Showing papers on "Inertial wave published in 2005"

Stable boundary-layer scaling regimes : The sheba data

Abstract: Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification. Scaling arguments and our analysis show that the SBL can be classified into four major regimes: (i) surface-layer scaling regime (weakly stable case), (ii) transition regime, (iii) turbulent Ekman layer, and (iv) intermittently turbulent Ekman layer (supercritical stable regime). These four regimes may be considered as the basic states of the traditional SBL. Sometimes these regimes, especially the last two, can be markedly perturbed by gravity waves, detached elevated turbulence (‘upside down SBL’), and inertial oscillations. Traditional Monin–Obukhov similarity theory works well in the weakly stable regime. In the transition regime, Businger–Dyer formulations work if scaling variables are re-defined in terms of local fluxes, although stability function estimates expressed in these terms include more scatter compared to the surface-layer scaling. As stability increases, the near-surface turbulence is affected by the turning effects of the Coriolis force (the turbulent Ekman layer). In this regime, the surface layer, where the turbulence is continuous, may be very shallow (< 5 m). Turbulent transfer near the critical Richardson number is characterized by small but still significant heat flux and negligible stress. The supercritical stable regime, where the Richardson number exceeds a critical value, is associated with collapsed turbulence and the strong influence of the earth’s rotation even near the surface. In the limit of very strong stability, the stress is no longer a primary scaling parameter.

Near-inertial waves in the ocean: beyond the ‘traditional approximation’

Abstract: The dynamics of linear internal waves in the ocean is analysed without adopting the ‘traditional approximation’, i.e. the horizontal component of the Earth's rotation is taken into account. It is shown that non-traditional effects profoundly change the dynamics of near-inertial waves in a vertically confined ocean. The partial differential equation describing linear internal-wave propagation can no longer be solved by separation of spatial variables; it was however pointed out earlier in the literature that a reduction to a Sturm–Liouville problem is still possible, a line that is pursued here. In its formal structure the Sturm–Liouville problem is the same as under the traditional approximation, but its eigenfunctions are no longer normal vertical modes of the full problem. The question is addressed of whether the solution found through this reduction is the general one: a set of eigenfunctions to the full problem is constructed, which depend in a non-separable way on the two spatial variables; these functions are orthogonal and form, under mild assumptions, a complete basis.In the near-inertial range, non-traditional effects act as a singular perturbation; this is seen from the sub-inertial short-wave limit, which is present whenever the ‘non-traditional’ terms are there, but disappears under the traditional approximation. In the dispersion relation the sub-inertial modes represent a smooth continuation of the super-inertial ones. The combined effect of the horizontal component of rotation and a vertical inhomogeneity in the stratification is found to play a crucial role in the dynamics of sub-inertial waves. They are trapped in waveguides localized around minima of the buoyancy frequency. The presence of horizontal inhomogeneities in the effective Coriolis parameter (such as shear currents or beta effect) are shown to enable a transition from super-inertial to sub-inertial waves (and thus effectively an irreversible transformation of large-scale into small-scale motions). It is suggested that this transformation provides a mechanism for mixing in the deep ocean.The notion of critical reflection of internal waves at a sloping bottom is also modified by non-traditional effects, and they strongly increase the probability of critical reflection in the near-inertial to tidal range.

Energy deposition by Alfvén waves into the dayside auroral oval: Cluster and FAST observations

Abstract: [1] We report in situ observations from the Cluster and FAST spacecraft showing the deposition of energy into the auroral ionosphere from broadband ULF waves in the cusp and low-latitude boundary layer A comparison of the wave Poynting flux with particle energy and flux at both satellites indicates that energy transfer from the broadband waves to the plasma occurs through field-aligned electron acceleration, transverse ion acceleration, and Joule heating These processes are shown to result in precipitating electron fluxes sufficient to drive bright aurora and cause outflows of energized electrons and O+ ions from the ionosphere into the low-latitude boundary layer By solving an eigenmode equation for Alfven waves in the observed plasma environment, it is shown that the broadband waves observed at Cluster and FAST are dispersive Alfven waves It is demonstrated that these waves have wavelengths perpendicular to the geomagnetic field extending from significant fractions of an L shell down to ion gyroradii and electron inertial lengths and wave frequencies in the plasma frame from 1 mHz up to 50 mHz These waves are shown to have wavelengths along the geomagnetic field of the order of the field line length between the ionosphere and the equatorial plane and become field line resonances (FLRs) when on closed field lines It is shown that the inclusion of nonlinear and/or nonlocal kinetic effects is required in the description of these waves to account for accelerated particles observed On the basis of the wave polarization and spectral properties observed from Cluster and FAST it is speculated that these waves are generated through the mode conversion of surface Alfven waves driven by tailward flows in the low-latitude boundary layer

Wave attractors and the asymptotic dissipation rate of tidal disturbances

Abstract: Linear waves in bounded inviscid fluids do not generally form normal modes with regular eigenfunctions. Examples are provided by inertial waves in a rotating fluid contained in a spherical annulus, and internal gravity waves in a stratified fluid contained in a tank with a non-rectangular cross-section. For wave frequencies in the ranges of interest, the inviscid linearized equations are spatially hyperbolic and their characteristic rays are typically focused onto wave attractors. When these systems experience periodic forcing, for example of tidal origin, the response of the fluid can become localized in the neighbourhood of a wave attractor. In this paper, I define a prototypical problem of this form and construct analytically the long-term response to a periodic body force in the asymptotic limit of small viscosity. The vorticity of the fluid is localized in a detached shear layer close to the wave attractor in such a way that the total rate of dissipation of energy is asymptotically independent of the viscosity. I further demonstrate that the same asymptotic dissipation rate is obtained if a non-viscous damping force is substituted for the Navier–Stokes viscosity. I discuss the application of these results to the problem of tidal forcing in giant planets and stars, where the excitation and dissipation of inertial waves may make a dominant, or at least important, contribution to the orbital and spin evolution.

Enhanced vertical propagation of storm-induced near-inertial energy in an eddying ocean channel model

Abstract: The interaction between inertial oscillations generated by a storm and a mesoscale eddy field is studied using a Southern Ocean channel model. It is shown that the leakage of near-inertial energy out of the surface layer is strongly enhanced by the presence of the eddies, with the anticyclonic eddies acting as a conduit to the deep ocean. Given the ubiquity of the atmospheric storm tracks (a source of near-inertial energy for the ocean) and regions of strong ocean mesoscale variability, we argue that this effect could be important for understanding pathways by which near-inertial energy enters the ocean and is ultimately available for mixing.

Origin of Tidal Dissipation in Jupiter. I. Properties of Inertial Modes

Abstract: We study global inertial modes with the purpose of unraveling the role they play in the tidal dissipation process of Jupiter. For spheres of uniformly rotating, neutrally buoyant fluid, we show that the partial differential equation governing inertial modes can be separated into two ordinary differential equations when the density is constant or when the density has a power-law dependence on radius. For more general density dependencies, we show that one can obtain an approximate solution to the inertial modes that is accurate to the second order in wavevector. Frequencies of inertial modes are limited to ω < 2Ω (Ω is the rotation rate), with modes propagating closer to the rotation axis having higher frequencies. An inertial mode propagates throughout much of the sphere with a relatively constant wavelength and a wave amplitude that scales with density as 1/. It is reflected near the surface at a depth that depends on latitude, with the depth being much shallower near the special latitudes θ = ±ω/2Ω. Around this region, this mode has the highest wave amplitude as well as the sharpest spatial gradient (the "singularity belt"), thereby incurring the strongest turbulent dissipation. Inertial modes naturally cause small Eulerian density perturbations, so they are only weakly coupled to the tidal potential. In a companion paper, we attempt to apply these results to the problem of tidal dissipation in Jupiter.

Near-inertial waves on the “nontraditional” β plane

Abstract: [1] Propagation of linear near-inertial waves on the β plane is considered, taking into account the horizontal component of the Earth's rotation, . (Terms, effects etc., due to this component will be referred to as “nontraditional,” for brevity.) It is shown that the combined effect of β and changes the dynamics in a fundamental way. For a vertically unbounded domain, an exact solution shows that near-inertial waves can pass through the inertial latitude, unlike under the traditional approximation. For parameter values typical of the ocean, the subinertial domain extends several hundreds of kilometers poleward of the inertial latitude. The solution undergoes a profound change if a vertically bounded, instead of unbounded, domain is considered. Part of the wave energy then accumulates at the poleward end of the subinertial domain, which involves an evolution toward infinitesimal horizontal and vertical scales. For vertically nonuniform stratification, examined here using the Garrett-Munk exponential profile, one finds a wedge-like waveguide, which becomes increasingly narrow in the poleward direction, and drives subinertial waves into the region of the weakest stratification, i.e., the abyss. For typical parameters, the relative amount of poleward traveling energy that gets trapped is estimated to lie between 10 and 30%; its dependence on latitude and stratification is also outlined. The observational evidence and possible implications for abyssal mixing are discussed.

Spring Mixing: Turbulence and Internal Waves during Restratification on the New England Shelf

Abstract: Integrated observations are presented of water property evolution and turbulent microstructure during the spring restratification period of April and May 1997 on the New England continental shelf. Turbulence is shown to be related to surface mixed layer entrainment and shear from low-mode near-inertial internal waves. The largest turbulent diapycnal diffusivity and associated buoyancy fluxes were found at the bottom of an actively entraining and highly variable wind-driven surface mixed layer. Away from surface and bottom boundary layers, turbulence was systematically correlated with internal wave shear, though the nature of that relationship underwent a regime shift as the stratification strengthened. During the first week, while stratification was weak, the largest turbulent dissipation away from boundaries was coincident with shear from mode-1 near-inertial waves generated by passing storms. Wave-induced Richardson numbers well below 0.25 and density overturning scales of several meters were observed. Turbulent dissipation rates in the region of peak shear were consistent in magnitude with several dimensional scalings. The associated average diapycnal diffusivity exceeded 10 3 m 2 s 1 . As stratification tripled, Richardson numbers from low-mode internal waves were no longer critical, though turbulence was still consistently elevated in patches of wave shear. Kinematically, dissipation during this period was consistent with the turbulence parameterization proposed by MacKinnon and Gregg, based on a reinterpretation of wave–wave interaction theory. The observed growth of temperature gradients was, in turn, consistent with a simple one-dimensional model that vertically distributed surface heat fluxes commensurate with calculated turbulent diffusivities.

Near-Inertial Waves on the New England Shelf: The Role of Evolving Stratification, Turbulent Dissipation, and Bottom Drag

Abstract: Energetic variable near-inertial internal waves were observed on the springtime New England shelf as part of the Coastal Mixing and Optics (CMO) project. Surface warming and freshwater advection tripled the average stratification during a 3-week observational period in April/May 1997. The wave field was dominated by near-inertial internal waves generated by passing storms. Wave evolution was controlled by a balance among wind stress, bottom drag, and turbulent dissipation. As the stratification evolved, the vertical structure of these near-inertial waves switched from mode 1 to mode 2 with associated changes in the magnitude and location of wave shear. The growth of mode-2 waves was attributable to a combination of changing wind stress forcing and a nonlinear coupling between the first and second vertical modes through quadratic bottom stress. To explore both forcing mechanisms, an open-ocean mixed layer model is adapted to the continental shelf. In this model, surface wind stress and bottom stre...

A Baroclinic Instability that Couples Balanced Motions and Gravity Waves

Abstract: Normal modes of a linear vertical shear (Eady shear) are studied within the linearized primitive equations for a rotating stratified fluid above a rigid lower boundary. The authors’ interest is in modes having an inertial critical layer present at some height within the flow. Below this layer, the solutions can be closely approximated by balanced edge waves obtained through an asymptotic expansion in Rossby number. Above, the solutions behave as gravity waves. Hence these modes are an example of a spatial coupling of balanced motions to gravity waves. The amplitude of the gravity waves relative to the balanced part of the solutions is obtained analytically and numerically as a function of parameters. It is shown that the waves are exponentially small in Rossby number. Moreover, their amplitude depends in a nontrivial way on the meridional wavenumber. For modes having a radiating upper boundary condition, the meridional wavenumber for which the gravity wave amplitude is maximal occurs when the tilts of the balanced edge wave and gravity waves agree.

A statistical study of gravity waves from radiosonde observations at Wuhan (30° N, 114° E) China

Abstract: . Several works concerning the dynamical and thermal structures and inertial gravity wave activities in the troposphere and lower stratosphere (TLS) from the radiosonde observation have been reported before, but these works were concentrated on either equatorial or polar regions. In this paper, background atmosphere and gravity wave activities in the TLS over Wuhan (30° N, 114° E) (a medium latitudinal region) were statistically studied by using the data from radiosonde observations on a twice daily basis at 08:00 and 20:00 LT in the period between 2000 and 2002. The monthly-averaged temperature and horizontal winds exhibit the essential dynamic and thermal structures of the background atmosphere. For avoiding the extreme values of background winds and temperature in the height range of 11-18km, we studied gravity waves, respectively, in two separate height regions, one is from ground surface to 10km (lower part), and the other is within 18-25km (upper part). In total, 791 and 1165 quasi-monochromatic inertial gravity waves were extracted from our data set for the lower and upper parts, respectively. The gravity wave parameters (intrinsic frequencies, amplitudes, wavelengths, intrinsic phase velocities and wave energies) are calculated and statistically studied. The statistical results revealed that in the lower part, there were 49.4% of gravity waves propagating upward, and the percentage was 76.4% in the upper part. Moreover, the average wave amplitudes and energies are less than those at the lower latitudinal regions, which indicates that the gravity wave parameters have a latitudinal dependence. The correlated temporal evolution of the monthly-averaged wave energies in the lower and upper parts and a subsequent quantitative analysis strongly suggested that at the observation site, dynamical instability (strong wind shear) induced by the tropospheric jet is the main excitation source of inertial gravity waves in the TLS.

Near-Inertial Wave Propagation in the Western Arctic

Abstract: From October 1997 through October 1998, the Surface Heat Budget of the Arctic (SHEBA) ice camp drifted across the western Arctic Ocean, from the central Canada Basin over the Northwind Ridge and across the Chukchi Cap. During much of this period, the velocity and shear fields in the upper ocean were monitored by Doppler sonar. Near-inertial internal waves are found to be the dominant contributors to the superinertial motion field. Typical rms velocities are 1–2 cm s−1. In this work, the velocity and shear variances associated with upward- and downward-propagating wave groups are quantified. Patterns are detected in these variances that correlate with underlying seafloor depth. These are explored with the objective of assessing the role that these extremely low-energy near-inertial waves play in the larger-scale evolution of the Canada Basin. The specific focus is the energy flux delivered to the slopes and shelves of the basin, available for driving mixing at the ocean boundaries. The energy and ...

Nonlinear Alfven, magnetosonic, sound, and electron inertial waves in fluid formalism

Abstract: [1] A fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas is presented. The model has been verified for plasma beta (ratio of kinetic/magnetic pressures) in a range between 0.1 and 15. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes, Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. Modes slower than the sound speed have left-handed polarization for the transverse magnetic field, while the faster modes have right-handed polarization. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits, it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas (β ≈ 1) and how trains of solitons (“mirror modes”) are produced in a hot, anisotropic plasma. The applicability of the model is illustrated by showing that the electric currents carried by nonlinear waves measured on Cluster spacecraft in the magnetosheath at β ≈ 15 are well reproduced by currents derived from the theoretical model.

Coastal winds and low-level jets: Simulations for sea gulfs

Abstract: The reasons for the relatively strong coastal afternoon surface winds observed along the Gulf of Finland were studied by using a high-resolution two-dimensional numerical model in typical summertime conditions. Sea breeze effects were included by defining a clear sky, whereas they were minimized by alternatively defining a thick cloud cover. The geostrophic wind was varied both in speed and direction. A case-study was made with a three-dimensional operational forecast model with results that agreed with the two-dimensional experiments and observations. Strongish afternoon surface winds nearly parallel with the coastline were obtained in the overcast gulf experiments. In these cases, well-mixed air entering the smooth sea slantwise from over land commenced an inertial oscillation downstream such that the emerging low-level jet maximum was located just above the opposite coast, causing the strong winds there. If the sky was clear, sea breezes and strong convective mixing further enhanced the coastal surface winds to supergeostrophic speeds. In contrast, weak coastal winds occurred when the sea breeze and the basic flow were nearly opposite. Given the gulf geometry, the sea breeze cell from the opposite coast could be advected over the gulf in a suitable basic flow, which resulted in another minimum in the coastal wind speed as a function of geostrophic wind direction. Copyright © 2005 Royal Meteorological Society.

Near-inertial oscillations interacting with mesoscale circulation in the southwestern Japan/East Sea

Abstract: [1] The near-inertial internal wave energy distribution is investigated in the southwestern Japan/East Sea using vertical round-trip travel time of sound (τ) data from 23 pressure-sensor-equipped inverted echo sounders (PIESs) and data from Aanderaa recording current meters (CMs). Currents associated with low-mode near-inertial internal waves are slightly inclined and displace the thermocline vertically, which can be detected in τ. The band-pass filtered τ records exhibit high near-inertial energy distributions that vary interannually with changes observed in mesoscale circulation. An explanation for this is offered as trapping of near-inertial energy in anticyclonic regions, which is supported by scatterplots of monthly-rms band-pass filtered τ at inertial frequency bands vs. monthly-mean relative vorticity. The spectra from all but one deep CM exhibit a blue shift, consistent with the equatorward propagation of near-inertial waves. The exception has the highest near-inertial wave energy, and is located near the center of a warm anticyclonic eddy.

Baroclinic and barotropic tides in the Weddell Sea

Abstract: Barotropic and baroclinic tides were simulated for the Weddell Sea using ROMS. The model estimates for both tidal elevations and velocities showed good agreement with existing observations. The rms differences were 9 cm for elevations and 1.2–1.7 cm s−1 for the major axes of the tidal ellipses for the semidiurnal constituents and 6–8 cm and 4.5 cm s−1 for the diurnal constituents, respectively. Most of the discrepancies occurred deep under the ice shelf for the semidiurnal tides and along the continental slope for the diurnal tides. Along the continental slope, the model overestimated the generation of diurnal continental shelf waves. The diurnal tides were barotropic throughout the basin. However, internal tides were generated at semidiurnal frequencies over rough topography. Over the continental slope, semidiurnal baroclinic tidal generation was enhanced by the existence of continental shelf waves, through their harmonics. Baroclinic tides generated over rough topography in the northern Weddell Sea incited inertial oscillations as they propagated south. These inertial oscillations varied with depth since they were incited at different depths at different times as the internal tide progressed. Both the baroclinic tides and inertial oscillations induced vertical shear in the water column and increased the divergence of the horizontal surface velocities.

Parametrically disciplined operation of a vibratory gyroscope

Abstract: Parametrically disciplined operation of a symmetric nearly degenerate mode vibratory gyroscope is disclosed. A parametrically-disciplined inertial wave gyroscope having a natural oscillation frequency in the neighborhood of a sub-harmonic of an external stable clock reference is produced by driving an electrostatic bias electrode at approximately twice this sub-harmonic frequency to achieve disciplined frequency and phase operation of the resonator. A nearly symmetric parametrically-disciplined inertial wave gyroscope that can oscillate in any transverse direction and has more than one bias electrostatic electrode that can be independently driven at twice its oscillation frequency at an amplitude and phase that disciplines its damping to zero in any vibration direction. In addition, operation of a parametrically-disciplined inertial wave gyroscope is taught in which the precession rate of the driven vibration pattern is digitally disciplined to a prescribed non-zero reference value.

Barotropic tide and baroclinic waves observations in the Río de la Plata Estuary

Abstract: [1] The first long-period ADCP series collected in two locations of the salinity front of the Rio de la Plata estuary are explored for periods less than 30 hours. Barotropic velocity shows tidal and mean currents consistent with what is known about the estuarine circulation in tidal and seasonal scales. Baroclinic currents provide the first evidence of the occurrence of internal waves, which can account for half of the total variance. In the northernmost location, predominantly zonal oscillations with semidiurnal period, and oscillations with a dominant meridional component and diurnal period, are found. Whereas the first ones can be related to the semidiurnal tide, the second ones seem to be atmospherically forced by the land/sea breeze. In the southernmost location, more rotational oscillations are observed, with periods around the inertial and diurnal ones. Inertial oscillations could result from wind relaxation, whereas diurnal oscillations also seem to be forced by breeze. Wave activity in the diurnal band was less frequent in the northernmost than in the southernmost location. This can be attributed to less frequent favorable stratification conditions in that area during the observed period. Wave activity in the southernmost location resulted weaker during the observed fall than during the summer. This could be a typical feature given that in autumn both the number of storms destroying the thermohaline structure increases and land/sea breeze is less frequent. This suggests a likely seasonal cycle in the diurnal wave activity in this area, given that those unfavorable conditions are even more marked during winter.

Waves in the Hall-magnetohydrodynamics model

Abstract: The three magnetohydrodynamic (MHD) waves are followed as they transition under the influence of an increasingly strong Hall current effect to the characteristic waves of the Hall-MHD model. Also followed are the wave normal surfaces and the ray surfaces (approximating wave fronts) of these waves. The changes in the nature of the waves are found to be considerable, and are described both analytically and numerically. Most notably, the incompressible MHD shear Alfven wave becomes a compressible fluid-dynamical wave with negligible perturbation of the electromagnetic field, while the two MHD compressible waves become incompressible, the fast wave becoming mostly electromagnetic and the slow wave becoming mostly fluid-dynamical.

Baroclinic instability of two-layer vortices in laboratory experiments

Abstract: The dynamics of a baroclinic vortex in a two-layer rotating stratified fluid is investigated. The vortex is produced by the classical geostrophic adjustment process, starting from an initial step in the layer interface. The experiments are performed on the 13m diameter Coriolis turntable, allowing investigation of inertial regimes, in which viscous friction effects are negligible. The velocity fields are measured in both layers by employing particle image velocimetry, thus providing a quantitative measure of the flow evolution. The baroclinic instability occurs much later in time than the initial inertial oscillations. The growth occurs in a hydrostatic regime, with velocity being independent of height in each layer. This process is described well by linear stability theory for a quasi-geostrophic disk vortex, or by the classical model of Phillips (1954) empirically adapted to the circular geometry. This stability prediction from the quasi-geostrophic model remains relevant even for a large initial interfacial step. For strong cyclones, the instability grows roughly twice as fast as these predictions. In the nonlinear stage of the instability, the initial vortex splits and reorganizes into vortex pairs propagating outward. These dipoles involve the interactions of positive and negative vortices, with components in the upper and in the lower layer. In the case of a large initial interface step, a clear asymmetry between anticyclones and cyclones is observed: the latter are more intense and compact, with a more barotropic structure. Our results are compared with numerical simulations, using a two-layer isopycnal model. Data assimilation is used to initiate the model with the same perturbations as in the laboratory experiments, thus providing a quantitative test of the dynamics. Furthermore, data assimilation is used to extrapolate the measurements, yielding the interface position and potential vorticity fields.

The Effect of a Bottom Shelf Front upon the Generation and Propagation of Near-Inertial Internal Waves in the Coastal Ocean

Abstract: A three-dimensional nonlinear baroclinic model in cross-sectional form is used to study the generation and propagation of wind-forced near-inertial internal waves in a coastal region in the presence of a bottom front. Initially calculations are performed with the front in an infinite domain region. By this means coastal effects are removed. The initial response is in terms of inertial oscillations in the surface layer. However, in the frontal area these are modified by interaction through the nonlinear momentum terms with regions of positive and negative vorticity associated with the alongfront flow. This leads to a change in amplitude, phase, and frequency of the inertial current, and a resulting Ekman pumping that drives near-inertial internal waves in the frontal region. On the positive vorticity side of the front these waves are at the superinertial frequency and rapidly propagate away. On the negative side they are at the subinertial frequency and are trapped and inertial energy leaks to dep...

Equatorial inertial-parametric instability of zonally symmetric oscillating shear flows

Abstract: This study revisits the problem of the zonally symmetric instability on the equatorial β-plane. Rather than treating the classical problem of a steady basic flow, it treats a sequence of problems of increasing complexity in which the basic flow is oscillatory in time with a frequency ω 0 . First, for the case of a homogeneous fluid, a time-oscillating barotropic shear forcing may excite a subharmonic parametric resonance of inertial oscillations. Because of the continuous distribution of inertial oscillation frequencies, this resonance occurs at critical inertial latitudes y c such that βy c = ±ω 0 /2. Next the effects of stratification, characterized by Brunt-Vaisala frequency N, are taken into account. It is shown analytically (in the asymptotic limit of a weak shear) that the forced temporal oscillation leads to an inertial-parametric instability, when a resonance condition between the basic flow frequency and the sum of two inertio-gravity free-mode frequencies is met. This inertial-parametric instability has a well-defined inviscid vertical scale selection favouring the high-vertical mode m c ∼ 7.45m 0 , where m 0 =βN/ω 2 0 is the equatorial vertical mode characteristic of frequency ω 0 . The viscous critical shear of inertial-parametric instability is lower than the steady inertial instability one. Finally, this type of setting naturally arises when the basic flow is considered to be an equatorial wave, so the problem is recast with the nonlinear adjustment of the vertically sinusoidal basic state of a zonally symmetric mixed Rossby-gravity (MRG) wave. Initial-value numerical simulations show that the same inertial-parametric instability exists leading to a resonant subharmonic excitation of free modes with vertical scales 7 and 8 times smaller than the basic-state wave. A simplified dynamical model of the instability is introduced, demonstrating that the oscillatory nature of the shear with height for the MRG wave necessarily implies a resonance between distinct vertical modes, the most unstable ones being modes 7 and 8 for a large enough Froude number of the MRG wave. The nonlinear action of the instability is described in terms of angular momentum and potential vorticity changes: a significant mixing due to the breaking of the excited high vertical modes creates a vertically averaged westward flow at the equator and extra-equatorial eastward flows. The ideas exposed may play a part in explaining layering phenomena and the latitudinal structure of the zonal flow in the equatorial oceans below the thermocline.

On Slow Inertial Waves in the Solar Convection Zone

Abstract: The problem of inertial modes in the solar convection zone is considered Of particular interest from the point of view of observations are slow, nearly geostrophic modes, for which approximate explicit dispersion relationships are given Typical properties of these modes are discussed, and their relationship to Rossby waves is clarified Possible applications to solar phenomena are mentioned

Observations of Inertial Wave Events near the Continental Slope off Goban Spur

Abstract: Near-inertial waves were observed during the Ocean Margin Exchange (OMEX-I) experiments with current meters over the continental slope near Goban Spur. The strongest inertial motion was observed in the bottom layer, about 50 m above the 1000-m isobath. There the waves were slightly (1.7%) superinertial and the bottom slope appeared to be critical for the near-inertial peak frequency, allowing the velocity vector to follow the sloping bottom. The vertical velocity component of this motion was responsible for the near-inertial spectral peak in the temperature spectrum, which was also observed in the bottom layer. Evidence was found supporting the speculative hypothesis that high-energy near-inertial wave events were produced during geostrophic adjustment in the variable deep eastern-boundary current over the slope near Goban Spur.

Doppler-shifted inertial oscillations on a β plane

Abstract: On the spherical earth, and in the absence of a background flow, the poleward propagation of near-inertial oscillations is restricted by the turning latitude. A background flow, on the other hand, provides a way to increase the apparent frequency of near-inertial waves through Doppler shifting. In this note, it is shown that near-inertial oscillations can be advected to latitudes higher than their turning latitude. Associated with the poleward advection there is a squeezing of the meridional wavelength. A numerical model is used to verify this result. The squeezed inertial oscillations are vulnerable to nonlinear interactions, which could eventually lead to small-scale dissipation and mixing.

Banding of suspended particles in a rotating fluid-filled horizontal cylinder.

Abstract: Non-Brownian particles suspended at low volume concentration in a rotating horizontal cylinder filled with a low-viscosity fluid are observed to segregate into well-defined periodic axial bands. We present an experimental investigation of the dependence of the phenomenon on particle characteristics, tube diameter and length, and fluid viscosity. A theoretical explanation of the phenomenon is suggested, in which the segregation occurs as a result of mutual interaction between the particles and inertial waves excited in the bounded fluid. This leads to the result that macroscopic suspended particles accumulate in alternate nodes of the wave excitation, which is in agreement with the experiments, and leads to two degenerate band patterns for each mode. Under some conditions the observed pattern oscillates between the two possible band configurations. The mechanism underlying the oscillations is unclear. A confirmation of the theoretical approach was obtained by means of a photographic capture of the flow field resulting from the inertial waves.