Engineering topics

Parker, E. N.

Publications and source records attributed to Parker, E. N..

At least 73 records · Page 4

NASA NTRS1982

The flux ejection dynamo with small diffusivity. I - Basic properties. II - Illustrative examples

In the first part of this paper, the flux ejection dynamo in an infinitely broad convective layer of finite depth is treated in the limit of electrical conductivity, where the convective layer upper surface is open to empty space while the lower surface is closed to the passage of fluid and field. The idealized convective overturning used allows an exact description of the symmetry and distribution of the magnetic field carried with the fluid. The total flux of the mean horizontal field grows linearly with the number of convective cycles. A discussion is given of the boundary conditions to be applied to an astronomical body whose flux ejection dynamo operates at its surface. In the second part, examples are presented which illustrate the consequences of reverse flux ejection from the surface of a convective layer of conducting fluid. Reverse flux ejection generally has the opposite effect of magnetic buoyancy, burying the fields rather than bringing them through the surface. Reverse flux injection at the surface of an alpha-omega dynamo profoundly alters the character of the solutions of dynamo equations.

Parker, E. N.↗

NASA NTRS1982

The dynamics of fibril magnetic fields. III - Fibril configurations in steady flows. IV - Trapping in closed convective rolls

The present investigation has the objective to provide an illustration of the equilibrium form of a hypothetical fibril field beneath the surface of the sun. Equilibrium fibril paths in static and moving atmospheres are considered. The provided examples are related to horizontal flows in an atmosphere in which the two anchor points of the arched fibril lie along the flow direction relative to each other. A brief introduction to the subject of the motion of horizontal fibrils in convective rolls is also presented, taking into account some implications for the sun. The equations of motion for a slender, buoyant flux tube extending horizontally along a closed convective roll are solved to illustrate the motion of the flux tube relative to the fluid, and attention is given to theoretical possibilities for the escape of flux tubes from a large horizontal convective roll in the sun.

Parker, E. N.↗

NASA NTRS1982

The dynamics of fibril magnetic fields. I - Effect of flux tubes on convection. II - The mean field equations

Observations have established the general fibril state of the magnetic field at the visible surface of the sun. This extraordinary state of the field, in separate intense flux tubes, implies that the convection has a relatively permanent, closed topology, in spite of the large Reynolds number. This paper explores some of the effects of the separate flux tubes on the convective motions, generally pushing the convective cells toward aligning their downdrafts with the flux tubes so as to minimize the dissipation.

Parker, E. N.↗

NASA NTRS1982

Compression of magnetic field in a viscous boundary layer

A simple analytical illustration is provided to complement the extensive numerical results already published regarding the compression of the magnetic field that occurs when the closed convective circulation of a viscous fluid with small resistivity breaks up a broad magnetic field into isolated filaments and proceeds to compress those filaments to field strengths beyond equipartition with the convective motions. This compression may occur in the solar corona or in interstellar space but not within the sun.

Parker, E. N.↗

NASA NTRS1982

The flux ejection dynamo effect

The mean-field effects of cyclonic convection become increasingly complex when the cyclonic rotation exceeds 1/2 pi. Net helicity is not required, with negative turbulent diffusion for instance, appearing in mirror symmetric turbulence. This paper points out a new dynamo effect arising in convective cells with strong asymmetry in the rotation of updrafts as against downdrafts. The creation of new magnetic flux arises from the ejection of reserve flux through the open boundary of the dynamo region. It is unlike the familiar alpha-effect in that individual components of the field may be amplified independently. Several formal examples are provided to illustrate the effect. Occurrence in nature depends upon the existence of fluid rotations of the order of pi in the convective updrafts. The flux ejection dynamo may possibly contribute to the generation of field in the convective core of earth and in the convective zone of the sun and other stars.

Parker, E. N.↗

NASA NTRS1982

The rapid dissipation of magnetic fields in highly conducting fluids

The dynamical conditions that exist when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array are treated. It is shown that in general there is no hydrostatic equilibrium. In place of equilibrium, there is a dynamical nonequilibrium, which leads to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting); this in turn forms tubes of large diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, being dissipated into small-scale motions of the fluid and thence into heat. Referring to the sun, it is pointed out that the twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above.

Parker, E. N.↗

NASA NTRS1981

Photospheric flow and stellar winds

The effect of the photospheric outflow on the expansion of the strongly bound coronas of dwarf main-sequence stars is examined. The extended temperatures of the strongly bound coronas cause the stars to expand and form tenuous stellar winds, with a slight mean upward motion of the gas in the photosphere to replenish the mass loss through the coronal expansion. A formal solution of the time-dependent hydrodynamic equations illustrates the effects of the photospheric velocity at large distances, and the effect of blocking the upward flow in the photosphere is calculated using the sun as an example. Results indicate that the expansion of a strongly bound corona is insensitive over historical time scales to the small outflow of gas in the photosphere.

Parker, E. N.↗

NASA NTRS1981

The dissipation of inhomogeneous magnetic fields and the problem of coronae. I - Dislocation and flattening of flux tubes. II - The dynamics of dislocated flux

Attention is given to the dynamical dissipation arising in a magnetic field extending up through a tenuous atmosphere when an elemental flux tube in the field (1) is displaced from its equilibrium position and/or (2) is inflated by an internal fluid pressure different from the external fluid pressure. It is pointed out that as a consequence the tension in the lines of force of the ambient field flattens the dislocated tube so that the thickness of the tube decreases without limit and that the local field gradients increase rapidly with the passage of time until destroyed by one or more dissipative effects. The magnetic energy of a dislocated flux tube is therefore soon converted into thermal energy no matter how low the molecule resistivity of the fluid. Some formal illustrations of local conditions along a misaligned flux tube are presented, showing the simultaneous onset of diffusion, fluid motion, and hydromagnetic wave propagation. The examples demonstrate that the total effect is complicated and subject only to estimation, rather than formal calculation, at the present time.

Parker, E. N.↗

NASA NTRS1981

Residual fields from extinct dynamos

The generation of magnetic fields in convective zones of declining vigor and/or thickness is considered, the goal being to explain the magnetic fields observed in A-stars. The investigation is restricted to kinematical dynamos in order to show some of the many possibilities, which depend on the assumed conditions of decline of the convection. The examples illustrate the quantitative detail required to describe the convection in order to extract any firm conclusions concerning specific stars. The first example treats the basic problem of diffusion from a layer of declining thickness. The second has a buoyant rise added to the field in the layer. The third deals with plane dynamo waves in a region with declining eddy diffusivity, dynamo coefficient, and large-scale shear. It is noted that the dynamo number may increase or decrease with declining convection, with an increase expected if the large-scale shear does not decline as rapidly as the eddy diffusivity. It is shown that one of the components of the field may increase without bound even when the dynamo number declines to zero.

Parker, E. N.↗

NASA NTRS1981

The spontaneous concentration of magnetic field in the photosphere of the sun

The basic physics of magnetic flux tubes in the solar photosphere is reviewed, with areas still open to conjecture pointed out. The question of the concentration of individual small flux tubes to levels of 1-2 kilogauss, when the average solar surface magnetic field is on the order of 10 gauss, by processes of twisting and the formation of flux ropes made up of tubes wound around each other is considered together with the effects of turbulence on the flux tube. Mechanisms for tube compression by the evacuation of the gas contained within a flux tube are then examined, and the possibility of field concentration through the cooling of the gas within the tube in a superadiabatic process is suggested. Attention is then given to possible mechanisms serving to maintain the concentration of flux tubes far below the surface of the sun which gives rise to sunspots and pores as the flux tree emerges through the surface.

Parker, E. N.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. IX - Umbral dots and longitudinal overstability

The dynamical properties of the sunspot field and of a column of hot gas confined by such a vertical magnetic field are examined in order to understand the umbral dot within the context of the magnetic sunspot structure. Attention is given to the conditions necessary for gas intrusion, longitudinal as well as convective overstability, the growing modes, and the even mode. With the hypothesis that the subsurface magnetic field of a sunspot splits into many separate flux tubes with field-free gas between, it is suggested that the field-free columns occasionally punch their way up through the overlying magnetic field to the surface, appearing there as the bright, field-free umbral dots. Effects fostering the phenomenon are also discussed, that is, the enhanced temperature of a column of rising gas, the strongly reduced overhead magnetic pressure, and the initiated upward intrusion; these effects are illustrated with examples.

Parker, E. N.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. VIII - Overstability in a magnetic field in a downdraft

The dynamical properties of convective overstability in a vertical magnetic field with a downdraft are considered. A variety of effects is illustrated. The overstability produces Alfven waves propagating both upward or downward along the magnetic field. The favored direction of emission may be upward or downward depending upon the magnitude of the heat transport coefficient. The largest asymmetry is produced by a difference in reflectivity between the upper and lower boundaries. It is shown that a very modest reflection coefficient of the upper boundary, with no reflection at the lower boundary, causes most of the waves to be emitted downward, and vice versa. Applying these results to the flux tubes extending up through the convective zone of the Sun, it follows that those flux tubes are dynamically active beneath the surface, as suggested earlier by ourselves and others, but there is no reason to expect any significant wave flux to appear in the field above the surface. The waves propagate downward into the Sun and are presumably dispersed there by the nonlinear interaction with the turbulent convection, etc.

Parker, E. N.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. VI - Convective propulsion. VII - Heat flow in a convective downdraft

The effect of negative aerodynamic drag in an ideal fluid subject to convective instability is considered. It is shown that a cylinder moving in such a fluid is propelled forward in its motion by the convective forces and that the characteristic acceleration time is comparable to the onset time of convective motions in the fluid. It is suggested that convective propulsion plays an important role in the dynamics of flux tubes extending through the surface of the sun. The suppression of the upward heat flow in a Boussinesq convective cell with free upper and lower boundaries by a downdraft is then analyzed. Application to the solar convection zone indicates that downdrafts of 1 to 2 km/s at depths of 1000 to 4000 km beneath the visible surface of the sun are sufficient to reduce the upward heat flux to a small fraction of the ambient value.

Parker, E. N.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. III - Aerodynamic lift

The aerodynamic lift exerted on a magnetic flux tube by the asymmetric flow around the two sides of the tube is calculated as part of an investigation of the physics of solar flux tubes. The general hydrodynamic forces on a rigid circular cylinder in a nonuniform flow of an ideal fluid are derived from the first derivatives of the velocity field. Aerodynamic lift in a radial nonuniform flow is found to act in the direction of the flow, toward the region of increased flow velocity, while in a shear flow, lift is perpendicular to the free stream and directed toward increasing flow velocity. For a general, three dimensional, large-scale stationary incompressible equilibrium flow, an expression is also derived relating the lift per unit length to the dynamical pressure, cylinder radius and the gradient of the free-stream velocity. Evidence from an asymmetric airfoil in a uniform flow indicates that lift is enhanced in a real fluid in the presence of turbulence.

Parker, E. N.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. V - Mutual hydrodynamic forces between neighboring tubes

The mutual hydrodynamic forces between parallel cylinders in a moving fluid are illustrated through several formal examples. Parallel tubes in a uniform flow are attracted or repelled depending on whether they are side by side or one ahead of the other, respectively. A pulsating or undulating tube attracts all other neighboring tubes toward itself. These hydrodynamic effects suggest that the separate flux tubes beneath the sunspots exert significant attractive forces on each other.

Parker, E. N.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. I - The general nature of the sunspot. II - Aerodynamic drag

Analysis of the dynamical stability of a large flux tube suggests that the field of a sunspot must divide into many separate tubes within the first 1000 km below the surface. Buoyancy of the Wilson depression at the visible surface and probably also a downdraft beneath the sunspot hold the separate tubes in a loose cluster. Convective generation of Alfven waves, which are emitted preferentially downward, cools the tubes. Aerodynamic drag on a slender flux tube stretched vertically across a convective cell is also studied. Since the drag is approximately proportional to the local kinetic energy density, the density stratification weights the drag in favor of the upper layers. Horizontal motions concentrated in the bottom of the convective cell may reverse this density effect. A downdraft of about two km/sec through the flux tubes beneath the sunspot is hypothesized.

Parker, E. N.↗

NASA NTRS1979

The instability of a horizontal magnetic field in an atmosphere stable against convection

The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3 of a solar radius beneath the surface of the sun, a field of 100 G develops ripples over a scale of 1000 km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10 billion years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether, the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.

Parker, E. N.↗

NASA NTRS1978

The mutual attraction of magnetic knots

It is observed that the magnetic knots associated with active regions on the sun have an attraction for each other during the formative period of the active regions, when new magnetic flux is coming to the surface. The attraction disappears when new flux ceases to rise through the surface. Then the magnetic spots and knots tend to come apart, leading to disintegration of the sunspots previously formed. The dissolution of the fields is to be expected, as a consequence of the magnetic repulsion of knots of like polarity and as a consequence of the hydromagnetic exchange instability. The purpose of this paper is to show that the mutual attraction of knots during the formative stages of a sunspot region may be understood as the mutual hydrodynamic attraction of the rising flux tubes. Two rising tubes attract each other, as a consequence of the wake of the leading tube when one is moving behind the other, and as a consequence of the Bernoulli effect when rising side by side.

Parker, E. N.↗