Showing papers on "Inertial wave published in 1990"

Generalized diffusion wave equation with inertial effects

Abstract: A generalized diffusion wave equation, which includes inertial effects, is derived on the basis of the linear analogs of the complete equations of continuity and motion of free-surface flow. Specializations of this equation lead to four types of diffusion wave models, depending on whether the inertia terms (local and convective) are excluded from or included in the formulation: (1) full inertial, (2) local inertial, (3) convective inertial, and (4) noninertial. Analysis of these diffusion wave models reveals substantial differences in their behavior, particularly with regard to the Froude number dependence of their hydraulic diffusivities. The full inertial and local inertial models have neutral Froude numbers, while the convective and noninertial models do not. In addition, the neutral Froude number of the full inertial model (wide channel with Chezy friction) simulates that of the complete equations (Fr = 2). For low Froude number flows the noninertial model is shown to be a good approximation to the full inertial model. The noninertial model is a better approximation to the full inertial model than either local or convective models.

Evidence of very-large-amplitude solitary waves in the atmosphere

Abstract: ATMOSPHERIC solitary waves are gravity waves that retain their integrity over long periods because of a near balance between nonlinearity and dispersion. They have been observed on various scales in many regions of the world1–3, but we present here detailed measurements of solitary waves with amplitudes comparable to the scale height of the lower troposphere. Two such waves were generated downstream of intense mid-tropospheric pressure troughs over the central United States. They propagated over 1,000km (several times their wavelength) with no appreciable change in structure within a 'waveguide' formed by surface inversion and a middle tropospheric critical level. Fluctuations in surface pressure associated with the two waves exceeded 6 mbar and 10 mbar. The waves caused banded patterns of precipitation and significantly influenced other meteorological phenomena. The restoration of balance between pressure-driven air flow and the Coriolis force ('geostrophic adjustment') seems to have a prominent role in the formation of these solitary waves.

Storm-Forced Baroclinic Near-Inertial Currents on the Grand Bank

Abstract: Current meter data for six mouths from the Grand Bank are analyzed to study inertial currents generated by moving storms. It is found that during periods of strong winds, but no well-defined storm system, the inertial motion exhibits no simple relationship to the local wind. During intense storms inertial currents up to 0.5 m s−1 were observed both in and below the mixed layer. Upper and lower layer currents are roughly equal in amplitude, but are 180° out of phase. To explain this observation, a two-layer, one-dimensional model is developed that successfully simulates the observed inertial currents. We show that under the conditions encountered during the storms only baroclinic inertial motion can be generated. The pressure gradient effect is not important, and the current below the mixed layer is produced by mass continuity. Wavelength computed from the continuity equation is consistent with that predicted by first-order linear theory. For inertial motion generated during periods of strong wind...

Dynamic coupling of sea ice and water for an ice field with free boundaries

Abstract: Ice-ocean dynamics is investigated using field data and a transient ice-ocean model. The measurements were made in April 1975 in the Bothnian Bay in an ice patch (100 km across) with free boundaries. The data consist of velocity time series of wind, ice, and currents at depths of 7, 10, 20 and 30 m from the ice. The ice-ocean model is used to examine the characteristics of the observations; the model consists of an unsteady free ice drift model and a transient Ekman flow model, which uses a two-equation turbulence model to achieve closure. For the surface wind at the altitude of 10 m, the estimated wind factor was 1.9%, and the deviation angle 21°, the ice-wind correlation being 0.90. The wind factor value is slightly low, probably due to biased wind data. The optimized oceanic boundary layer parameters are: roughness length 0.05 m and displacement height (due to ice ridge keels) 5 m. The model simulations predict significant inertial oscillations in the whole ice–ocean system, but in the ice measurements, they are missing and appear as highly damped in the current measurements. The reason for this discrepancy is probably due to the internal friction of the ice. Using the ocean model forced by observed ice drift data, a better fit to the current data was achieved and the inertial oscillations in the current calculations were correctly damped. DOI: 10.1034/j.1600-0870.1990.t01-2-00007.x

Inertial wave eigenfrequencies for a nonuniformly rotating fluid

Abstract: A perturbation method is used to calculate the inertial wave eigenfrequencies for an inviscid, nonuniformly rotating fluid The general results from this calculation for an arbitrary departure from uniform rotation are specialized for differential rotations The method is checked by verifying that it gave the same result as found analytically for the case of a solid body perturbation In our analysis the eigenfrequencies are real thus verifying that the differential rotation is a stable perturbation for inertial waves The method is used to model the experimentally observed collapse of inertial waves near resonance where the differential rotation is a rectified flow Another application of this work is its extension to the inverse problem of determining the differential rotation of the Earth’s fluid outer core The recent gravimetric observations of inertial waves detected after large deep earthquakes provide the necessary data for this inversion

Evidence of inertial oscillations of the surface wind at Marcus Island

Abstract: Near-inertial oscillations of the surface wind were observed at Marcus Island (24°N, 154°E) in the subtropical Pacific area. Kinetic energy spectra of the surface wind show a peak at a period of 1.1 days in the clockwise component spectrum. This period is slightly (6%) shorter than the local inertial period (1.2 days). The peak period varies slightly during the record analyzed, but tends to remain below the local inertial period. Complex demodulation with a filter shows that the large inertial amplitudes occur intermittently and decay rapidly. Most of the occurrences of large inertial events seem to be related to passing cold frontal systems or migrating low-pressure systems.

Current Shear–Inertial Wave Interaction in the Sargasso Sea

Abstract: Acoustic Doppler profiler measurements of inertial waves embedded within the high shell region of a cold core ring in the Sargasso Sea are described. By repeatedly traversing the same point from different directions, a sampling pattern resembling an asterisk was obtained. The data reveal the presence of two different wave signals which are advected through the test region: a strong, monochromatic, downgoing wave, and a less well defined ensemble of mostly downgoing waves. Calculations of the phase of the vertical shear and coherence in the vertical and horizontal planes establishes the horizontal and vertical wavenumbers. These are 33 m and 11.8 km, respectively, and the wave propagates in a nearly cross-stream direction. The weaker ensemble of waves advected through the test region later in the experiment has similar dominant scales: ∼30 m in the vertical and a horizontal wavelength in the range 11.6–30.0 km. For all of these waves, the ratio of vertical to horizontal wavelength is small and the...

Subseismic description of the Slichter modes in a rotating Earth

Abstract: This thesis reports a study of the triplet of (purely translational) Slichter modes of inner core oscillation for a simplified uniformly rotating Earth model with spherical elastic inner core, spherical rigid fixed mantle and neutrally stratified, compressible liquid core. A variational principle is used to solve the subseismic wave equation, which is used to model the liquid core dynamics. The investigation shows the utility of the subseismic wave equation for describing a long-period oscillation, with the effects of higher order harmonics in the displacement field taken into account. For the first time, a numerical estimate of error involved in making the subseismic approximation is given for a particular mode. The eigenperiod of the Slichter mode is found to be around 5 hours for neutrally stratified liquid core with total mass constrained by PREM (1981) data. The effect of the Earth's rotation is to split the mode into a triplet with eigenperiods 12% shorter, 2% shorter, and 10% longer. The effects of compressibility of the liquid core and elasticity of the inner core are to increase the eigenperiod by about 0.6% and 9% respectively. The study can be regarded as a preliminary numerical attempt to describe gravitational/inertial oscillations of the Earth by the subseismic wave equation.

Exact Traveling‐Wave Solutions for Model Geophysical Systems

Abstract: Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Generations of waves at an inertial surface due to explosions.

Abstract: This paper is concerned with the generation of surface waves by an axially symmetric initial disturbance applied at an inertial surface in an ocean of finite depth. This initial disturbance can be either in the form of an impulse or an elevation or depression. The depression of the inertial surface is obtained as an infinite integral in each case. The method of stationary phase is applied to evaluate the integral for large values of time and distance.

Low-frequency oscillations of rotating massive stars

Abstract: Stellar rotation significantly modifies the property of nonradial oscillations when the frequencies (in the co-rotating frame) are comparable to or less than the frequency of rotation. The angular dependence of the amplitude of such an oscillation cannot be expressed by a single spherical harmonic, Ylm (θ, φ). The amplitude of a g-mode tends to be confined to a narrow equatorial region compared to the non-rotating case. In addition to g-modes, which exist in a radiative equilibrium region, inertial (oscillatory convective) modes exist in a convective region. Half of the inertial modes have negative energy, while all the g-modes have positive energy. When the oscillation frequency of a positive energy mode is close to that of a negative energy mode, resonance coupling between the two modes occurs and energy flows from the negative energy mode to the positive one to increase the amplitude of both modes; i.e., to lead to the overstability of the oscillations. Therefore, overstable g-mode oscillations are possible for all rotating stars with inner convective and outer radiative regions. The resonance excitation of g-modes in the radiative envelope by inertial oscillations in the rotating convective core give natural explanation for rapid variations of early type stars. From observed periods of a variable early type star we can obtain information on the superadiabatic temperature gradient and the angular rotation frequency of the convective core.

Asymptotic analysis of inertial waves in the convective envelope of the sun

Abstract: Inertial waves are propagative in convective regions of rotating stars. Half of the inertial waves have positive energy of oscillations and the other half negative energy. The inertial waves with negative energy become overstable when they are in resonance with waves having positive energy such as internal gravity waves or when they dissipate energy of oscillations through nonadiabatic effects. We calculate a frequency spectrum of inertial (oscillatory convective) modes with negative energy propagating in the surface convective zone of the sun by using an asymptotic method of nonradial oscillations of rotating stars. It is shown that the inertial modes have large amplitudes only at high latitudes. The inertial modes with negative energy have very low frequencies seen in the corotating frame and hence if they are observed in an inertial frame their frequencies are approximately equal to −mΩ⊙.

Long progressive waves in rotating fluid

Abstract: We propose a general theoretical framework which emcompasses all possible long progressive waves in rotating fluid, whether in a channel or in an infinite or semi-infinite ocean. There are different governing equations depending upon the value of the Coriolis parameter (f). When f is large, we find either nonlinear solitary Kelvin waves or nonlinear Poincare waves in a channel, or nonlinear Sverdrup waves in an infinite ocean. But in the latter, there are no solitary waves in an infinite ocean. When f is small, such waves may exist. For intermediate values of f, there are either solitary waves with a horizontal crest in an infinite ocean, or Poincare type of waves in a channel. In that last case, we recover the equation first established by Grimshaw and Melville (1989).