Showing papers on "Inertial wave published in 1985"

Near-Inertial Wave Propagation In Geostrophic Shear

Abstract: An approximate dispersion relation for near-inertial internal waves propagating in geostrophic shear is formulated that includes straining by the mean flow shear. Near-inertial and geostrophic motions have similar horizontal scales in the ocean. This implies that interaction terms involving mean flow shear of the form (v·Δ)V as well as the mean flow itself [(V·Δ)v] must be retained in the equations of motion. The vorticity ζ shifts the lower bound of the internal waveband from the planetary value of the Coriolis frequency f to an effective Coriolis frequency feπ = f + ζ/2. A ray tracing approach is adopted to examine the propagation behavior of near-inertial waves in a model geostrophic jet. Trapping and amplification occur in regions of negative vorticity where near-inertial waves' intrinsic frequency &omega0 can be less than the effective Coriolis frequency of the surrounding ocean. Intense downward-propagating near-inertial waves have been observed at the base of upper ocean negative vorticity...

Effect of rotation on isotropic turbulence - Computation and modelling

Abstract: This paper uses numerical simulation to analyse the effects of uniform rotation on homogeneous turbulence. Both large-eddy and full simulations were made. The results indicate that the predominant effect of rotation is to decrease the rate of dissipation of the turbulence and increase the lengthscales, especially those along the axis of rotation. These effects are a consequence of the reduction, due to the generation of inertial waves, of the net energy transfer from large eddies to small ones. Experiments are also influenced by a more complicated interaction between the rotation and the wakes of the turbulence-generating grid which modifies the nominal initial conditions in the experiment. The latter effect is accounted for in simulations by modifying the initial conditions. Finally, a two-equation model is proposed that accounts for the effects of rotation and is able to reproduce the experimental decay of the turbulent kinetic energy.

Mechanics of continua and wave dynamics

Abstract: I Theory of Elasticity.- 1. The Main Types of Strain in Elastic Solids.- 1.1 Equations of Linear Elasticity Theory.- 1.1.1 Hooke's Law.- 1.1.2 Differential Form of Hooke's Law. Principle of Superposition.- 1.2 Homogeneous Strains.- 1.2.1 An Elastic Body Under the Action of Hydrostatic Pressure.- 1.2.2 Longitudinal Strain with Lateral Displacements Forbidden.- 1.2.3 Pure Shear.- 1.3 Heterogeneous Strains.- 1.3.1 Torsion of a Rod.- 1.3.2 Bending of a Beam.- 1.3.3 Shape of a Beam Under Load.- 1.4 Exercises.- 2. Waves in Rods, Vibrations of Rods.- 2.1 Longitudinal Waves.- 2.1.1 Wave Equation.- 2.1.2 Harmonic Waves.- 2.2 Reflection of Longitudinal Waves.- 2.2.1 Boundary Conditions.- 2.2.2 Wave Reflection.- 2.3 Longitudinal Oscillations of Rods.- 2.4 Torsional Waves in a Rod. Torsional Vibrations.- 2.5 Bending Waves in Rods.- 2.5.1 The Equation for Bending Waves.- 2.5.2 Boundary Conditions. Harmonic Waves.- 2.5.3 Reflection of Waves. Bending Vibrations.- 2.6 Wave Dispersion and Group Velocity.- 2.6.1 Propagation of Nonharmonic Waves.- 2.6.2 Propagation of Narrow-Band Disturbances.- 2.7 Exercises.- 3. General Theory of Stress and Strain.- 3.1 Description of the State of a Deformed Solid.- 3.1.1 Stress Tensor.- 3.1.2 The Strain Tensor.- 3.1.3 The Physical Meaning of the Strain Tensor's Components.- 3.2 Equations of Motion for a Continuous Medium.- 3.2.1 Derivation of the Equation of Motion.- 3.2.2 Strain-Stress Relation. Elasticity Tensor.- 3.3 The Energy of a Deformed Body.- 3.3.1 The Energy Density.- 3.3.2 The Number of Independent Components of the Elasticity Tensor.- 3.4 The Elastic Behaviour of Isotropic Bodies.- 3.4.1 The Generalized Hooke's Law for an Isotropic Body.- 3.4.2 The Relationship Between Lame's Constants and E and v.- 3.4.3 The Equations of Motion for an Isotropic Medium.- 3.5 Exercises.- 4. Elastic Waves in Solids.- 4.1 Free Waves in a Homogeneous Isotropic Medium.- 4.1.1 Longitudinal and Transverse Waves.- 4.1.2 Boundary Conditions for Elastic Waves.- 4.2 Wave Reflection at a Stress-Free Boundary.- 4.2.1 Boundary Conditions.- 4.2.2 Reflection of a Horizontally Polarized Wave.- 4.2.3 The Reflection of Vertically Polarized Waves.- 4.2.4 Particular Cases of Reflection.- 4.2.5 Inhomogeneous Waves.- 4.3 Surface Waves.- 4.3.1 The Rayleigh Wave.- 4.3.2 The Surface Love Wave.- 4.3.3 Some Features of Love's Waves.- 4.4 Exercises.- 5. Waves in Plates.- 5.1 Classification of Waves.- 5.1.1 Dispersion Relations.- 5.1.2 Symmetric and Asymmetric Modes.- 5.1.3 Cut-Off Frequencies of the Modes.- 5.1.4 Some Special Cases.- 5.2 Normal Modes of the Lowest Order.- 5.2.1 Quasi-Rayleigh Waves at the Plate's Boundaries.- 5.2.2 The Young and Bending Waves.- 5.3 Equations Describing the Bending of a Thin Plate.- 5.3.1 Thin Plate Approximation.- 5.3.2 Sophie Germain Equation.- 5.3.3 Bending Waves in a Thin Plate.- 5.4 Exercises.- II Fluid Mechanics.- 6. Basic Laws of Ideal Fluid Dynamics.- 6.1 Kinematics of Fluids.- 6.1.1 Eulerian and Lagrangian Representations of Fluid Motion.- 6.1.2 Transition from One Representation to Another.- 6.1.3 Convected and Local Time Derivatives.- 6.2 System of Equations of Hydrodynamics.- 6.2.1 Equation of Continuity.- 6.2.2 The Euler Equation.- 6.2.3 Completeness of the System of Equations.- 6.3 The Statics of Fluids.- 6.3.1 Basic Equations.- 6.3.2 Hydrostatic Equilibrium. Vaisala Frequency.- 6.4 Bernoulli's Theorem and the Energy Conservation Law.- 6.4.1 Bernoulli's Theorem.- 6.4.2 Some Applications of Bernoulli's Theorem.- 6.4.3 The Bernoulli Theorem as a Consequence of the Energy-Conservation Law.- 6.4.4 Energy Conservation Law in the General Case of Unsteady Flow.- 6.5 Conservation of Momentum.- 6.5.1 The Specific Momentum Flux Tensor.- 6.5.2 Euler's Theorem.- 6.5.3 Some Applications of Euler's Theorem.- 6.6 Vortex Flows of Ideal Fluids.- 6.6.1 The Circulation of Velocity.- 6.6.2 Kelvin's Circulation Theorem.- 6.6.3 Helmholtz Theorems.- 6.7 Exercises.- 7. Potential Flow.- 7.1 Equations for a Potential Flow.- 7.1.1 Velocity Potential.- 7.1.2 Two-Dimensional Flow. Stream Function.- 7.2 Applications of Analytical Functions to Problems of Hydrodynamics.- 7.2.1 The Complex Flow Potential.- 7.2.2 Some Examples of Two-Dimensional Flows.- 7.2.3 Conformal Mapping.- 7.3 Steady Flow Around a Cylinder.- 7.3.1 Application of Conformal Mapping.- 7.3.2 The Pressure Coefficient.- 7.3.3 The Paradox of d'Alembert and Euler.- 7.3.4 The Flow Around a Cylinder with Circulation.- 7.4 Irrotational Flow Around a Sphere.- 7.4.1 The Flow Potential and the Particle Velocity.- 7.4.2 The Induced Mass.- 7.5 Exercises.- 8. Flows of Viscous Fluids.- 8.1 Equations of Flow of Viscous Fluid.- 8.1.1 Newtonian Viscosity and Viscous Stresses.- 8.1.2 The Navier-Stokes Equation.- 8.1.3 The Viscous Force.- 8.2 Some Examples of Viscous Fluid Flow.- 8.2.1 Couette Flow.- 8.2.2 Plane Poiseuille Flow.- 8.2.3 Poiseuille Flow in a Cylindrical Pipe.- 8.2.4 Viscous Fluid Flow Around a Sphere.- 8.2.5 Stokes' Formula for Drag.- 8.3 Boundary Layer.- 8.3.1 Viscous Waves.- 8.3.2 The Boundary Layer. Qualitative Considerations.- 8.3.3 Prandl's Equation for a Boundary Layer.- 8.3.4 Approximate Theory of a Boundary Layer in a Simple Case.- 8.4 Exercises.- 9. Elements of the Theory of Turbulence.- 9.1 Qualitative Considerations. Hydrodynamic Similarity.- 9.1.1 Transition from a Laminar to Turbulent Flow.- 9.1.2 Similar Flows.- 9.1.3 Dimensional Analysis and Similarity Principle.- 9.1.4 Flow Around a Cylinder at Different Re.- 9.2 Statistical Description of Turbulent Flows.- 9.2.1 Reynolds' Equation for Mean Flow.- 9.2.2 Turbulent Viscosity.- 9.2.3 Turbulent Boundary Layer.- 9.3 Locally Isotropic Turbulence.- 9.3.1 Properties of Developed Turbulence.- 9.3.2 Statistical Properties of Locally Isotropic Turbulence.- 9.3.3 Kolmogorov's Similarity Hypothesis.- 9.4 Exercises.- 10. Surface and Internal Waves in Fluids.- 10.1 Linear Equations for Waves in Stratified Fluids.- 10.1.1 Linearization of the Hydrodynamic Equations.- 10.1.2 Linear Boundary Conditions.- 10.1.3 Equations for an Incompressible Fluid.- 10.2 Surface Gravity Waves.- 10.2.1 Basic Equations.- 10.2.2 Harmonic Waves.- 10.2.3 Shallow- and Deep-Water Approximations.- 10.2.4 Wave Energy.- 10.3 Capillary Waves.- 10.3.1 "Pure" Capillary Waves.- 10.3.2 Gravity-Capillary Surface Waves.- 10.4 Internal Gravity Waves.- 10.4.1 Introductory Remarks.- 10.4.2 Basic Equation for Internal Waves. Boussinesq Approximation.- 10.4.3 Waves in an Unlimited Medium.- 10.5 Guided Propagation of Internal Waves.- 10.5.1 Qualitative Analysis of Guided Propagation.- 10.5.2 Simple Model of an Oceanic Waveguide.- 10.5.3 Surface Mode. "Rigid Cover" Condition.- 10.5.4 Internal Modes.- 10.6 Exercises.- 11. Waves in Rotating Fluids.- 11.1 Inertial (Gyroscopic) Waves.- 11.1.1 The Equation for Waves in a Homogeneous Rotating Fluid.- 11.1.2 Plane Harmonic Inertial Waves.- 11.1.3 Waves in a Fluid Layer. Application to Geophysics.- 11.2 Gyroscopic-Gravity Waves.- 11.2.1 General Equations. The Simplest Model of a Medium.- 11.2.2 Classification of Wave Modes.- 11.2.3 Gyroscopic-Gravity Waves in the Ocean.- 11.3 The Rossby Waves.- 11.3.1 The Tangent of ?-Plane Approximation.- 11.3.2 The Barotropic Rossby Waves.- 11.3.3 Joint Discussion of Stratification and the ?-Effect.- 11.3.4 The Rossby Waves in the Ocean.- 11.4 Exercises.- 12. Sound Waves.- 12.1 Plane Waves in Static Fluids.- 12.1.1 The System of Linear Acoustic Equations.- 12.1.2 Plane Waves.- 12.1.3 Generation of Plane Waves. Inhomogeneous Waves.- 12.1.4 Sound Energy.- 12.2 Sound Propagation in Inhomogeneous Media.- 12.2.1 Plane Wave Reflection at the Interface of Two Homogeneous Media.- 12.2.2 Some Special Cases. Complete Transparency and Total Reflection.- 12.2.3 Energy and Symmetry Considerations.- 12.2.4 A Slowly-Varying Medium. Geometrical-Acoustics Approximation.- 12.2.5 Acoustics Equations for Moving Media.- 12.2.6 Guided Propagation of Sound.- 12.3 Spherical Waves.- 12.3.1 Spherically-Symmetric Solution of the Wave Equation.- 12.3.2 Volume Velocity or the Strength of the Source. Reaction of the Medium.- 12.3.3 Acoustic Dipole.- 12.4 Exercises.- 13. Magnetohydrodynamics.- 13.1 Basic Concepts of Magnetohydrodynamics.- 13.1.1 Fundamental Equations.- 13.1.2 The Magnetic Pressure. Freezing of the Magnetic Field in a Fluid.- 13.1.3 The Poiseuille (Hartmann) Flow.- 13.2 Magnetohydrodynamic Waves.- 13.2.1 Alfven Waves.- 13.2.2 Magnetoacoustic Waves.- 13.2.3 Fast and Slow Magnetoacoustical Waves.- 13.3 Exercises.- 14. Nonlinear Effects in Wave Propagation.- 14.1 One-Dimensional Nonlinear Waves.- 14.1.1 The Nonlinearity Parameter.- 14.1.2 Model Equation. Generation of Second Harmonics.- 14.1.3 The Riemann Solution. Shock Waves.- 14.1.4 Dispersive Media. Solitons.- 14.2 Resonance Wave Interaction.- 14.2.1 Conditions of Synchronism.- 14.2.2 The Method of Slowly-Varying Amplitudes.- 14.2.3 Multiwave Interaction.- 14.2.4 Nonlinear Dispersion.- 14.3 Exercises.- Appendix: Tensors.- Bibliographical Sketch.

Steady Deep‐Water Waves on a Linear Shear Current

Abstract: The behavior of steady, periodic, deep-water gravity waves on a linear shear current is investigated. A weakly nonlinear approximation for the small amplitude waves is constructed via a variational principle. A local analysis of those large amplitude waves with sharp crests, called extreme waves, is also provided. To construct solutions for all waveheights (especially the limiting ones) a convenient mathematical formulation which involves only the wave profile and some constants of the motion is derived and then solved by numerical means. It is found that for some shear currents the highest waves are not necessarily the extreme waves. Furthermore a certain non-uniqueness in the sense of a fold is shown to exist and a new type of limiting wave is discovered.

Inertial Oscillations due to a Moving Front

Abstract: A solution for a concentrated line front translating at speed U is given. It is shown that the frequency is near-inertial if U≫c1, where c1 is the long internal wave speed of the first baroclinic mode. Each more has a charactristic frequency ωn associated with it. The spectra contain a near-inertial primary peak, composed of the higher modes, whose blue shift increases with depth. They also contain secondary peaks at higher internal wave frequencies if U is only slightly larger than c1. The flow field is intermittent, and involves a continuous interchange of energy between the surface layer and the stratified interior. The dominant period of this intermittency is the beating period of the first mode with a purely inertial oscillation. Short periods of apparent subinertial motion are also generated. Several features of the solution are in agreement with observations.

Viscous flow through a rotating square channel

Abstract: Fully developed flow of an incompressible Newtonian fluid driven by a pressure gradient through a square channel that rotates about an axis perpendicular to the channel roof is analyzed here with the aid of the penalty/Galerkin/finite element method Coriolis force throws fast‐moving fluid in the channel core in the direction of the cross product of the mean fluid velocity with the channel’s angular velocity Two vortex cells form when convective inertial force is weak Asymptotic limits of rectilinear flow and geostrophic plug flow are approached when viscous force or Coriolis force dominates, respectively A flow structure with an ageostrophic, virtually inviscid core is uncovered when Coriolis and convective inertial forces are both strong This ageostrophic two‐vortex structure becomes unstable when the strength of convective inertial force increases past a critical value The two‐vortex family of solutions metamorphoses into a family of four‐vortex solutions at an imperfect bifurcation composed of a pair of turning points

Suppression of Stationary Planetary Waves by Internal Gravity Waves in the Mesosphere

Abstract: The suppression of stationary planetary waves by internal gravity waves in the mesosphere is treated using a quasi-geostrophic model on a midlatitude beta-plane. The drag forces due to internal gravity waves are parameterized based on the wave breaking assumption recently proposed by Lindzen. In the present model the vertical propagation of internal gravity waves is affected not only by mean zonal wind distribution but also by eastward and northward velocity perturbations associated with stationary planetary waves, viz., the total local velocity. Numerical mulls show that the drag force due to breaking internal gravity waves acts like a Rayleigh friction, and the amplitudes of stationary planetary waves in the mesosphere are much reduced by this effect. Equivalent Rayleigh friction coefficients are also presented.

Accretion disk oscillations - A local analysis in a disk of finite thickness

Abstract: Two types of oscillations are observed to occur in dwarf novae: 'coherent' and 'quasi-periodic' oscillations. These may be associated with the pulsation of the white dwarf or the accretion disk components of the dwarf nova. Here a local (short-wavelength) analysis is utilized to study the oscillation of a self-consistent, two-dimensional model of an accretion disk. The linearized equations describing adiabatic, inviscid, nonaxisymmetric oscillations are used to derive a fifth-order algebraic equation for the (complex) pulsation frequency of the disk. The solutions of this equation for various values of the wavevector k reveal that the disk is capable of supporting (1) a pair of high-frequency acoustic modes (p-modes); (2) a pair of intermediate-frequency modes which may share the characteristics of internal gravity waves (g-modes) and inertial waves; and (3) a mode associated with a dynamical instability (purely imaginary frequency). The role played by the shear in determining the stability or instability of these modes is also considered. Finally, the global oscillation frequencies of the disk are discussed.

Inertial oscillations in the solar convection zone. I. Spherical shell model

Abstract: Axisymmetric inertial oscillations, oscillations in which the Coriolis force provides the principal restoring force, are investigated theoretically for a model solar convection zone. The fluid flow equations, describing such oscillations in an adiabatically stratified, differentially rotating spherical shell, are written in the form of a modified eigenvalue problem. The modified eigenvalue equations in finite-difference form are numerically solved on a staggered grid (19 points in radius by 43 points in latitude). Solutions, each consisting of 817 different meridional stream functions (Psi) and corresponding zonal velocities (U), are obtained for several combinations of convection zone depth and rotation profile. We discuss general characteristics of the solutions, as revealed in contour plots of the stream functions and U-velocities. A low-latitude frequency (..omega..) versus latitudinal wavenumber (k) diagram is defined for the oscillations. Ridge structure in this ..omega..-k diagram is found to be sensitive to both the convection zone's depth and its rotation profile. Since the two effects are distinct, observing the oscillations with sufficient frequency and spatial resolution to resolve the ridges in the ..omega..-k diagram will enable an independent determination of the convective envelope's depth and its rotation profile. We discuss the possibilities of observing these modes with the Fourier Tachometer.

On the motion of very small bodies in water waves

Abstract: The equation of motion of a small isolated body that moves in translational motion through a fluid which is itself in unsteady and nonuniform motion is established on the assumption that actual forces acting on the body can be split up in gravity; a drag component, which accounts for viscosity and vorticity effects; and an inertial force with the same formal expression as the force that would act on the body if the flow were irrotational (this force is obtained for an unrestricted irrotational flow in the appendix). By assuming that flow acceleration is small compared with that due to gravity and that ϵ = wƒω/g ≪ 1, which defines what here is called “very small body” (wƒ being still water terminal fall velocity, ω angular frequency, and g acceleration due to gravity), some approximate equations are obtained using a perturbation scheme. Subsequently, a simple expression is derived for the leading order approximation of the velocity of very small bodies in water waves. This solution shows that, at least under certain conditions, the hypothesis of some delay time (Kennedy and Locher, 1972) is sound, although this time is not the same, in general, for the vertical velocity component as for the horizontal one. From a practical point of view, owing to the assumptions involved in this derivation, the applicability of the solution must be restricted to suspended sediment particles in low concentrations and to reasonably well-behaved wave conditions, including superposition of linear waves (particularly standing waves and irregular wave fields), slightly nonlinear waves, and weak currents superimposed on waves. The direct application of the results of this investigation to flows with a high degree of turbulence intensity must be precluded because of the existence of large flow accelerations.

Rotating turbulence evolving freely from an initial quasi 2D state

Abstract: Recent experiments demonstrated the existence of quasi-twodimensional turbulence in a boundary-forced fluid system subjected to strong rotation. The principal results are briefly recalled and an inertial wave mechanism is proposed as an explaination for the observed sudden transition from 3D turbulence to a quasi-twodimensional turbulent flow. The main contribution of the paper is however concerned with the freely evolving state, obtained when the forcing is suddenly stopped. Experiments show an increase in time of the turbulence length scale, indicating an inverse energy flux. These observations are analysed in terms of a similarity theory derived for evolving turbulence with Ekman friction. The scale increase is by pairing of vortices of like sign and by large scale unsteady meandering motions.

Inertial oscillations in the solar convection zone. II. A cylindrical model for equatorial regions

Abstract: We present axisymmetric inertial oscillations found from a simplified, cylindrical model applicable to equatorial latitudes and compare these results with those obtained by numerical methods in Paper I for a spherical shell. The equations for the cylindrical model are solved using analytical methods. We derive analytically the asymptotic behavior of inertial mode frequencies in the limits of very large and very small axial (corresponding to latitudinal) wavenumber and show that inertial oscillations arise only when the angular momentum per unit mass increases outward. We also demonstrate how convection zone depth and differential rotation affect the different radial orders of inertial modes. As in the spherical case, we find that the deeper the layer, the closer together are successive radial orders. We find that in a convection zone 1.5 x 10 cm in depth, rotation rate increasing inward leads to decreased oscillation frequency for a given radial order and axial wavenumber, the opposite of the result for the spherical shell. Deeper zones in the cylindrical case give increased frequencies for rotation rate either decreasing or increasing inward, unless the outermost part of the convection zone is removed from the model. In that case, the cylindrical and spherical shell results agree formore » deep convection zones. The differences in the results between spherical and cylindrical models are shown to be due to the different geometries.« less

Hamiltonian description of almost geostrophic flow

Abstract: Geostrophic flow in the theory of a shallow rotating fluid is exactly analogous to the drift approximation in a strongly magnetized electrostatic plasma. This analogy is developed and exhibited in detailed to derive equations for the slow nearly geostrophic motion. The key ingredient in the theory is the isolation, to whatever order in Rossby number desired, of the fast motion near the inertial frequency. One of the remaining degrees of freedom represents a new approximate constant of the motion for nearly geostrophic flow. This is the analogue of the familiar magnetic moment adiabatic invariant in the plasma problem. The procedure is a Rossby number expansion of the Hamiltonian for the fluid expressed in Lagrangian, rather than Eulerian variables. The fundamental Poisson brackets of the theory are not expanded so desirable properties such as energy conservation are maintained throughout.

Derivation and analysis of a McPhee-like damping term for inertially oscillating ice drift

Abstract: It is shown that the empirical McPhee [8] damping term for inertial oscillations in time-dependent ice-ocean motion can be derived as a first-order correction when the air stress is quadratic in air relative to ice velocity. Analytical expressions are derived for the leading term transient ice and surface oceanic boundary-layer velocities and the mass transport function of a perturbation expansion in a small parameter e[O(10-1)-O(10-2)], the ratio of scale ice speed to air speed.

Magnetohydrodynamic waves in structured atmospheres

Abstract: The effect of structuring, in the form of magnetic or density inhomogeneities, on the magnetohydrodynamic (mhd) waves of an infinite plasma is investigated. The appropriate dispersion formulae, in both Cartesian and cylindrical polar coordinate geometries, are derived. The main properties of the allowable modes in structured plasmas are described, particularly those featuring in a slender inhomogeneity. The inclusion of non-adiabatic effects is examined, specifically for a thermally dissipative, unstratified, finite structure and for a slender inhomogeneity in a stratified medium. The dissipative time scales of slender structures are shown to have a dependence on the Peclet number. Growth factors appropriate to these time scales for the overstable motions of a thermally dissipative, Boussinesq fluid are derived. For the linear analysis of a slender structure it is shown that the dispersive nature of the waves is deducible from the simplified one-dimensional equations. The analysis is extended, for slender structures, to nonlinear motions and the governing equation representing an effective balance between nonlinear, dispersive and dissipative effects, the Benjamin-Ono-Burgers equation, is established. The solutions of this equation are considered and, for weakly-dissipative systems, are shown to be slowly decaying solitons. The importance, in the context of group velocity, of the dispersive nature of waves in ducted structures is discussed and analogies are made with other ducted waves, for example, the Love waves of seismology. It is suggested that the behaviour of such waves, following an impulse, may account for the range of oscillatory behaviour, the quasi-periodic and short time scales, observed in both the solar corona and Earth's magnetosphere. Density variations across a structure and the structure's curvature, with possible applications to coronal loops, are also considered. Further suggestions for possibly identifying some of the theoretical results with observed behaviour in sunspots, chromospheric fibrils and spicules are also made. I Patricia Mary Edwin hereby certify that this thesis has been written by me, that it is the record of work carried out by me, and that it has not been submitted in any previous application for a higher degree. Signature of Candidate Date ... ~~~ ... r~~t .. 4,.~~~ I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate to the degree of [loclor of Philosophy of the University of St Andrev:s and that she is qualified to submit this thesis in "'plication for that degree. Signature of Supervisor Date .... ?-:() ... ~t. .. 1 J.'6. Lf I was admitted as a research student under Ordinance No 12 in October, 1979 and as a candidate for the degree of Ph.D. in October, 1980; the higher study for which this is a record was carried out in the Uni versi ty of St Andrevis between 1979 and 1984. Signature of Candidate

Shuttle Contamination Modeling: The Plasma Wave Field of Spacecraft.

Abstract: : We investigate the behavior of waves and shock-like disturbances produced by the interaction of spacecraft with the plasma environment. We find that (1) there are tree ranges of wave frequency for which waves can propagate to large distances from the spacecraft, (2) that waves in these frequency ranges are confined to propagate within specific ranges of directions, and (3) that it is possible for these waves to form shocks. Approximate analytic solutions are given to describe the behavior of waves and shocks of spacecraft origin. The waves that are important to these phenomena can be classed as Alfven, whistler, and upper hybrid waves. While we believe it unlikely to occur, we have identified analystically those conditions necessary for extremely rapid spatial wave growth near the spacecraft. Keywords include: Shock waves, Alfven waves, Whistler waves, Upper hybrid waves, and Plasma waves.

Resonantly Forced Rossby Waves

Abstract: A shallow, rotating layer of fluid that supports Rossby waves is subjected to turbulent friction through an Ekman layer at the bottom and is driven by a wave that exerts a shear stress on the upper boundary and for which the phase approximate that of a Rossby wave. The steady-state response may be either 1) a single wave that is synchronous with the driving wave or 2) a resonant triad of waves, one of which is synchronous with the driving wave. The triadic solutions constitute a one-parameter family, of which not more than one member is stable. The evolution equations for the slowly varying complex amplitudes of the responding waves, the fixed points of which correspond to the solutions 1) and 2), are established. The stability of these fixed points, and hence the stability boundaries for 1) and 2), are determined. There are no Hopf bifurcations of the fixed-point solutions, and the evolution equations apparently do not admit periodic (limit cycle), multiply periodic or chaotic solutions.