Showing papers on "Inertial wave published in 1992"

Breakdown regimes of inertia waves in a precessing cylinder

Abstract: A series of experimental studies have been made of the fluid behaviour in a completely filled, precessing, right circular cylinder. The tank was spun about its axis of symmetry and subjected to a forced precession at various excitation frequencies ω, nutation angles θ and at various Ekman numbers. This forcing excites a subset of the modes, called inertia waves, that are made possible by the Coriolis force that arises in a spinning environment. In these experiments, the fluid flow breakdown phenomena are investigated. Here the fluid, when forced near a resonant frequency, exhibits a transition to disordered or turbulent flow. This paper presents a categorization of some of the breakdown regimes, of which the ‘resonant collapses’ (McEwan 1970) are the most catastrophic members.The studies reported in this paper used entirely visual observations and measurements. The experimental observations employed a visualization technique that gave no information on fluid velocities, but provided an excellent picture of the flow structure. Quantitative data were extracted in the form of the time for the breakdown to occur. The breakdown phenomena, while readily produced over a large region of parameter space, are complex and varied. The observations show that our system is extraordinarily rich, exhibiting, for example, recurrent breakdowns which may be explained in terms of chaotic intermittency. A detailed description of some of the different breakdown regimes indicates that no single model will explain the behaviour throughout parameter space. This research is motivated by the instability problems of spinning spacecraft containing liquid fuels.

Storage of magnetic flux tubes in a convective overshoot region

Abstract: The suppression of the radial and polar escape of magnetic flux in form of toroidal flux tubes (flux rings) from low latitudes in the overshoot region below the solar convection zone through the combined action of the subadiabatic ambient stratification and the rotationally induced forces is considered. It is shown that a flux ring which is initially in thermal equilibrium with its environment and rotates with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding, non-magnetic gas. Flux rings perform superposed buoyancy and inertial oscillations around their equilibrium positions

Inertial Instability and Rossby Wave Breaking in a Numerical Model

Abstract: A mechanistic model of the middle atmosphere is used to study the interaction between Rossby waves forced at the extratropical tropopause and inertial instability in the equatorial lower mesosphere. The impact of cross-equatorial shear strength and Rossby wave forcing amplitude is explored. Model results support the hypothesis, based on satellite temperature observations, that Rossby waves organize regions of equatorial inertial instability into coherent large-scale circulations. Horizontal convergence and divergence maxima are found stacked over the boundaries of regions of anomalous potential vorticity (PV). This supports observational diagnoses and theoretical expectations that parcel inertial accelerations arise in regions of anomalous PV, with divergence and convergence occurring at the boundaries. Although cross-equatorial shear determines the initial volume of inertially unstable air, Rossby waves arriving from the winter hemisphere deform PV contours such that zonally confined regions of ...

Consequences of rotation in energetics of accretion disks

Abstract: A synthesis on recent results about rotating turbulence is done. They prove that rotation tends to inbibit energy transfer from large scales to small scales because of the generation of strong inertial waves aligned with the rotation axis. Implications on the theory of turbulent transport in accretion disks are discussed. It is argued that the concept of turbulent viscosity should be revisited to take into account the possibility of nonlocal transport by large scale wave-dominated turbulence. An energetic puzzle resulting from a possible inverse cascade of energy is brought out

Deriving inertial wave characteristics from surface drifter velocities: Frequency variability in the tropical Pacific

Abstract: Two techniques were developed for estimating statistics of inertial oscillations from satellite-tracked drifters that overcome the difficulties inherent in estimating such statistics from data dependent upon space coordinates that are a function of time. Application of these techniques to tropical surface drifter data collected during the NORPAX, EPOCS, and TOGA programs reveals a latitude-dependent, statistically significant 'blue shift' of inertial wave frequency. The latitudinal dependence of the blue shift is similar to predictions based on 'global' internal-wave spectral models, with a superposition of frequency shifting due to modification of the effective local inertial frequency by the presence of strongly sheared zonal mean currents within 12 deg of the equator.

Chaotic Trajectories of Tidally Perturbed Inertial Oscillations

Abstract: It is shown that tidal perturbations of a geopotential height in an inviscid, barotropic atmosphere can turn a purely inertial, predictable trajectory of a Lagrangian particle chaotic. Hamiltonian formulation of both the free, inertial, and the tidally forced problems permitted the application of the twist and KAM theorems, which predicts the existence of chaotic trajectories in the latter case The chaotic behavior manifests itself in extreme sensitivity of both the trajectory and the energy spectra to initial conditions and to the precise value of the perturbation's amplitude. In some cases dispersion of initially close particles can be very fast, with an e-folding time of the rms particle separation as high as one day. A vigorous mixing is induced by the chaotic advection associated with the tidal forcing through the stretching and folding of material surfaces.

A finite-element method for inertial waves in a frustum

Abstract: A finite-element method has been developed to model inertial waves in a frustum of a cone, since analytical methods have proved inadequate. The governing Poincar6 problem is posed as a variational principle and approximate eigensolutions are computed. The numerical results are used to complete the interpretation of the experimental results of Beardsley (1970) for a frustum of a cone. The significant role played by characteristic surfaces partly explains the enigmatic nature of the ill-posed boundary-value problem that describes inertial wave resonances.

On inertial waves in the Earth's fluid core

Abstract: New classes of inertial oscillation mode in the form of equatorially trapped boundary waves are discovered The structure and frequency of the waves are hardly affected by the presence of an inner sphere if the azimuthal wavenumber where η = ri/ro, the radius ratio of a spherical shell Also discovered is that equatorially symmetric inertial waves belong to particular subclasses of thermal instabilities The problem of the inertial waves can therefore be understood within the framework of instability theory The findings provide valuable insights into many geophysical phenomena, not only for the Earth's fluid core but atmospheres and oceans as well

Eigenfunction expansion of the flow in a spinning and nutating cylinder

Abstract: Spin‐stabilized projectiles with liquid payloads may experience different types of flight instabilities caused by the fluid motion in the payload cylinder. The first type is known to occur in low viscosity fluids, i.e., at high Reynolds numbers owing to resonance with inertial waves at critical frequencies. The second type originates from a forced secondary flow at arbitrary frequency and is most pronounced for fluids of high viscosity, i.e., relatively low Reynolds numbers. In this paper a method is developed that permits unified analysis of both types of instability since it can be used for flows at high Reynolds numbers inaccessible to other approaches. The method is based on a spatial eigenfunction expansion of the axial velocity component and reduces the three‐dimensional problem to one dimension. The eigenfunctions are given in closed form and the eigenvalues are determined numerically by solving a system of nonlinear equations.

Inertial mode oscillations of Jupiter

Abstract: The properties of the inertial modes of Jupiter are investigated using several different models for that planet. The inertial modes are rotationally induced oscillation modes for which the kinetic energy generally dominates the potential energy of oscillation. The frequency spectrum of the inertial modes mainly depends on the density stratification of Jupiter and sensitively reflects the existence or nonexistence of density discontinuities in the interior. A particularly interesting consequence of the calculations is that observations of the inertial oscillations of Jupiter may enable us to determine whether or not the dense hydrogen in the envelope of this planet undergoes the plasma phase transition (PPT). This may provide an astrophysical test of current theories of the thermodynamic properties of dense hydrogen. It is also found that the discontinuity modes associated with the PPT have observable amplitdues at the surface. These modes may provide an independent test of the interior structure of Jupiter.

Experimental and Field Research Statistical characteristics and the variability of currents over the western Black Sea shelf

Abstract: Statistical characteristics and the parameters of the temporal variability of currents are analysed using data on current measurements conducted by five moored autonomous buoy stations over Bulgaria's shelf. Estimates of the specific contribution to the variability of synoptic (60%) and mesoseale (40%) oscillations are derived. The qualitative spectrum of the currents is defined, constituted by synoptic osciUa- tions, short-period synoptic oscillations, inertial oscillations, and internal waves. Estimates of periods and oscillation amplitudes are also derived. The kinetic energy of the currents is calculated and the specific contribution of the energy of different-scale oscillations and their interrelations are determined. The pattern of currents in the coastal (shelf) Black Sea area is extremely complicated as the currents evolve as a result of the effect of multiple factors, among which the fol- lowing are the most important: synoptic eddies, inertial and breeze oscillations, internal waves, and piling up. The currents have been best studied off the Caucasian shore, pri- marily owing to the lengthy (5.5 years) continual hourly observations by stabilized buoys (1,2) and by the numerous moored autonomous buoy stations occupied from 1955 to 1984 (3). As these measurements show, a specific regime of coastal currents appears as follows. The main Black Sea current stream travels some 13-15 miles off the Caucasian shore. A horizontal anticyclonic (clockwise) vorticity occurs to the right of the current (between the mainstream and the shore) and a cyclonic one evolves to the left of it (in the open sea). This prompts the generation of anticyclonic and cyclonic eddies on the right-hand side (in the coastal zone) and on the left-hand side of the mainstream, re- spectively. During the transition of the anticyclonic eddies, the current, being affected by the orbital vortical motion, reverses its direction in the coastal area and then the main Black Sea current reconstructs itself and resumes its original direction. As the anticyclonic eddies travel regularly along the shore, the currents in the coastal area appear as essentially cyclic, reciprocal motions of water oriented predominantly along the shoreline, the probability of the direction distribution being of bimodel type (1, 3). Since the main Black Sea current follows the entire Black Sea coast, it may be sup- posed that such a regime of coastal currents is also characteristic of the other sections of the basin, for example, of Bulgaria's shelf zone, this deduction being supported by the available, though scarce, experimental data (4), as well as by the diagnostic calculations of currents (5). This paper examines the currents' characteristics over Bulgaria's shelf area observed in the course of a joint Soviet-Bulgarian oceanographic expedition from September to October 1976, during which long series of current measurements (16-32 days) by five autonomous buoy stations were made. The arrangement of the buoy stations is shown

The propagation and stability of linear wave motions in rapidly rotating spherical shells: Weak magnetic fields

Abstract: +The propagation properties and stability of wave motions in a spherical fluid shell, rotating uniformly in a co-rotating zonal magnetic field, are studied. Various profils of magnetic field and temperature gradient are examined. The fluid is viscous and electrically and thermally conducting. The analysis is applicable when the rotation rate is very high and the Elsasser number A 1. (Λ measures the ratio of Lorentz to Coriolis forces). The wave motions occur in the form of annular cylindrical cells whose thickness is determined by the rotation rate and magnetic field amplitude (Eltayeb and Kumar, 1977). It is shown that an infinity of modes exists and both westward and eastward phase propagation is possible.

Statistical characteristics and the variability of currents over the western Black Sea shelf

Abstract: Statistical characteristics and the parameters of the temporal variability of currents are analysed using data on current measurements conducted by five moored autonomous buoy stations over Bulgaria's shelf. Estimates of the specific contribution to the variability of synoptic (60%) and mesoscale (40%) oscillations are derived. The qualitative spectrum of the currents is defined, constituted by synoptic oscillations, short-period synoptic oscillations, inertial oscillations, and internal waves. Estimates of periods and oscillation amplitudes are also derived. The kinetic energy of the currents is calculated and the specific contribution of the energy of different-scale oscillations and their interrelations are determined.

The influence of inertial waves on the structure of vortex cores

Abstract: The paper reports on numerical results concerning the influence of waves in the hollow core of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom. The numerical algorithm used was based on the Los Alamos SOLA-VOF algorithm. The computations produced free-surface elevation profiles that agree closely with the experiments. The computed secondary toroidal vortex structures, taking place in the radial-azimuthal plane, and the vortex core wandering during the spin-up process correspond to experimental visualizations. Under prevailing conditions the numerical solutions show that the core surface is modulated by a single or the superposition of waves. In the future, the developed scheme might enable one to construct the state manifold.

Numerical experiments on the tropical air-sea interaction waves

Abstract: By means of the numerical method,the tropical air-sea interaction waves are studied.The results show that whenthe Kelvin waves are filtered out and only the equatorial Rossby waves are reserved both in the atmosphere and in theocean,the disturbances can also propagate eastward because of the air-sea interaction.The critical wavelength of theeastward propagating waves is related to the intensity of the air-sea interaction.The stronger the air-sea interaction,thelarger the eastward propagating components of the air-sea interaction waves.The results of the numerical experimentsare in good agreement with those of the theoretical analysis(Chao and Zhang,1988).

PDF turbulence modeling and DNS

Abstract: The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

The propagation of inertia-gravity waves and their influence on zonal mean flow part two: Wave breaking and critical levels

Abstract: The gravity wave breaking is crucial to the large-scale circulation of middle atmosphere. In this paper, we follow Lindzen (1981) to draw out the parameterization of two-dimensional gravity wave breaking including inertial effect. Also we present some properties of critical levels and inertial critical levels.