Showing papers on "Inertial wave published in 2001"

Inertial waves in a rotating spherical shell : attractors and asymptotic spectrum

Abstract: We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero. We first consider the mapping made by the characteristics of the hyperbolic equation (Poincare's equation) satisfied by inviscid solutions. Charac- teristics are straight lines in a meridional section of the shell, and the mapping shows that, generically, these lines converge towards a periodic orbit which acts like an attrac- tor (the associated Lyapunov exponent is always negative or zero). We show that these attractors exist in bands of frequencies the size of which decreases with the number of reflection points of the attractor. At the bounding frequencies the associated Lyapunov exponent is generically either zero or minus infinity. We further show that for a given frequency the number of coexisting attractors is finite. We then examine the relation between this characteristic path and eigensolutions of the inviscid problem and show that in a purely two-dimensional problem, convergence towards an attractor means that the associated velocity field is not square-integrable. We give arguments which generalize this result to three dimensions. Then, using a sphere immersed in a fluid filling the whole space, we study the critical latitude singularity and show that the velocity field diverges as 1/ √ d, d being the distance to the characteristic grazing the inner sphere. We then consider the viscous problem and show how viscosity transforms singularities into internal shear layers which in general betray an attractor expected at the eigenfre- quency of the mode. Investigating the structure of these shear layers, we find that they are nested layers, the thinnest and most internal layer scaling with E 1/3 -scale, E being the Ekman number; for this latter layer, we give its analytical form and show its simi- larity to vertical 1 -shear layers of steady flows. Using an inertial wave packet traveling around an attractor, we give a lower bound on the thickness of shear layers and show how eigenfrequencies can be computed in principle. Finally, we show that as viscosity decreases, eigenfrequencies tend towards a set of values which is not dense in (0,2), contrary to the case of the full sphere ( is the angular velocity of the system). Hence, our geometrical approach opens the possibility of describing the eigenmodes and eigenvalues for astrophysical/geophysical Ekman numbers (10 −10 − 10 −20 ), which are out of reach numerically, and this for a wide class of containers.

Near‐inertial mixing: Modulation of shear, strain and microstructure at low latitude

Abstract: We report direct, quantitative measurements of mixing associated with three cycles of a single, energetic, downward-propagating near-inertial wave in the Banda Sea at 6.5°S, 128°E during October 1998. The wave dominates the shear, containing 70% of the total variance. Simultaneous depth/time series of shear, strain, Froude number (Fr), and microstructure allow direct computation of their coherence and phase from 50–120 m, for 14 days. In this depth range, 72% of diapycnal diffusivity (68% of dissipation) occurs in three distinct pulses, spaced at the inertial period of 4.4 days. These are collocated with maxima of transverse shear, strain and Fr. Inertial-band log diapycnal diffusivity, log10 Kρ, is coherent at the 95% confidence level with both components of shear and Froude number. In this data set, strain is more important than shear in modulating Fr. Owing to the low latitude, the inertial frequency (fo = 1/4.4 cycles per day) is much smaller than the diurnal and tidal frequencies. Consequently, near-inertial motions may be studied separately from tides and other motions via time-domain filtering. Semiempirical WKB plane-wave solutions with observed frequency ωo = 1.02fo and vertical scale 100 m explain 66% and 42% of inertial-band shear and strain variance, respectively. On the basis of the observed phase relationship between shear and strain, the wave is propagating equatorward, toward 295° true. Ratios of shear to strain and of parallel to transverse shear suggest that the wave's intrinsic frequency ωI ≈ 1.18feff. This indicates that background vorticity ζ has lowered the effective Coriolis frequency, feff = fo + ζ/2, relative to its planetary value, fo [Kunze, 1985]. Ray tracing suggests that the wave was generated near 6.9°S, 130.6°E, ∼20 days prior to the cruise, coincident with the end of high winds associated with the SE monsoon. A slab mixed layer model [Pollard and Millard, 1970], forced with National Center for Environmental Prediction (NCEP) model surface winds, confirms that fluxes from the wind to the ocean at this time were sufficient to generate the wave. A very simple model shows that mixing by monsoon-generated inertial waves may add an important and strongly time-dependent aspect to some regions' energy budgets.

Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model

Abstract: We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallow-water dynamics. The only assumptions made are the well-defined scale of disturbance and the smallness of the Rossby number Ro. By systematically using the multi-time-scale perturbation expansions in Rossby number it is shown that the resulting field is split in a unique way into slow and fast components evolving with characteristic time scales f−10 and (f0Ro)−1 respectively, where f0 is the Coriolis parameter. The slow component is not influenced by the fast one and remains close to the geostrophic balance. The algorithm of its initialization readily follows by construction.The scenario of adjustment depends on the characteristic scale and/or initial relative elevation of the free surface ΔH/H0, where ΔH and H0 are typical values of the initial elevation and the mean depth, respectively. For small relative elevations (ΔH/H0 = O(Ro)) the evolution of the slow motion is governed by the well-known quasi-geostrophic potential vorticity equation for times t [les ] (f0Ro)−1. We find modifications to this equation for longer times t [les ] (f0Ro2)−1. The fast component consists mainly of linear inertia–gravity waves rapidly propagating outward from the initial disturbance.For large relative elevations (ΔH/H0 [Gt ] Ro) the slow field is governed by the frontal geostrophic dynamics equation. The fast component in this case is a spatially localized packet of inertial oscillations coupled to the slow component of the flow. Its envelope experiences slow modulation and obeys a Schrodinger-type modulation equation describing advection and dispersion of the packet. A case of intermediate elevation is also considered.

Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids

Abstract: Rotating fluids support waves. These inertial waves propagate obliquely through the fluid, with an angle that is fixed with respect to the rotation axis. Upon reflection, their wavelength is unchanged only when the wall obeys the local reflectional symmetry, that is, when it is either parallel or perpendicular to the rotation axis. For internal gravity waves in a density-stratified fluid, sloping boundaries thus break the symmetry of ray paths, in a two-dimensional container, predicting their focusing upon attractors: particular paths onto which the wave rays, and hence the energy, converge, and to which the wave energy returns after a small number of refections. Laboratory observations, presented here, show that, despite the intrinsic three-dimensionality of inertial waves, attractors still occur. The intensified wave energy on the attractor encourages centrifugal instabilities, leading to a mean flow. Evidence of this comes from dye spreading, observed to develop most rapidly over the location where the attractor reflects from the sloping wall, being the place where focusing and instabilities occur. This mean flow, resulting from the mixing of angular momentum, accompanying the intensification of the wave field at that location, has geophysical implications, because the ocean, atmosphere and Earth's liquid outer core can be regarded as asymmetrically contained. The relevance of wave focusing in a rotating, spherical shell, the modifications due to the addition of radial stratification, and its implications for observed equatorial current patterns and inertial oscillations are discussed. The well-known universality of oceanic, gravito-inertial wave spectra might reflect complementary, divergent (chaotic) wave-ray behaviour, which occurs in containers obeying the reflectional symmetry, but in which symmetry is broken in the horizontal plane. Periodic orbits still exist, but now repell.

On inertial waves in a rotating fluid sphere

Abstract: Several new results are obtained for the classical problem of inertial waves in a rotating fluid sphere which was formulated by Poincare more than a century ago. Explicit general analytical expressions for solutions of the problem are found in a rotating sphere for the first time. It is also discovered that there exists a special class of three-dimensional inertial waves that are nearly geostrophic and always travel slowly in the prograde direction. On the basis of the explicit general expression we are able to show that the internal viscous dissipation of all the inertial waves vanishes identically for a rotating fluid sphere. The result contrasts with the finite values obtained for the internal viscous dissipation for all other cases in which inertial waves have been studied.

Experimental evidence of inertial waves in a precessing spheroidal cavity

Abstract: We have demonstrated experimentally the ex- istence of inertial waves in a slowly precessing spheroid of fluid. Although such oscillatory internal shear layers have been predicted theoretically and numerically, previous pre- cessionexperimentshadshownnoevidenceoftheirpresence. Using an ultrasonic Doppler velocimetry technique, proles of radial velocity have been measured in our precession ex- periment. Comparison of these proles with their synthetic counterparts obtained numerically, proves the presence of the predicted internal shear layers. They are emitted from the breakdown of the Ekman layer at the two critical lat- itudes of the fluid (around 30 and 30) and propagate through the entire volume on conical surfaces. The asymp- totic laws for these oscillatory layers, conrmed experimen- tally and numerically, lead us to predict an oscillatoryflow of 10 6 m/s along such characteristic cones in the Earth's

Coastal Boundary Layer Characteristics during Summer Stratification in Lake Ontario

Abstract: Simultaneous measurements of Eulerian and Lagrangian currents along the north shore of Lake Ontario are analyzed to provide the mean flow properties and horizontal turbulent exchange characteristics in the coastal boundary layer (CBL). The summer coastal boundary layer is characterized by a frictional boundary layer (FBL) of a width of ∼3 km, in which shore and bottom friction affects the flow. In this regime the currents are predominantly shore parallel and persistent. The outer boundary layer also called an inertial boundary layer (IBL), typically of the order of 5–6 km wide, is a consequence of the adjustment of inertial oscillations to the lateral boundary. During the summer season within the CBL, the current motions are associated with thermocline displacements. The eastward (westward) wind stress causes thermocline elevation (depression) causing upwelling (downwelling). The mean subsurface westward currents associated with downwelling events are typically stronger in comparison to weak east...

Evolution of Near-Inertial Waves during an Upwelling Event on the New Jersey Inner Shelf*

Abstract: A 1996 field program provided a nearly three-dimensional view of the temporal evolution of near-inertial motion toward the end of an upwelling event on New Jersey’s inner shelf. The appearance of near-inertial motion is marked by a rapid rise in kinetic energy at the surface that is of the same magnitude and temporal structure of the work done by the wind, indicating that the inertial motions are forced by local winds. The incipient near-inertial motion is surface intensified and spatially coherent. It has a horizontal wavelength of 300 km and a mean kinetic energy of 0.04 m2 s−2, both of which decrease to less than 100 km and 0.01 m2 s−2 within two inertial periods. An energy budget suggests that the rapid decline in surface kinetic energy is primarily due to vertical propagation into the thermocline. Near-inertial motion in the thermocline is heterogeneous suggesting interaction between near-inertial motion and subinertial shears. The heterogeneous nature of near-inertial waves poses a practica...

On Rossby waves and vortices with differential rotation

Abstract: We present a simplied model for linearized perturbations in a fluid with both dierential rotation and dierential vorticity. Without the latter the model reduces to the classical Shearing Sheet used in the description of spiral density waves in astrophysical disks. Without the former it reduces to the -plane approximation, used in the description of Rossby waves. Retaining both, our model allows one to discuss the coupling between density waves and Rossby waves, resulting in what is known as the \corotation resonance" for density waves. Here we will derive, as a rst application of this model, the properties of Rossby waves in a dierentially rotating disk. We nd that their propagation is quenched by dierential rotation: after a limited number of oscillations, a Rossby wave collapses to a singular vortex, as fluid elements are sheared apart by dierential rotation. In a Keplerian disk, this number of oscillations is always lower than one. We also describe how, in a similar manner, a vortex is sheared in a very short time.

Effects of Coriolis force and centrifugal force on acoustic waves propagating along the surface of a piezoelectric half-space

Abstract: This article presents an analysis on the effect of rotation upon surface acoustic waves propagating in a piezoelectric half-space. It shows that the Rayleigh wave and the Bleustein-Gulyaev wave may be suppressed by rotation, depending on the physical properties of materials, and that these surface waves, if they exist, are generally dispersive. The effects of the Coriolis force and the centrifugal force on dispersion are generally of the same order. Some numerical results generated using PZT-5H as the model material are included for illustration.

Observations of highly nonlinear internal solitons generated by near-inertial internal waves off the east coast of Korea

Abstract: Solitary internal wave packets were observed in May 1999, propagating toward the east coast of Korea with thermocline displacements up to twentysix meters downward from the initial depth of twenty meters. High nonlinearity of these waves is represented by the second-order KdV model better than KdV equations. Regular occurrence of solitary internal wave packets with the period of about nineteen hours suggests the generation by near-inertial internal waves, which has not been reported in the literature yet.

Radiation of Mixed Layer Near-Inertial Oscillations into the Ocean Interior

Abstract: The radiation from the mixed layer into the interior of the ocean of near-inertial oscillations in the presence of the beta effect is reconsidered as an initial-value problem. Making use of the fact that the mixed layer depth is much smaller than the total depth of the ocean, the solution is obtained in the limit of an ocean that is effectively infinitely deep. For a uniform initial condition, analytical results for the velocity, horizontal kinetic energy density, and fluxes are obtained. This is the canonical solution for the radiation of near-inertial oscillations in the vertical, which captures the basic mechanisms due to the beta effect, and leads to the formation of small scales in the vertical. By superposing events, an average vertical wavenumber spectrum is constructed. The predicted decay of near-inertial mixed layer energy in the presence of the beta effect occurs on a timescale similar to that observed.

Numerical simulation of secondary planetary waves arising from the nonlinear interaction of the normal atmospheric modes

Abstract: A steady state two-dimensional linearised numreical model of the global structure of planetary waves has been used to simulate the production and propagation of the secondary waves originating as a result of the nonlinear interaction between the 2- and 16-day primary planetary waves. The results of the numerical simulation show that in the case of planetary waves the forcing terms arising from the non-linear interaction between different waves and from the self-interaction of primary waves are comparable in magnitude. The atmospheric response to the nonlinear forcing is strongly dependent on the propagation characteristics of the secondary waves, and in the mesosphere/lower-thermosphere region the secondary planetary wave with small zonal wave number, having the frequency that is the difference of the frequencies of the interacting primary waves, is dominant. Further perspectives are provided regarding future studies of the non-linear interaction between planetary waves in the middle and upper atmosphere.

Inertial oscillations in the Korea Strait

Abstract: Inertial oscillations (IO) are examined in the Korea Strait based on measurements from 13 acoustic Doppler current profilers covering the time period May 1999 through March 2000. Strong IO responses to wind stress occur during summer. A simple linear model predicts that winter wind stress is expected to generate inertial responses of the same order of magnitude as those in summer. However, the observed winter IO response is much weaker than predicted. During summer, the currents within the mixed layer and below the mixed layer are of comparable amplitude but in opposite directions. The depth at which the currents reverse directions varies throughout the year as the mixed layer deepens from about 40 m during summer to the bottom of the water column in November. During winter, the velocity structure is more uniform in depth with currents in the same direction throughout the water column. One possible explanation for these phenomena is related to the combined effect of the strait boundaries and the strong summer stratification. The stratification prevents the wind stress momentum flux from mixing downward below the thermocline and thus allows the development of a bottom current separate from the surface current. Such a velocity structure is necessary to satisfy the no-flow condition through the land boundaries.

Dispersion of capillary-gravity waves: A derivation based on conservation of energy

Abstract: Waves on fluids provide an excellent context for introducing some important topics in fluid dynamics. In this paper we first discuss the behaviour of standing surface waves and present their special properties. Next the dispersion relation of surface waves is derived in a novel way by applying the conservation of energy to the case of standing waves.

Evolution of electron beam generated waves resulting in transverse ion heating and filamentation of the plasma

Abstract: We present here a systematic simulational study on electron beam driven waves and their consequences in terms of plasma electrodynamics. The study is performed by using three-dimensional particle-in-cell code, parallelized to simulate a large volume of plasma. Our simulation shows that an initial electron beam of finite radius with beam velocity along the ambient magnetic field triggers a series of events in the evolution of the waves and the plasma. In the initial stage (t ≤ 200 ωpo−1, ωpo being the electron plasma frequency with the total electron density n0), high frequency waves near ω ∼ ωpo are driven. These waves progressively disappear giving way to the dominance of lower hybrid (LH) waves. The phase of the lower hybrid waves lasts over the time interval 200<˜tωpo<˜1000. In this time period the LH waves stochastically accelerate ions transverse to B0, and the beam electrons are scattered outside the initial beam volume to occupy the entire volume of the simulation plasma. The ion acceleration leads to the formation of elongated tail in the perpendicular velocity distribution. The large-amplitude LH waves are seen to undergo a parametric decay into resonance cone waves at frequencies ω < Ωi, the ion cyclotron frequency. Such extremely low-frequency (ELF) waves are the electrostatic version of the inertial Alfven waves. The phase of the strong LH waves is followed by a stage in which HF waves with frequencies ω ∼ ωpo appear again, but in this stage they are strongly modulated by the already present ELF waves and other low-frequency waves in the frequency range near the ion cyclotron frequency Ωi and its harmonics. Beginning with the LH wave stage and continuing into the late stages of ELF waves, the plasma density is highly filamented and the filaments oscillate with the ELF frequencies. The relevance of our results to the observations on plasma waves from satellites is brought out.

Barotropic response in a lake to wind-forcing

Abstract: . We report results gained with a three-dimensional, semi-implicit, semi-spectral model of the shallow water equations on the rotating Earth that allowed one to compute the wind-induced motion in lakes. The barotropic response to unidirectional, uniform winds, Heaviside in time, is determined in a rectangular basin with constant depth, and in Lake Constance, for different values and vertical distributions of the vertical eddy viscosities. It is computationally demonstrated that both the transitory oscillating, as well as the steady state current distribution, depends strongly upon the absolute value and vertical shape of the vertical eddy viscosity. In particular, the excitation and attenuation in time of the inertial waves, the structure of the Ekman spiral, the thickness of the Ekman layer, and the exact distribution and magnitude of the upwelling and downwelling zones are all significantly affected by the eddy viscosities. Observations indicate that the eddy viscosities must be sufficiently small so that the oscillatory behaviour can be adequately modelled. Comparison of the measured current-time series at depth in one position of Lake Constance with those computed on the basis of the measured wind demonstrates fair agreement, including the rotation-induced inertial oscillation. Key words. Oceanography: general (limnology) – Oceanography: physical (Coriolis effects; general circulation)

Long‐term sea ice dynamics simulations using an elastic‐plastic constitutive law

Abstract: A quasi-steady elastic-plastic sea ice dynamics model is introduced for long-term simulations. Tidal and inertial oscillations are removed by discarding the negligible inertia term. With this assumption the model is integrated using an implicit numerical scheme. Results are shown for a one-dimensional case. This approach eliminates the elastic waves that typically contaminate elastic-plastic simulations and allows the elastic-plastic constitutive law to be integrated over longer time periods, with the potential for being used effectively for climate dynamics studies.

The zonal drift associated with time‐dependent particle motion on the earth

Abstract: The zonal drift associated with the time-dependent particle velocity on the rotating earth, such as the inertial motion–westward in midlatitudes and eastward in the tropics–is shown to result from the conservation of angular momentum. This finding follows from a transformation of Newton's second law of motion on the earth into a dynamical system where the angular momentum is a system variable, a procedure similar to that used in the description of a spinning top's dynamics. In near-geostrophic zonal motion (i.e. time-dependent motion in the presence of a fixed meridional pressure gradient), where the angular momentum is conserved, and for angular momentum that is below a threshold value, the dynamical system possesses two elliptic points located off the equator. The fixed points of the dynamical system correspond to the steady, geostrophic, zonal motion so the time-dependent velocity of the small-amplitude motion (when the latitudinal particle excursion is not too large) deviates only slightly from the geostrophic velocity. The explicit expressions derived for the drift near the elliptic points imply that in near-geostrophic, eastward (westward) motion in midlatitudes the geostrophic, steady, speed provides an overestimate (underestimate) of the temporally averaged drift. This difference between the steady motion and the average of the periodic motion characterizes nonlinear systems. At large values of the angular momentum a single elliptic point exists on the equator and the drift is directed eastwards. This drift, too, can be quantified near the fixed point associated with a fixed zonal velocity on the equator, where the Coriolis force vanishes. At large oscillation amplitude in midlatitudes, when the oscillation encompasses a large latitude band and the instantaneous velocity deviates significantly from the geostrophic velocity, the zonal drift is strongly affected by the presence of a hyperbolic point at the equator. Explicit expressions for the zonal drift are not available in this case, but numerical results show that the effect of this nonlinearity is to greatly enhance the westward drift in midlatitudes compared with the small-amplitude case.

The Coriolis force and the geostrophic wind (Coriolis Part 5)

Abstract: Parker, D. E., Gordon, M., Cullum, D. P. N., Sexton, D. M. H., Folland, C. K. and Rayner, N. (1997) A new gridded radiosonde temperature data base and recent temperature trends. Geophys. Res. Len., 24, pp. 1499-1502 Spencer, R. W. and Christy, J. R. (1993) Precision lower stratospheric temperature monitoring with the MSU: technique, validation and results 19791991.3 Clim.,6,pp. 1194-1204 World Meteorological Organization (1 999) Scientific assessment of ozone depletion: 1998. WMO Global Ozone Research and Monitoring Project Report 44, Geneva

Linear and nonlinear waves on the charged surface of liquid hydrogen

Abstract: The results of research on the properties of linear and nonlinear waves on the charged surface of liquid hydrogen in a cylindrical cell are reported. It is found that the spectrum of oscillations of linear waves softens with increasing applied electric field. Weak turbulence in a system of capillary waves on the charged surface of liquid hydrogen is investigated. The formation of a Kolmogorov cascade is observed in the inertial interval from 100 Hz to 10 kHz. It is found that the correlation function of the deviation of the surface from its flat equilibrium state can be described by a power-law function of the frequency, with an exponent m=−3.7±0.3 when the surface is excited at a single resonance frequency, and m=−3.0±0.3 in the case of two-frequency excitation. The results of these studies are in qualitative agreement with the theoretical predictions.

Momentum transfer at the ocean-atmosphere interface: the wave basis for the inertial coupling approach

Abstract: The inertial coupling approach for the momentum transfer at the ocean–atmosphere interface, which is based on the assumption of a similarity hypothesis in which the ratio between the water and air reference velocities is equal to the square root of the ratio between the air and water densities, is reviewed using a wave model In this model, the air and water reference velocities are identified, respectively, with the spectrally weighted phase velocity of the gravity waves and the Stokes velocity at the water roughness length, which are evaluated in terms of the dimensionless frequency limits in Toba's equilibrium spectrum It is shown that the similarity hypothesis is approximately satisfied by the wave model over the range of wave ages encountered in typical sea states, and that the predicted values of the dimensionless surface drift velocity, the dimensionless water reference velocity, and the Charnock constant are in reasonable agreement with observational evidence The application of the bulk relationship for the surface shear stress, derived from the inertial coupling hypothesis in general circulation modeling, is also discussed

Frequency shifts of Rossby waves in the inertial subranges of β-plane turbulence

Abstract: Nonlinear interactions between waves and turbulence cause systematic frequency shifts in Rossby waves. The frequency shifts in the inertial subranges of statistically steady β-plane turbulence were examined theoretically and numerically. The theoretical analysis is based on the Lagrangian closure called the Lagrangian renormalized approximation and predicts that when the β effect is small, the frequency shifts of Rossby waves are proportional to kx/k4/3 in the inverse energy transfer range, while they are proportional to kx with or without a log-correction term in the enstrophy transfer range, depending on the flow conditions, where kx is the wave number in the eastward direction. Numerical simulations using 10242 grid points of forced β-plane turbulence that exhibit the inertial subranges, show fairly good agreement with theoretical predictions.

Stationary Rossby wave propagation in a shear flow along a reflective boundary

Abstract: This study investigates the impact of lateral boundary conditions on the propagation and dispersion of locally excited Rossby waves in a zonally periodic, barotropic, quasigeostrophic channel model on the β-plane. We use basic flows with either a linear meridional shear or a jet-like profile. On the southern boundary of the channel we impose either a rigid wall or a radiation condition, whereas the northern sidewall is permeable for Rossby waves. We compare the numerical solutions found for a reflecting southern boundary in a weakly dissipative flow to the solutions obtained from a WKB-analysis for the corresponding unforced nondissipative situation. Furthermore, we compare the generalized Eliassen-Palm flux vectors to the ray paths of Rossby wave packets, obtained from WKB ray tracing. In particular, we focus our investigation on the two-dimensional structure of trapped modal waves and wavetrains in a simple linear numerical model. Summarizing our results, we find that along the reflective wall, trapped modal wave structures as well as reflected wavetrains occur with characteristics (e.g., wavenumbers, turning latitudes) similar to the ones computed using asymptotic methods. In a linear sheared flow wave packets are trapped for all zonal wave numbers in contrast to a jet-like mean flow which has a selective effect on the waves; i.e., a turning latitudes phenomenon between the coast and the flow maximum occurs for short waves, while long waves can propagate freely across the zonal mean flow. This comes out clearly when studying the stream lines of the Eliassen-Palm flux vectors of the numerical model simulations. Furthermore, due to the reflected wave activity, the dispersion of Rossby waves is influenced by the southern boundary condition not only in the vicinity of the border but also in regions away from the boundary. These results appear to be important on the one hand for the existence of trapped Rossby waves in large-scale oceanic shear flows along a zonally oriented coast. And, on the other hand for large-scale boundary waves in conceptional atmospheric channel models which can lead to unwanted resonance effects.

Spiral magneto-electron waves in interstellar gas dynamics

Abstract: We discuss possible observational consequences resulting from the propagation of transverse magneto-electron waves in the interstellar medium. We briefly describe a magnetohydrodynamic model for the cyclotron waves with emphasis on their analogy with hydrodynamic inertial waves. It is shown that the cyclotron waves are heavily damped in the interstellar medium and, therefore, cannot affect the gas dynamics of star-forming molecular clouds. We developed an analytical model of the helicoidal magneto-electron waves based on the electromagnetic induction equation for the magnetic flux density driven by the Hall and Ohmic components of the electric field generated by flows of thermal electrons. It is established that the helicons can propagate in the interstellar medium without any noticeable attenuation. The presented numerical estimates for the group velocity of the intercloud helicons suggest that spiral circularly polarized magneto-electron waves of this type can be responsible for the broadening of molecular lines detected from dark interstellar clouds.