Engineering topics

Wu, C. C.

Publications and source records attributed to Wu, C. C..

At least 19 records

NASA NTRS1995

Magnetohydrodynamic Riemann problem and the structure of the magnetic reconnection layer

We present a complete solution for a set of magnetohydrodynamic (MHD) Riemann problems in which the upstream and downstream states have the same total pressure, and in which the normal component of the magnetic field is very small. These solutions are pertinent to subfast flows in the earth's magnetic tail and near the magnetopause. In a coplanar situation a family of solutions exists that depend on two parameters as well as on dissapation mechanisms. In the parallel case the transverse magnetic field either does not change direction or changes the direction twice by involving two intermediate shocks. In the antiparallel case an intermediate shock is always required, except when the solution consists of two switch-off shocks. In a noncoplanar case the solution is not self-similar as a function of x/t, but continues to evolve. At early times the evolution is similar to the coplanar case. In general two time-dependent intermediate shocks are required to rotate the magnetic fields. The velocity shear has a strong effect on the Riemann solution. In some cases no Riemann solution can exist because of the cavitation caused by the slow refraction waves. The calculated magnetopause structure resembles the observed structure for northward interplanetary magnetic field (IMF). However, for southward IMF, the MHD result shows the existence of a depletion layer, which is not supported by observations. We also show that on the magnetosheath side, the Walen relation, which is exact for a rotational discontinuity, can also be well satisfied by a slow shock, an intermediate shock, or the head of a slow rarefaction wave.

Wu, C. C.↗

NASA NTRS1994

A model of sonoluminescence

A bubble of air, trapped at the center of a spherical container of water on the surface of which spherical sound waves are maintained by transducers, may emit light, a phenomenon known as sonoluminescence. The surface of the bubble expands and contracts in obedience to the Rayleigh-Lamb equation, which requires knowledge of the gas pressure on the surface of the bubble. In many investigations of bubble pulsations, it is assumed that the air in the bubble moves adiabatically. To understand sonoluminescence, however, it is necessary to allow for the possibility that shocks are generated within the bubble. We couple the Rayleigh-Lamb equation governing the bubble radius to Euler's equations governing the motion of air in the bubble, and solve the two equations simultaneously. The air is modelled by a van der Waals gas. Results are presented for a number of slightly different conditions of excitation, but in which the response of the system is widely different.

Wu, C. C.↗

NASA NTRS1993

The small amplitude magnetohydrodynamic Riemann problem

The small-amplitude MHD Riemann problem is studied using the Cohen-Kulsrud-Burgers equations. Unlike the coplanar Riemann problem, the evolution of noncoplanar Riemann problems is not self-similar and its flow structures could change in time. But its large-time behavior is very simple and a time-dependent 2 - 3 intermediate shock is always involved for the noncoplanar field rotations. The time-dependent 2 - 3 intermediate shock has a well-defined structure and exists for any degree of field rotation.

Wu, C. C.↗

NASA NTRS1993

Shock-wave propagation in a sonoluminescing gas bubble

The motion of the bubble radius and of the air trapped inside the bubble during sonoluminescence are determined self-consistently by coupling the solution of the Rayleigh-Plesset equation governing the bubble radius to the solution of Euler's equations for the motion of air in the bubble. Results are presented for three slightly different conditions of excitation, in two of which shocks are formed during the collapse of the bubble, and in which such high temperatures are attained that the air is ionized. Estimates are made of the duration and intensity of the light then radiated by the plasma.

Wu, C. C.↗

NASA NTRS1992

Structural relations for time-dependent intermediate shocks

A quantitative description of time-dependent (MHD) intermediate shocks is formulated. In non-coplanar Riemann problems, time-dependent 2 yields 3 intermediate shocks evolve in time as a localized self-similar structure whose strength decreases as 1/sq rt t, and whose width expands as sq rt t. We derive structural relations, similar to Rankine-Hugoniot relations, between the plasma properties and the magnitude of the transverse magnetic field, which we hope can help identify time-dependent 2 yields 3 intermediate shocks at the magnetopause, in the solar wind, and elsewhere in space. The analytic forms of the structural relations agree with our numerical results.

Wu, C. C.↗

NASA NTRS1992

MHD flow past an obstacle - Large-scale flow in the magnetosheath

As a step to the study of the large-scale flow in the magnetosheath, the MHD flow past an obstacle is investigated. A time asymptotic method is used to obtain 3D steady-state solutions. The results indicate the formation of a depletion layer near the obstacle due to the increase of the magnetic field. Along the earth-sun line the plasma density increases first and then decreases from the post bow shock to the magnetopause. The local density maximum in front of the magnetopause may correspond to what was recently observed. When the interplanetary magnetic field direction is tilted from the solar wind flow, the IMF influences the shape of the bow shock as well as the location of the stagnation point at the magnetopause in a way consistent with observation. In addition, the results show the existence of a magnetosheath current in the post parallel-shock region.

Wu, C. C.↗

NASA NTRS1992

Structure and evolution of time-dependent intermediate shocks

A quantitative description of time-dependent intermediate shocks is formulated using the Cohen-Kulsrud-Burgers equations. In noncoplanar Riemann problems, time-dependent two-three transition intermediate shocks evolve in time as a localized self-similar structure whose strength decreases as 1/the square root of t, and whose width expands as the square root of t. Time-dependent intermediate shocks offer a way of solving the noncoplanar MHD Riemann problem.

Wu, C. C.↗

NASA NTRS1992

Forecasting the arrival of fast coronal mass ejecta at Earth by the detection of 2-20 keV neutral atoms

Studies have shown that Earth passages of fast coronal mass ejections (CMEs) trigger geomagnetic storms. Early identification of fast earth-directed CME can help provide storm warnings, but detection of such by coronagraphs is extremely difficult. We suggest that energetic hydrogen atoms (EHA) between 2 and 10 keV produced during the transit phase of an Earth-directed CME by recombination between protons and electrons in the CME can travel ahead of the CME and act as harbingers of a magnetic storm. This forecasting scheme should work if enough EHA are produced, because while CMEs decelerate continuously after their ejection, the EHA fluxes produced in the initial phase of fast CMEs propagate at their initial high speeds. Model simulations support this proposed mechanism.

Hsieh, K. C.↗

NASA NTRS1991

Alfven shock trains

The Cohen-Kulsrud-Burgers equation (CKB) is used to consider the nonlinear evolution of resistive, quasi-parallel Alfven waves subject to a long-wavelength, plane-polarized, monochromatic instability. The instability saturates by nonlinear steepening, which proceeds until the periodic waveform develops an interior scale length comparable to the dissipation length; a fast or an intermediate shock then forms. The result is a periodic train of Alfven shocks of one or the other type. For propagation strictly parallel to the magnetic field, there will be two shocks per instability wavelength. Numerical integration of the time-dependent CKB equation shows that an initial, small-amplitude growing wave asymptotes to a stable, periodic stationary wave whose analytic solution specifies how the type of shock embedded in the shock train, and the amplitude and speed of the shock train, depend on the strength and phase of the instability. Waveforms observed upstream of the earth's bowshock and cometary shocks resemble those calculated here.

Malkov, M. A.↗

NASA NTRS1991

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.↗

NASA NTRS1991

Formation of intermediate shocks in both two-fluid and hybrid models

Intermediate shocks 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 in both models intermediate shocks can be formed through wave steepening, meaning that they are stable and possess shock structures.

Wu, C. C.↗

NASA NTRS1990

Formation, structure, and stability of MHD intermediate shocks

It was recently shown by Wu (1987) that intermediate shocks are admissible and can be formed through nonlinear wave steepening from continuous waves. In this paper, the formation, structure, and stability of intermediate shocks in dissipative MHD are considered in detail. The differences between the conventional theory and the present one are pointed out and clarified. It is shown that all four types of intermediate shocks can be formed from smooth waves. It is also shown that there are free parameters in the structure of the intermediate shocks, and that these parameters are related to the shock stability. In addition, the paper shows that a rotational discontinuity can not exist with finite width, indicates how this is related to the existence of time-dependent intermediate shocks, and shows why the conventional theory is not a good approximation to dissipative MHD solutions whenever there is rotation in magnetic field.

Wu, C. C.↗

NASA NTRS1990

Structure and evolution of small-amplitude intermediate shock waves

A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier-Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine-Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.

Kennel, C. F.↗

NASA NTRS1989

Steady state magnetic field configurations for the earth's magnetotail

A two-dimensional, force-balance magnetic field model is presented. The theoretical existence of a steady state magnetic field configuration that is force-balanced and consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD is demonstrated. A numerical solution is obtained for a two-dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The results are consistent with the convection time sequences reported by Erickson (1985).

Hau, L.-N.↗

NASA NTRS1986

Kelvin-Helmholtz instability at the magnetopause boundary

An MHD model is defined for the convective Kelvin-Helmholtz instability (CKHI) which satellite data indicates produces vortices in the near-earth region of the plasma sheet through turbulence caused by shear flow. The MHD equations are solved as an initial value problem, which reveals that the CKHI growth rate is the same as that of the periodic KHI (PKHI). However, the CKHI is not as limited in the range of amplitude as is the PKHI, which experiences stability in nonlinear growth because of the periodic characteristics of the growth. A perpendicularly moving CKHI can produce a large vortex flow and shocks off the vortex boundary. The satellite data indicate that the vortices are in the size range of 10-20 earth radii. Additional effects can include the expulsion of magnetic flux and the formation of the boundary layer. The success of the model up to the point of formation of the boundary layer is taken as an incentive for further model development using more realistic magnetospheric data.

Wu, C. C.↗

NASA NTRS1985

The effects of northward IMF on the structure of the magnetosphere

Effects of northward IMF on the structure of the magnetosphere were studied by using a global MHD model. The model suggests a mechanism for creating high latitude sunward convection. The mechanism is not due to magnetic merging over the cusp region. Instead, the model indicates that the northward IMF field lines, which move around the magnetosphere, tend to squeeze the magnetotail at the boundary. This leads to formation of vortex flows in the tail and the observed sunward convection in the polar cap.

Wu, C. C.↗

NASA NTRS1985

Slender body theory and Space Shuttle transonic aerodynamics

A computational implementation of transonic slender body theory and the equivalence rule has been utilized to study transonic flow field around the Space Shuttle Orbiter. The far field is described by a nonlinear axisymmetric Karman-Guderley model and the near field by a cross flow Laplace equation boundary value problem. The latter is treated using a source panel method. Preliminary comparisons with experiments give encouraging indications that the model can be useful for quick turnaround estimates. Areas of refinement to obtain more accurate predictions are discussed.

Malmuth, N. D.↗

NASA NTRS1985

An MHD model of the earth's magnetosphere

It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.

Wu, C. C.↗