Engineering topics

Hurlburt, Neal E.

Publications and source records attributed to Hurlburt, Neal E..

7 records

NASA NTRS1998

Turbulent Compressible Convection with Rotation: Mean Flows and Differential Rotation - 2

The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.

Brummell, Nicholas H.↗

NASA NTRS1996

Turbulent Compressible Convection with Rotation: Flow Structure and Evolution - Part 1

The effects of Coriolis forces on compressible convection are studied using three-dimensional numerical simulations carried out within a local modified f-plane model. The physics is simplified by considering a perfect gas occupying a rectilinear domain placed tangentially to a rotating sphere at various latitudes, through which a destabilizing heat flux is driven. The resulting convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers, evaluating conditions where the influence of rotation is both weak and strong. Given the computational demands of these high-resolution simulations, the parameter space is explored sparsely to ascertain the differences between laminar and turbulent rotating convection. The first paper in this series examines the effects of rotation on the flow structure within the convection, its evolution, and some consequences for mixing. Subsequent papers consider the large-scale mean shear flows that are generated by the convection, and the effects of rotation on the convective energetics and transport properties. It is found here that the structure of rotating turbulent convection is similar to earlier nonrotating studies, with a laminar, cellular surface network disguising a fully turbulent interior punctuated by vertically coherent structures. However, the temporal signature of the surface flows is modified by inertial motions to yield new cellular evolution patterns and an overall increase in the mobility of the network. The turbulent convection contains vortex tubes of many scales, including large-scale coherent structures spanning the full vertical extent of the domain involving multiple density scale heights. Remarkably, such structures align with the rotation vector via the influence of Coriolis forces on turbulent motions, in contrast with the zonal tilting of streamlines found in laminar flows. Such novel turbulent mechanisms alter the correlations which drive mean shearing flows and affect the convective transport properties. In contrast to this large-scale anisotropy, small-scale vortex tubes at greater depths are randomly orientated by the rotational mixing of momentum, leading to an increased degree of isotropy on the medium to small scales of motion there. Rotation also influences the thermodynamic mixing properties of the convection. In particular, interaction of the larger coherent vortices causes a loss of correlation between the vertical velocity and the temperature leaving a mean stratification which is not isentropic.

Brummell, Nicholas H.↗

NASA NTRS1995

Local-area simulations of rotating compressible convection and associated mean flows

The dynamics of compressible convection within a curved local segment of a rotating spherical shell are considered in relation to the turbulent redistribution of angular momentum within the solar convection zone. Current supercomputers permit fully turbulent flows to be considered within the restricted geometry of local area models. By considering motions in a curvilinear geometry in which the Coriolos parameters vary with latitude, Rossby waves which couple with the turbulent convection are thought of as being possible. Simulations of rotating convection are presented in such a curved local segment of a spherical shell using a newly developed, sixth-order accurate code based on compact finite differences.

Hurlburt, Neal E.↗

NASA NTRS1994

Penetration below a convective zone

Two-dimensional numerical simulations are used to investigate how fully compressible nonlinear convection penetrates into a stably stratified zone beneath a stellar convection zone. Estimates are obtained of the extent of penetration as the relative stability S of the stable to the unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The dynamics is dominated by downward-directed plumes which can extend far into the stable material and which can lead to the excitation of a broad spectrum of internal gravity waves in the lower stable zone. The convection is highly time dependent, with the close coupling between the lateral swaying of the plumes and the internal gravity waves they generate serving to modulate the strength of the convection. The depth of penetration delta, determined by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kinetic energy carried into the stable layer by the plumes and the buoyancy braking they experience there. A passive scalar is introduced into the unstable layer to evaluate the transport of chemical species downward. Such a tracer is effectively mixed within a few convective overturning times down to a depth of delta within the stable layer. Analytical estimates based on simple scaling laws are used to interpret the variation of delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exceeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S(exp -1) and S(exp -1/4). These estimates are in accord with the penetration results from the simulations.

Hurlburt, Neal E.↗

NASA NTRS1990

Supersonic convection

Numerical simulations with high spatial resolution are used to study that the combined effects of stratification, pressure gradients, and nonadiabatic processes can lead to the formation of regions of supersonic motions near the upper thermal boundary layer. Within these regions, the dynamics is dominated by nonstationary shock structures. These form near the downflow sites and propagate upstream along the boundary layer to the upflow regions where they weaken and eventually disappear. The shock cycle, consisting of the formation, propagation, and disappearance of shock structures, has a time scale comparable to the sound crossing time over a portion of the convective cell, giving rise to vigorous time dependence in the convection.

Cattaneo, Fausto↗

NASA NTRS1990

Three-dimensional compressible convection at low Prandtl numbers

Numerical simulations are used to study fully compressible thermal convection at large Rayleigh numbers. Results are presented from a sequence of three-dimensional simulations that reveal a transition from gradually-evolving laminar convection to nearly turbulent convection as the Prandtl number is reduced from a value of unity to one-tenth. The convective flows form irregular cellular patterns near the upper surface, possesing a network of fast downflow at cell peripheries and gentler upflow at cell centers. At greater depths the curving sheets of downflow collapse into plumes which may twist and possess substantial vertical vorticity. For the lowest Prandtl number, the convection near the bottom of the layer appears to be turbulent, yet the rapidly varying small-scale flow structure there is accompanied by more ordered sites of wavering upflow, with the latter able to penetrate all the way to the upper boundary. Thus a significant component of the flow is able to extend over multiple density scale heights, in contrast to what is argued in formulating mixing-length models for stellar convection. Results are also shown from two-dimensional simulations carried out with very high spatial resolution, which reveal that supersonic convection with fluttering shock systems can be realized.

Toomre, Juri↗

NASA NTRS1986

Nonlinear compressible convection penetrating into stable layers and producing internal gravity waves

Penetrative convection spanning multiple scale heights is studied within a simple stellar envelope consisting of three layers: a convectively unstable middle layer bounded above and below by stably stratified polytropes. Two-dimensional numerical simulations are used to investigate the fully compressible nonlinear motions that ensue. The cellular flows display prominent downward-directd plumes surrounded by broader regions of upflow. Such asymmetry arises because pressure fluctuations accentuate buoyancy driving in the concentrated plumes and can even lead to weak buoyancy braking in the surrounding ascending flows. As the plumes plunge downward into a region of stable stratification, they serve to excite a broad spectrum of internal gravity waves there. The induced waves are not passive, for they feed back upon the plumes by deflecting them sideways, thereby modulating the amplitude of the convection in time even in the unstable layer. The penetrative motions that billow upward into the upper stable zone are distinctly weaker, and they cascade back downward toward the unstable zone over a broad horizontal scale. The strong excitation of gravity waves by the convection has implications for gradual mixing deep within a star.

Hurlburt, Neal E.↗