67 results for Oughton, Sean, Journal article

Selective decay and coherent vortices in twodimensional incompressible turbulence
Matthaeus, William H.; Stribling, W.; Martinez, Daniel; Oughton, Sean; Montgomery, David (1991)
Journal article
University of WaikatoNumerical solution of twodimensional incompressible hydrodynamics shows that states of a nearminimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the latetime similarity of the streamlines to Ewald potential contours.
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The influence of a mean magnetic field on threedimensional magnetohydrodynamic turbulence
Oughton, Sean; Priest, Eric R.; Matthaeus, William H. (1994)
Journal article
University of WaikatoBuilding on results from twodimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully threedimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B₀) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B₀). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B₀ to inhibit development of turbulence is also examined.
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Magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field
Stribling, Troy; Matthaeus, William H.; Oughton, Sean (1995)
Journal article
University of WaikatoA computational investigation of magnetic helicity of the fluctuatingmagnetic fieldHm in ideal and freely decaying three‐dimensional (3‐D) magnetohydrodynamics (MHD) in the presence of a uniform mean magnetic field is performed. It is shown that for ideal 3‐D MHDHm, which is a rugged invariant in the absence of a mean magnetic field [Frisch et al., J. Fluid Mech. 77, 796 (1975)], decays from its initial value and proceeds to oscillate about zero. The decay of Hm is shown to result from the presence of a new ‘‘generalized’’ helicity invariant, which includes contributions from the uniform magnetic field. The loss of invariance of Hm will diminish the effects of inverse transfer of Hm on freely decaying turbulence. This is demonstrated in a discussion of the selective decay relaxation process.
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Evolution of energycontaining turbulent eddies in the solar wind
Matthaeus, William H.; Oughton, Sean; Pontius, Duane H.; Zhou, Ye (1994)
Journal article
University of WaikatoPrevious theoretical treatments of fluidscale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasiequilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple twolengthscale models for transport of MHD turbulence in a weakly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the twodimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence. Numerical solutions are shown for several cases of interest that demonstrate the advantages of this approach. We suggest that this model may prove useful in studies of solar wind heating and acceleration, as well as in describing the response of interplanetary turbulence to wave energy injected by pickup ions and planetary upstream waves.
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Properties of massloading shocks, 2. Magnetohydrodynamics
Zank, Gary P.; Oughton, Sean; Neubauer, F. M.; Webb, G. M. (1992)
Journal article
University of WaikatoThe onedimensional magnetohydrodynamics of shocked flows subjected to significant mass loading are considered. Recent observations at comets GiacobiniZinner and Halley suggest that simple nonreacting MHD is an inappropriate description for active cometary bow shocks. The thickness of the observed cometary shock implies that mass loading represents an important dynamical process within the shock itself, thereby requiring that the RankineHugoniot condition for the mass flux possess a source term. In a formal sense, this renders massloading shocks qualitatively similar to combustion shocks, except that mass loading induces the shocked flow to shear. Nevertheless, a large class of stable shocks exist, identified by means of the Lax conditions appropriate to MHD. Thus massloading shocks represent a new and interesting class of shocks, which, although found frequently in the solar system, both at the head of comets and, under suitable conditions, upsteam of weakly magnetized and nonmagnetized planets, has not been discussed in any detail. Owing to the shearing of the flow, massloading shocks can behave like switchon shocks regardless of the magnitude of the plasma beta. Thus the behavior of the magnetic field in massloading shocks is significantly different from that occurring in nonreacting classical MHD shocks. It is demonstrated that there exist two types of massloading fronts for which no classical MHD analogue exists, these being the fast and slow compound massloading shocks. These shocks are characterized by an initial deceleration of the fluid flow to either the fast or the slow magnetosonic speed followed by an isentropic expansion to the final decelerated downstream state. Thus these transitions take the flow from a supersonic to a supersonic, although decelerated, downstream state, unlike shocks which occur in classical MHD or gasdynamics. It is possible that such structures have been observed during the GiottoHalley encounter, and a brief discussion of the appropriate Halley parameters is therefore given, together with a short discussion of the determination of the shock normal from observations. A further interesting new form of massloading shock is the “slowintermediate” shock, a stable shock which possesses many of the properties of intermediate MHD shocks yet which propagates like a slow mode MHD shock. An important property of massloading shocks is the large parameter regime (compared with classical MHD) which does not admit simple or stable transitions from a given upstream to a downstream state. This suggests that it is often necessary to construct compound structures consisting of shocks, slip waves, rarefactions, and fast and slow compound waves in order to connect given upstream and downstream states. Thus the Riemann problem is significantly different from that of classical MHD.
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Reply to “Comment on ‘Evolution of energycontaining turbulent eddies in the solar wind’ by W. H. Matthaeus, S. Oughton, D. H. Pontius Jr., and Y. Zhou”
Matthaeus, William H.; Oughton, Sean; Pontius, Duane H.; Zhou, Ye (1995)
Journal article
University of WaikatoIn their preceding comment on our paper [Matthaeus et al., 1994] (hereinafter reffered to as paper 1), Tu and Marsh [this issue] object vehemently to what they perceive as undeserved criticism of the class of solar wind turbulence models developed by Tu and coworkers[Tu et al., 1984, Tu, 1987, 1988]. Our intent was not to slight the valuable contributions made in those groundbreaking theories for incorporating turbulence into models for spatial transport. Rather, we wished to point out certain shortcomings in existing theories and suggest how they might be improved.
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Phenomenology for the decay of energycontaining eddies in homogeneous MHD turbulence
Hossain, Murshed; Gray, Perry C.; Pontius, Duane H.; Matthaeus, William H.; Oughton, Sean (1995)
Journal article
University of WaikatoWe evaluate a number of simple, one‐point phenomenological models for the decay of energy‐containing eddies in magnetohydrodynamic(MHD) and hydrodynamicturbulence. The MHDmodels include effects of cross helicity and Alfvénic couplings associated with a constant mean magnetic field, based on physical effects well‐described in the literature. The analytic structure of three separate MHDmodels is discussed. The single hydrodynamic model and several MHDmodels are compared against results from spectral‐method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHDturbulence, where practical difficulties make it more difficult to study physical examples. When the triple‐decorrelation time and effects of spectral anisotropy are properly taken into account, particular MHDmodels give decay rates that remain correct to within a factor of 2 for several energy‐halving times. A simple model of this type is likely to be useful in a number of applications in space physics, astrophysics, and laboratory plasma physics where the approximate effects of turbulence need to be included.
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Linear transport of solar wind fluctuations
Oughton, Sean; Matthaeus, William H. (1995)
Journal article
University of WaikatoNumerical solutions for the linear transport of solar wind fluctuations are presented. The model used takes into account the effects of advection, expansion, and wave propagation, as well as the recently illuminated effects of (nonWKB) “mixing” terms. The radial evolution of the fluctuating kinetic and magnetic energies and of the cross helicity is computed, and it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In more general cases, however, where the fluctuations consist of a superposition of various types of turbulence, mixing leads to solutions which differ substantially from those predicted by WKB theory. The degree of mixing shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 ∼ AU, of the ratio of “inward” and “outward” fluctuation energies and the ratio of kinetic and magnetic fluctuation energies. The transport properties described here may provide a partial explanation for the observed decrease of cross helicity with increasing heliocentric distance in the solar wind.
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Phenomenology of hydromagnetic turbulence in a uniformly expanding medium
Matthaeus, William H.; Zank, Gary P.; Oughton, Sean (1996)
Journal article
University of WaikatoA simple phenomenology is developed for the decay and transport of turbulence in a constantspeed, uniformly expanding medium. The fluctuations are assumed to be locally incompressible, and either of the hydrodynamic or nonAlfvénic magnetohydrodynamic (MHD) type. In order to represent local effects of nonlinearities, a simple model of the KaármáDryden type for locally homogeneous turbulent decay is adopted. A detailed discussion of the parameters of this familiar onepoint hydrodynamic closure is given, which has been shown recently to be applicable to nonAlfvénic MHD as well. The effects of the largescale flow and expansion are incorporated using a twoscale approach, in which assumptions of particular turbulence symmetries provide simplifications. The derived model is tractable and provides a basis for understanding turbulence in the outer heliosphere, as well as in other astrophysical applications.
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Ion parallel viscosity and anisotropy in MHD turbulence
Oughton, Sean (1996)
Journal article
University of WaikatoWe report on results from direct numerical simulation of the incompressible three dimensional magnetohydrodynamic (MHD) equations, modified to incorporate viscous dissipation via the strongly anisotropic ionparallel viscosity term. Both linear and nonlinear cases are considered, all with a strong background magnetic field. It is found that spectral anisotropy develops in almost all cases, but that the contribution from effects associated with the ionparallel viscosity is relatively weak compared with the previously reported nonlinear process. Furthermore, and in contrast to this earlier work, it is suggested that when B₀ is large, the anisotropy will develop and persist for many largescale turnover times even for nondissipative runs. Resistive dissipation is found to dominate over viscous even when the resistivity is several orders of magnitude smaller than the ion parallel viscosity. A variance anisotropy effect and anisotropy dependence on the polarization of the fluctuations are also observed.
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Massloading and parallel magnetized shocks
Zank, Gary P.; Oughton, Sean; Neubauer, F. M.; Webb, G. M. (1991)
Journal article
University of WaikatoRecent observations at comets GiacobiniZinner and Halley suggest that simple nonreacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that massloading is an important dynamical process within the shock itself, thereby requiring that the RankineHugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. We consider parallel magnetized shocks subjected to massloading, describe some properties which distinguish them from classical MHD parallel shocks, and establish the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the cometsolar wind interaction.
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Properties of massloading shocks: 1. Hydrodynamic considerations
Zank, Gary P.; Oughton, Sean (1991)
Journal article
University of WaikatoThe onedimensional hydrodynamics of flows subjected to mass loading are considered anew, with particular emphasis placed on determining the properties of massloading shocks. This work has been motivated by recent observations of the outbound Halley bow shock (Neubauer et al., 1990), which cannot be understood in terms of simple hydrodynamical or magnetohydrodynamical descriptions. By including mass injection at the shock, we have investigated the properties of the RankineHugoniot conditions on the basis of a geometric formulation of the entropy condition. Such a condition, which is more powerful than the usual thermodynamical formulation, serves to determine those solutions to the RankineHugoniot conditions which correspond to a physically realizable downstream state. On this basis a concise theoretical description of hydrodynamic massloading shocks is obtained. We show that massloading shocks have more in common with combustion shocks than with ordinary nonreacting gas dynamical shocks. It is shown that for decelerated solutions to the RankineHugoniot conditions to exist, the upstream flow speed u0 must satisfy u0 > ucrit > cs, where cs is the sound speed. Besides the usual supersonicsubsonic transition, massloading fronts can also admit a decelerating supersonicsupersonic transition, the structure of which consists of a sharp decrease in the flow velocity preceding a recovery and an increase in the final downstream flow speed. We suggest the possibility that such structures may describe the inbound Halley bow shock (Coates et al., 1987a). Both parallel and oblique shocks are considered, the primary difference being that oblique shocks are subjected to a shearing stress due to mass loading. It is conjectured that such a shearing may destabilize the shock.
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Transport theory and the WKB approximation for interplanetary MHD fluctuations
Matthaeus, William H.; Zhou, Ye; Zank, Gary P.; Oughton, Sean (1994)
Journal article
University of WaikatoAn alternative approach, based on a multiple scale analysis, is presented in order to reconcile the traditional WKB approach to the modeling of interplanetary fluctuations in a mildly inhomogeneous largescale flow with a more recently developed transport theory. This enables us to compare directly, at a formal level, the inherent structure of the two models. In the case of noninteracting, incompressible (Alfvén) waves, the principle difference between the two models is the presence of leadingorder couplings (called “mixing effects”) in the nonWKB turbulence model which are absent in a WKB development. Within the context of linearized MHD, two cases have been identified for which the leading order nonWKB “mixing term” does not vanish at zero wavelength. For these cases the WKB expansion is divergent, whereas the multiplescale theory is well behaved. We have thus established that the WKB results are contained within the multiplescale theory, but leading order mixing effects, which are likely to have important observational consequences, can never be recovered in the WKB style expansion. Properties of the higherorder terms in each expansion are also discussed, leading to the conclusion that the nonWKB hierarchy may be applicable even when the scale separation parameter is not small.
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Anisotropic threedimensional MHD turbulence
Matthaeus, William H.; Ghosh, Sanjoy; Oughton, Sean; Roberts, D. Aaron (1996)
Journal article
University of WaikatoDirect spectral method simulation of the threedimensional magnetohydrodynamics (MHD) equations is used to explore anisotropy that develops from initially isotropic fluctuations as a consequence of a uniform applied magnetic field. Spectral and variance anisotropies are investigated in both compressible and incompressible MHD. The nature of the spectral anisotropy is consistent with the model of Shebalin et al. [1983] in which the spectrum broadens in the perpendicular wavenumber direction, the anisotropy being greater for smaller wavenumbers. Here this effect is seen for both incompressible and polytropic compressible MHD. In contrast, the longitudinal (compressive) velocity fluctuations remain isotropic. Variance anisotropy is observed for low plasma beta compressible MHD but not for incompressible MHD. Solar wind observations are qualitatively consistent with both variance and spectral anisotropies of the type discussed here.
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Solar wind fluctuations: waves and turbulence
Oughton, Sean (2003)
Journal article
University of WaikatoWe present a brief review of observations and theory regarding the nature and radial evolution of MHD‐scale solar wind fluctuations. Emphasis is placed on the fact that the fluctuations consist of both waves and turbulence, and on their dual dynamical roles.
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Generation of Xpoints and secondary islands in 2D magnetohydrodynamic turbulence
Wan, Minping; Matthaeus, William H.; Servidio, Sergio; Oughton, Sean (2013)
Journal article
University of WaikatoWe study the time development of the population of Xtype critical points in a twodimensional magnetohydrodynamic model during the early stages of freely decaying turbulence. At sufficiently high magnetic Reynolds number Rem, we find that the number of neutral points increases as Rem3/2, while the rates of reconnection at the most active sites decrease. The distribution of rates remains approximately exponential. We focus in particular on delicate issues of accuracy, which arise in these numerical experiments, in that the proliferation of Xpoints is also a feature of underresolved simulations. The “splitting” of neutral points at high Reynolds number appears to be a fundamental feature of the cascade that has important implications for understanding the relationship between reconnection and turbulence, an issue of considerable importance for the Magnetospheric Multiscale and Solar Probe missions as well as observation of reconnection in the solar wind.
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Current singularities at finitely compressible threedimensional magnetic null points
Dmitruk, Pablo; Matthaeus, William H.; Oughton, Sean (20050715)
Journal article
University of WaikatoThe formation of current singularities at linetied two and threedimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, linetied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed.
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The impact of smallscale turbulence on laminar magnetic reconnection
Watson, P.G.; Oughton, Sean; Craig, Ian J.D. (200703)
Journal article
University of WaikatoInitial states in incompressible twodimensional magnetohydrodynamics that are known to lead to strong current sheets and (laminar) magnetic reconnection are modified by the addition of smallscale turbulent perturbations of various energies. The evolution of these states is computed with the aim of ascertaining the influence of the turbulence on the underlying laminar solution. Two main questions are addressed here: (1) What effect does smallscale turbulence have on the energy dissipation rate of the underlying solution? (2) What is the threshold turbulent perturbation level above which the original laminar reconnective dynamics is no longer recognizable. The simulations show that while the laminar dynamics persist the dissipation rates are largely unaffected by the turbulence, other than modest increases attributable to the additional small length scales present in the new initial condition. The solutions themselves are also remarkably insensitive to smallscale turbulent perturbations unless the perturbations are large enough to undermine the integrity of the underlying cellular flow pattern. Indeed, even initial states that lead to the evolution of smallscale microscopic sheets can survive the addition of modest turbulence. The role of a largescale organizing background magnetic field is also addressed.
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Solar wind fluctuations and the von Kármán–Howarth equations: The role of fourthorder correlations
Oughton, Sean; Wan, Minping; Matthaeus, William H.; Servidio, Sergio (2013)
Journal article
University of WaikatoThe von KármánHowarth (vKH) hierarchy of equations relate the secondorder correlations of the turbulent fluctuations to the thirdorder ones, the thirdorder to the fourthorder, and so on. We recently demonstrated [1] that for MHD, selfsimilar solutions to the vKH equations seem to require at least two independent similarity lengthscales (one for each Elsässer energy), so that compared to hydrodynamics a richer set of behaviors seems likely to ensue. Moreover, despite the wellknown anisotropy of MHD turbulence with a mean magnetic field (B₀), the equation for the secondorder correlation does not contain explicit dependence on B₀. We show that there is, however, implicit dependence on B₀ via the thirdorder correlations, which themselves have both explicit B₀dependence and also their own implicit dependence through fourthorder correlations. Some subtleties and consequences of this implicitexplicit balance are summarized here. In addition, we present an analysis of simulation results showing that the evolution of turbulence can depend strongly on the initial fourthorder correlations of the system. This leads to considerable variation in the energy dissipation rates. Some associated consequences for MHD turbulence are discussed.
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Energy dynamics in linear MHD with ion parallel viscosity
Oughton, Sean (1997)
Journal article
University of WaikatoAnalytic results for the time dependences of the kinetic and magnetic energies of an incompressible magneto fluid threaded by a strong uniform magnetic field B₀ are obtained. The governing equations are the linearised magnetohydrodynamic (MHD) ones, but with the conventional Laplacian dissipation replaced by ion parallel viscous effects. The behaviour is shown to depend on the relative sizes of the Alfvén frequency and the viscous and resistive dissipation rates. For many cases equipartition of the kinetic and magnetic energy holds at the (Fourier) modal level. An important exception to this behaviour occurs for twodimensional fluctuations, that is when the wavevectors are perpendicular to B₀.
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