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At least 109 records · Page 6

An analysis of the stability of the compressible Ekman boundary layer

The linear stability problem for the compressible Ekman boundary layer common to rotating fluids is formulated and the stability properties determined numerically. Three classes of unstable waves are identified (called class A, B, and C), their properties are described. The class C waves have only recently been reported in the literature and are present only in compressible Ekman boundary layers. Most of the calculations presented here are for uranium hexafluoride gas; however, critical Reynolds numbers are also computed for air and ammonia gas. Compressibility is generally found to decrease the critical Reynolds number for each class of wave. A comparison of results for the three different gases shows the stability to be largely unaffected by changes in the gas properties. Maximum growth rate calculations for each wave show the class A and B waves to be the dominant instabilities.

Spall, J. R.↗

The Hadley and Rossby regimes in a spherical atmosphere

The properties of the steady Hadley and Rossby regimes for a thermally forced rotating fluid on a sphere are studied. The two layer modified geostrophic model is employed which allows for thermal advection by the divergent wind and time dependent static stability. Heating processes are parameterized using the Newtonian approximation and Rayleigh friction is accounted for. The equations are transformed to spectral form using spherical harmonics and then truncated retaining a simple axisymmetric state and initial, one wave. A time independent Hadley circulation is obtained which is neutral to axisymmetric disturbances but unstable to wave like perturbations for intermediate values of the meridional temperature gradient, indicating the existence of both an upper and lower symmetric Hadley regime. An analytical solution for the steady Rossby circulation is determined for values of the meridional temperature gradient where the Hadley regime is unstable. Linear perturbation theory is used to show that within the steady Rossby regime two or more waves cannot exist simultaneously.

Feldstein, S. B.↗

Convection without eddy viscosity: An attempt to model the interiors of giant planets

In the theory of hydrostatic quasi-geostrophic flow in the Earth's atmosphere the principal results do not depend on the eddy viscosity. This contrasts with published theories of convection in deep rotating fluid spheres, where the wavelength of the fastest growing disturbance varies as E sup 1/3, where E, the Ekman number, is proportional to the eddy viscosity. A new theory of quasi-columnar motions in stably stratified fluid spheres attempts to capture the luck of the meteorologists. The theory allows one to investigate the stability of barotropic and baroclinic zonal flows that extend into the planetary interior. It is hypothesized that the internal heat Jupiter and Saturn comes out not radially but on sloping surfaces defined by the internal entropy distribution. To test the hypothesis one searches for basic states in which the wavelength of the fastest-growing disturbance remains finite as E tends to zero, and is which the heat flux vector is radially outward and poleward.

Ingersoll, A. P.↗

Quasi-geostrophic free mode models of long-lived Jovian eddies: Forcing mechanisms and crucial observational tests

Observations of Jupiter and Saturn long-lived eddies, such as Jupiter's Great Red Spot and White Ovals, are presently compared with laboratory experiments and corresponding numerical simulations for free thermal convection in a rotating fluid that is subject to horizontal differential heating and cooling. Difficulties in determining the essential processes maintaining and dissipating stable eddies, on the basis of global energy budget studies, are discussed; such difficulties do not arise in considerations of the flow's potential vorticity budget. On Jupiter, diabatically forced and transient eddy-driven flows primarily differ in the implied role of transient eddies in transporting potential vorticity across closed geostrophic streamlines in the time mean.

Read, P. L.↗

Nonaxisymmetric instabilities in rotating shear flows - Internal gravity modes in stratified media and analogies with plane flows

The role of the internal gravity modes in mediating the growth of nonaxisymmetric instabilities is investigated by studying the instability of stratified incompressible differentially rotating fluid cylinders to global nonaxisymmetric modes. The results indicate that, in addition to a modified version of the well-known principal branch mediated by surface modes of the system (analogous to f-modes of stars), there exist unstable branches of the dispersion relation mediated by internal gravity modes of the system (similar to the g-modes of stars). These branches arise due to the interaction between the g-modes. It is shown that the maximum growth rate on one of the new branches can sometimes equal or exceed that on the principal branch, thus modifying the principal branch.

Ghosh, P.↗

GASCAN 2 payload integration

This MQP is an ongoing part of the NASA Advanced Space Design Program which examines the integration of the WPI/MITRE Get Away Special Canister (GASCan 2). GASCan 2 contains the Ionospheric Properties and Propagation, Micro-Gravity Ignition, and Rotational Fluid Flow experiments, as well as the integrated support structure. The objectives this year were to finalize the power supply system, connections for experiments, mechanical design of the IPPE's antenna, and to update the structural and vibrational analysis of the integrated support structure.

Brown, Henry B., Jr.↗

Parasitic instabilities in magnetized, differentially rotating disks

Velikhov, Chandrasekhar, Balbus & Hawley have discovered a MHD instability of differentially rotating fluids that may explain the effective viscosity of accretion disks. If the unperturbed magnetic energy density is much less than the gas pressure, this `magnetorotational' instability (MRI) arises on small scales and is approximately incompressible. If the unperturbed field is suffiently, strong, the MRI is suppressed. We therefore ask whether the MRI mechanism can amplify even very weak initial fields until they reach equipartition with the gas pressure. We show that in the total incompressible limit, the MRI modes are exact solutions of the nonlinear fluid equations, even if the perturbed magnetic field is much larger than the unperturbed field. Also, we present a new exact solution in the opposite limit that the magnetic pressure is much larger than that of the gas. On the other hand, we show that the incompressible MRI modes are themselves subject to parasitic instabilities with instantaneous growth rates proportional to the MRI amplitude. Some of the parasitic instabilities are of the Kelvin-Helmholtz type, while others are less familiar. The eigenfunctions of the latter group suggest that they may promote rapid reconnection of the MRI field. Thus, parasitic modes may stop MRI growth at subequipartition amplitudes if it developes from a sufficiently weak initital field.

Goodman, Jeremy↗

GASCan 2 payload integration

This project, conducted in cooperation with the NASA Advanced Space Design Program, is part of an ongoing effort to place an experiment package into space. The goal of this project is to build and test flight-ready hardware that can be launched from the Space Shuttle. Get Away Special Canister 2 (GASCan 2) consists of three separate experiments. The Ionospheric Properties and Propagation Experiment (IPPE) determines effects of the ionosphere on radio wave propagation. The Microgravity Ignition experiment (MGI) tests the effects of combustion in a microgravity environment. The Rotational Fluid Flow experiment (RFF) examines fluid behavior under varying levels of gravity. This year the following tasks were completed: design of the IPPE antenna, X- and J-cell battery boxes, J-cell battery box enclosure, and structural bumpers; construction of the MGI canisters, MGI mounting brackets, IPPE antenna, and battery boxes; and the selection of the RFF's operating fluid and the analysis of the fluid behavior under microgravity test conditions.

Cody, Dennis J.↗

On Multiple-Layered Vortices

As part of an ongoing effort to find ways to make vortex flow fields decompose more quickly, photographs and observations are presented of vortex flow fields that indicate the presence of multiple layers of fluid rotating about a common axis. A survey of the literature indicates that multiple-layered vortices form in waterspouts, tornadoes and lift-generated vortices of aircraft. An explanation for the appearance of multiple-layered structures in vortices is suggested. The observations and data presented are intended to improve the understanding of the formation and persistence of vortex flow fields.

Rossow, Vernon J.↗

Passive Stabilization of Rotating Spacecraft Using Dynamic Fluid-Pressure Equilibrium

Rotating spacecraft can provide artificial gravity for long-term space missions, but the design of a Guidance and Control scheme for these vehicles is nuanced. For a three-segment vehicle with the propulsion element located at the center of mass, the vehicle must stabilize itself about this point even in the event of various off-nominal circumstances. Thus, a robust and passive spin stabilization system is needed. In this paper, the dynamics of this system are explored and constraints are placed on the performance and controllability. A controller is thus developed based on assumptions regarding the fluid transfer between elements, and the result is simulated. Generalized methodology is then extracted and extended applications are explored, such as a conceptual fluid ring and active mass displacement for attitude control.

Rotating↗

Thermal stability during rotation in space - A scaling and numerical analysis

An analysis of thermal stability in a fluid during rotation is presented. The conditions resulting in thermal stability are examined and numerically verified. It is shown that at least one thermal field exists for any rotating fluid, with or without a gravitational background field, where convection does not occur. The numerical model used is fully nonlinear and 3D. Results are presented on the basis of both steady-state and fully transient models. The thermally stable condition is further investigated in the context of the average net acceleration and the inhomogeneous part of the acceleration field (gradient of acceleration). It is shown that in the thermally stable condition the flow that would result from the average net acceleration is equal and opposite to the flow that would result from the inhomogeneous part of the acceleration field. It is concluded that the thermally stable condition is actually a flow mode transition at Ad = 1.

Arnold, William A.↗

Ageostrophic instabilities in a two fluid system with rotation

The stability of synoptic scale waves formed on a frontal surface is studied including nongeostrophic effects with the basic flow subjected to both vertical and horizontal shear. Spectral method is used to obtain the desired solutions. The stability characteristics of the developed unstable modes are presented as a function of shears of the basic flow. With the inclusion of barotropic shear the spectrum of instabilities increase. The lower speeded member of the mixed mode (gravitational-rotational) pair is influenced by the barotropic shear in the basic current and it appears at lower vertical shears. The structure of the height perturbations are utilized to distinguish the various unstable modes developed in the system together with their stability characteristics. This investigation has shown that the ageostrophic effects can be a significant factor in the development of synoptic scale waves on a frontal surface.

Ramanathan, N.↗

On rotational discontinuities in both two-fluid and hybrid models

Rotational discontinuities are studied in a two-fluid model that includes finite ion inertia dispersion and in a hybrid model in which the full ion dynamics is retained while the electrons are treated as a massless fluid. It is shown that as in previous dissipative MHD studies, a rotational discontinuity is unstable in both models and evolves to a 2-3 intermediate shock, a slow rarefaction wave, and other waves. In addition, it is shown that the so-called Walen relation, which holds exactly for rotational discontinuities, can also be well satisfied by tran-Alfvenic intermediate shocks. Thus intermediate shocks can be candidates for those observed structures that satisfy the Walen relation.

Wu, C. C.↗