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At least 109 records · Page 6

Spatial Linear Instability of Confluent Wake/Boundary Layers

The spatial linear instability of incompressible confluent wake/boundary layers is analyzed. The flow model adopted is a superposition of the Blasius boundary layer and a wake located above the boundary layer. The Orr-Sommerfeld equation is solved using a global numerical method for the resulting eigenvalue problem. The numerical procedure is validated by comparing the present solutions for the instability of the Blasius boundary layer and for the instability of a wake with published results. For the confluent wake/boundary layers, modes associated with the boundary layer and the wake, respectively, are identified. The boundary layer mode is found amplified as the wake approaches the wall. On the other hand, the modes associated with the wake, including a symmetric mode and an antisymmetric mode, are stabilized by the reduced distance between the wall and the wake. An unstable mode switching at low frequency is observed where the antisymmetric mode becomes more unstable than the symmetric mode when the wake velocity defect is high.

Liou, William W.↗

Gravitational instabilities in protostellar disks

The nonaxisymmetric stability of self-gravitating, geometrically thick accretion disks has been studied for protostellar systems having a wide range of disk-to-central object mass ratios. Global eigenmodes with four distinctly different characters were identified using numerical, nonlinear hydrodynamic techniques. The mode that appears most likely to arise in normal star formation settings, however, resembles the 'eccentric instability' that was identified earlier in thin, nearly Keplerian disks: It presents an open, one-armed spiral pattern that sweeps continuously in a trailing direction through more than 2-pi radians, smoothly connecting the inner and outer edges of the disk, and requires cooperative motion of the point mass for effective amplification. This particular instability promotes the development of a single, self-gravitating clump of material in orbit about the point mass, so its routine appearance in our simulations supports the conjecture that the eccentric instability provides a primary route to the formation of short-period binaries in protostellar systems.

Tohline, J. E.↗

Laboratory experiments on stability and entrainment of oceanic stratocumulus. Part 1: Instability experiment

The existence and persistence of marine stratocumulus play a significant role in the overall energy budget of the earth. Their stability and entrainment process are important in global climate studies, as well as for local weather forecasting. The purposes of the experimental simulations are to study this process and to address this paradox. The effects of buoyancy reversal is investigated, followed by two types of experiments. An instability experiment involves the behavior of a fully turbulent wake near the inversion generated by a sliding plate. Due to buoyancy reversal, the heavy, mixed fluid starts to sink, turning the potential energy created by the mixing process into kinetic energy, thereby increasing the entrainment rate. An entrainment experiment, using a vertically oscillating grid driven by a controllable speed motor, produces many eddy-induced entrainments at a surface region on scales much less than the depth of the layer.

Shy, Shenqyang S.↗

Global Analysis of Nonlinear Second-Mode Development in a Mach-6 Boundary Layer From High-Speed Schlieren Data

The second-mode instability on a 7◦ half-angle sharp cone at Mach 6 is analyzed using high-speed calibrated schlieren imagery at a frame rate near the expected fundamental frequency. Experiments were conducted in the NASA Langley 20-Inch Mach 6 facility at unit Reynolds number between 6.56×106 and 9.71×106 m−1. Time-resolved pixel intensity signals throughout the boundary layer are reconstructed using spatially available data in the schlieren images to recover an effective sampling rate of over 10 MHz; these are then converted to quantitative density gradients using a thin-lens-based calibration technique. A global analysis is performed on the schlieren data to investigate the nonlinear growth of the second-mode fundamental and harmonic content. Point-wise measures of the auto-bicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities were found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s time-series and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. Comparisons between the bispectral quantities and second-mode power show that nonlinear interactions, particularly resonance interactions, are closely correlated with space-time modulation of disturbances during the nonlinear stage of transition.

boundary layer transition↗

Diurnal tide in the Martian atmosphere

Classical atmospheric tidal theory is extended to include the effects of large-amplitude planetary-scale variations of the terrain height. Utilizing simple models of the thermotidal forcing, the resulting technique is used to compute the diurnal tide in both the dust-free and the dust-laden Martian atmosphere. The main effect of the Martian variable terrain is to drive topographic tidal modes which can propagate vertically and to excite the possibly resonant diurnal Kelvin mode. The resulting surface wind can exceed 20 m/sec and may determine the preferred location for the initiation of global dust storms. In the middle Martian atmosphere (30-80 km) static and shear instabilities embedded within the tidal fields will generate extensive, though variable, regions of turbulence. Vertical mixing by this turbulence and transport by the tide itself may help to stabilize the middle Martian atmosphere against photolysis.

Zurek, R. W.↗

Thermal evolution of a differentiated Ganymede and implications for surface features

Thermodynamic models are developed for the processes which controlled the evolution of the surface Ganymede, an icy Jovian satellite assumed to have a rock-rich core surrounded by a water-ice mantle. Account is taken of a heat pulse which would have arisen from a Rayleigh-Taylor instability at a deep-seated liquid-solid water interface, rapid fracturing from global stresses imposed by warm ice diapiric upwelling, impacts by large meteorites, and resurfacing by ice flows (rather than core formation). Comparisons are made with existing models for the evolution of Callisto, and the difficulties in defining a mechanism which produced the groove terrain of Ganymede are discussed.

Kirk, R. L.↗

Turbulization of shear flows in astrophysics

The problem of instability in shear flows is treated in a number of works which present a global analysis of irrotational (potential) modes in a 2-D compressible shear flow, implying that, in the presence of reflecting boundaries, those modes can increase and that the characteristic time of the increase is several orders as high as the dynamic time in the medium. Due to the slowness of the increase of irrotational modes and to the problematic character of the theory's applicability for thin accretion disks, an attempt was made to develop an alternative theory of turbulization shear flows. It is quite contrary to the above theory. Instead of the global analysis, a local one is made far from the flow boundaries. Instead of irrotational perturbations, vortical ones are examined. Lastly, the medium is considered to be incompressible. The flow in the accretion disk can be modeled by a plane Couette flow, without regard for boundary conditions: it can be modeled by a plane shear flow in infinite incompressible fluid. According to this scenario, there is a critical perturbation level in the free shear flow. If the level of initial perturbations exceeds the critical one, the flow is turbulized.

Chagelishvili, G. D.↗

Rapid transition from primary to secondary crust building on the Moon explained by mantle overturn

Geochronology indicates a rapid transition (tens of Myrs) from primary to secondary crust building on the Moon. The processes responsible for initiating secondary magmatism, however, remain in debate. Here we test the hypothesis that the earliest secondary crust (Mg-suite) formed as a direct consequence of density-driven mantle overturn, and advance 3D mantle convection models to quantify the resulting extent of lower mantle melting. Our modeling demonstrates that overturn of thin ilmenite-bearing cumulates ≤ 100 km triggers a rapid and short-lived episode of lower mantle melting which explains the key volume, geochronological, and spatial characteristics of early secondary crust building without contributions from other energy sources, namely KREEP (potassium, rare earth elements, phosphorus, radiogenic U, Th). Observations of globally distributed Mg-suite eliminate degree-1 overturn scenarios. We propose that gravitational instabilities in magma ocean cumulate piles are major driving forces for the onset of mantle convection and secondary crust building on differentiated bodies.

Moon↗

Magnetothermal instability in cooling flows

The effect of magnetic fields on thermal instability in cooling flows is investigated using linear, Eulerian perturbation analysis. As contrasted with the zero magnetic-field case, hydromagnetic stresses support perturbations against acceleration caused by buoyancy - comoving evolution results and global growth rates are straightforward to obtain for a given cooling flow entropy distribution. In addition, background and induced magnetic fields ensure that conductive damping of thermal instability is greatly reduced.

Loewenstein, Michael↗

The whistler heat flux instability: Threshold conditions in the solar wind

Solar wind electrons are observed often to consist of two components: a core and a halo. The anisotropics and relative average speeds of these components correspond to a heat flux that has the potential to excite several different electromagetic instabilities; wave-particle scattering by the resulting enhanced fluctuations can limit this heat flux. This manuscript describes theoretical studies using the linear Vlasco dispersion equation for drifting bi-Maxwellian component distributions in a homogeneous plasma to examine the threshold of the whistler heat flux instability. Expressions for this threshold are obtained from two different parametric baselines: a local model that yields scalings as functions of local dimensionless plasma paramaters, and a global model based on average electron properties observed during the in-eliptic phase of the Ulysses mission. The latter model yields an expression for the heat flux at threshold of the whistler instability as a function of helisopheric radius that scales in the same way as the average heat flux observed form Ulysses and that provides an approximate upper bound for that same quantity. This theoretical scaling is combined with the observational results to yield a semi-empirical closure relation for the average electron heat flux in the solar wind between 1 and 5 AU.

Gary, S. Peter↗

Angular momentum transfer by gravitational torques and the evolution of binary protostars

The efficiency of angular momentum transport by gravitational torques is investigated semianalytically for two idealized models. The first model, a rotating ellipsoid embedded within another ellipsoid, is compared with numerical results for the fission instability of a radpidly-rotating polytrope. The fission instability is aborted by the rapid transfer of angular momentum outward by gravitational torques. The global rates of angular momentum transfer by gravitational torques in rotating gas clouds such as the presolar nebula are shown to be comparable to the rates assumed to be appropriate for transfer by turbulent stresses. The second model is a binary system embedded within a rotating ellipsoid. The binary orbital angular momentum decreases significantly when the phase angle with the ellipsoid is constant; the binary separation may then decrease by a factor of 100 within about an orbital period. For a variable phase angle, little secular loss of orbital angular momentum occurs. Binaries which form in the isothermal regime of the theory of hierarchical fragmentation will not undergo orbital decay, whereas very close binaries composed of nonisothermal fragments may decay and merge into single objects.

Boss, A. P.↗

Extensional Flow of a Polystyrene Boger Fluid Through a 4:1:4 Axisymmetric Contraction/Expansion

The creeping flow of a dilute (0.025 wt%) monodisperse polystyrene/polystyrene Boger fluid through a 4:1:4 axisymmetric contraction/expansion is experimentally observed for a wide range of Deborah numbers. Pressure drop measurements across the orifice plate show a large extra pressure drop that increases monotonically with Deborah number above the value observed for a similar Newtonian fluid at the same flow rate. This enhancement in the dimensionless pressure drop is not associated with the onset of a flow instability, yet it is not predicted by existing steady-state or transient numerical computations with simple dumbbell models. It is conjectured that this extra pressure drop is the result of an additional dissipative contribution to the polymeric stress arising from a stress-conformation hysteresis in the strong non-homogeneous extensional flow near the contraction plane. Such a hysteresis has been independently measured and computed in recent studies of homogeneous transient uniaxial stretching of PS/PS Boger fluids. Flow visualization and velocity field measurements using digital particle image velocimetry (DPIV) show large upstream growth of the corner vortex with increasing Deborah number. At large Deborah numbers, the onset of an elastic instability is observed, first locally as small amplitude fluctuations in the pressure measurements, and then globally as an azimuthal precessing of the upstream corner vortex accompanied by periodic oscillations in the pressure drop across the orifice.

Rothstein, Jonathan P.↗

Reducing US Oil Dependence Using Simulation

People across the world are addicted to oil; as a result, the instability of oil prices and the shortage of oil reserves have influenced human behaviors and global businesses. Today, the United States makes up only 5% of the global population but consumes 25% of the. world total energy. Most of this energy is generated from fossil fuels in the form of electricity. The contribution of this paper is to examine the possibilities of replacing fossil fuel with renewable energies to generate electricity as well as to examine other methods to reduce oil and gas consumption. We propose a system dynamics model in an attempt to predict the future US dependence on fossil fuels by using renewable energy resources such as, nuclear, wind, solar, and hydro powers. Based on the findings of our model, the study expects to provide insights towards promising solutions of the oil dependency problem.

Ayoub, Fadi↗

The structure and dynamics of reacting plane mixing layers

Experimental studies of the combusting mixing layers formed over a rearward facing step and between two parallel streams are reported. The steady behavior of the mean properties of the reacting flows is similar to that of nonreacting flows except for the global effects of thermodynamic property changes. Vortices form by the two-dimensional K-H instability and grow by subharmonic combination until the layer begins to interact with the walls. Unsteady behavior occurs when there are resonator interactions with the K-H instability or the instability associated with the recirculation vortex in the rearward facing step flow.

Keller, J. O.↗

Current loop coalescence studied by 3-D electromagnetic particle code

Solar flare plasma data from the Yohkoh satellite is analyzed. The interactions of current loops were observed in the active regions on the Sun. This observation pointed out the importance of the idea that the solar flare is generated by the coalescence of current loops. The three dimensional electromagnetic particle simulations are to help in understanding the global interaction between two current loops including the evolution of the twist of loops due to instabilities. Associated rapid dynamics of current loop coalescence such as reconnection, shock waves and associated kinetic processes such as energy transfer, acceleration of particles, and electromagnetic emissions are to be studied by the code to complement analytical theories and magnetohydrodynamic simulations of the current loop coalescence. The simulation results show the strong interactions between two current loops, beam and whistler instabilities, and associated parallel and perpendicular particle heating.

Nishikawa, Ken-Ichi↗

Planetesimal Formation in the Protoplanetary Nebula

In this talk we will address two distinct phases of planetesimal formation, each of which is fundamentally dependent upon the coupled interactions of particles and turbulent nebula gas. It has been shown both numerically and experimentally that 3-D (three dimensional) turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Rev(sub m)/cH, where v(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha is greater than 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C is approximately equal to 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation. Once large particles (meter-size mass equivalent) reach the midplane, perhaps in the form of dense aggregates of the sort formed in 3D turbulence, they remain stable against gravitational instability but might grow rapidly by accretion of their drifting neighbors, depending on the level of global turbulence.

Cuzzi, Jeffrey N.↗

Modeling of the Convection and Interaction of Ring Current, Plasmaspheric and Plasma Sheet Plasmas in the Inner Magnetosphere

Distinctive sources of ions reside in the plasmasphere, plasmasheet, and ring current regions at discrete energies constitute the major plasma populations in the inner/middle magnetosphere. They contribute to the electrodynamics of the ionosphere-magnetosphere system as important carriers of the global current system, in triggering; geomagnetic storm and substorms, as well as critical components of plasma instabilities such as reconnection and Kelvin-Helmholtz instability at the magnetospheric boundaries. Our preliminary analysis of in-situ measurements shoves the complexity of the plasmas pitch angle distributions at particularly the cold and warm plasmas, vary dramatically at different local times and radial distances from the Earth in response to changes in solar wind condition and Dst index. Using an MHD-ring current coupled code, we model the convection and interaction of cold, warm and energetic ions of plasmaspheric, plasmasheet, and ring current origins in the inner magnetosphere. We compare our simulation results with in-situ and remotely sensed measurements from recent instrumentation on Geotail, Cluster, THEMIS, and TWINS spacecraft.

Fok, Mei-Ching↗

Embedded mesh solution of the 2-D Euler equations - Evaluation of interface formulations

Solution of the steady 2-D Euler equations using mesh embedding, or local grid refinement, with a cell-centered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.

Allmaras, S. R.↗