertial electrode model （often used in the quartz resonator analysis） are illustrated in detail, which shows that an elastic electrode model is indeed needed for the accurate analysis of FBAR. These results can be used as an accurate criterion to calibrate the 2-D theoretical model for a real finite-size structure of FBAR.

THE FOUNDATION AND MOVEMENT OF TROPICAL SEMI-GEOSTROPHIC ADAPTATION

The breakdown and foundation of geostrophic balance is one of the important movements in the mid-and high-latitude atmosphere and oceans.In the tropical area,the value of Coriolis pa- rameter is so small that it is difficult to satisfy the bi-geostrophic equilibrium between the pressure and velocity fields.However,in the tropical area,the zonal velocity of some motions in the atmo- sphere and oceans is large,so the Coriolis force is not small,geostrophic balance can exist in zonal direction,i.e.semi-geostrophic balance.Furthermore,in the dominant area of Hadley circulation in the atmosphere or the area near the ocean meridional boundary,the meridional velocity is large, so geostrophic balance can also exist in meridional direction.In this paper,the process of the dis- persion of inertial gravity wave and the foundation of semi-geostrophic balance are first discussed. Second,the adjustment process between the velocity and pressure fields after adaptation is also viewed,and the scale criterion of the semi-geostrophic adaptation is discussed,i.e.for the motion with meridional scale greater than the equatorial Rossby radius of deformation,the velocity and pressure fields after adaptation change to fit the initial pressure field;on the contrary,the fields change to fit the initial zonal velocity field,and the strength of the fields after adaptation depends on the zonal scale.