von Karman correlation similarity in solar wind magnetohydrodynamic turbulence.

A major development underlying hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth, here extended empirically to plasma turbulence in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here, we analyze an ensemble of Elsässer autocorrelation functions computed from Advanced Composition Explorer data at 1 astronomical unit (AU), and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman's hypothesis applied to weakly compressive magnetohydrodynamic turbulence. This provides a firm empirical basis for employing the similarity decay hypothesis to the Elsässer correlations that represent the incompressive turbulence cascade. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.

Ensemble Space-Time Correlation of Plasma Turbulence in the Solar Wind.

Single point measurement turbulence cannot distinguish variations in space and time. We employ an ensemble of one- and two-point measurements in the solar wind to estimate the space-time correlation function in the comoving plasma frame. The method is illustrated using near Earth spacecraft observations, employing ACE, Geotail, IMP-8, and Wind data sets. New results include an evaluation of both correlation time and correlation length from a single method, and a new assessment of the accuracy of the familiar frozen-in flow approximation. This novel view of the space-time structure of turbulence may prove essential in exploratory space missions such as Solar Probe Plus and Solar Orbiter for which the frozen-in flow hypothesis may not be a useful approximation.

Anisotropic third-moment estimates of the energy cascade in solar wind turbulence using multispacecraft data.

The first direct determination of the inertial range energy cascade rate, using an anisotropic form of Yaglom's law for magnetohydrodynamic turbulence, is obtained in the solar wind with multispacecraft measurements. The two-point mixed third-order structure functions of Elsässer fluctuations are integrated over a sphere in magnetic field-aligned coordinates, and the result is consistent with a linear scaling. Therefore, volume integrated heating and cascade rates are obtained that, unlike previous studies, make only limited assumptions about the underlying spectral geometry of solar wind turbulence. These results confirm the turbulent nature of magnetic and velocity field fluctuations in the low frequency limit, and could supply the energy necessary to account for the nonadiabatic heating of the solar wind.

Spatial correlation of solar-wind turbulence from two-point measurements.

Interplanetary turbulence, the best studied case of low frequency plasma turbulence, is the only directly quantified instance of astrophysical turbulence. Here, magnetic field correlation analysis, using for the first time only proper two-point, single time measurements, provides a key step in unraveling the space-time structure of interplanetary turbulence. Simultaneous magnetic field data from the Wind, ACE, and Cluster spacecraft are analyzed to determine the correlation (outer) scale, and the Taylor microscale near Earth's orbit.

Spectral distribution of the cross helicity in the solar wind.

There are a variety of theoretical and observational indications that fluctuation energy in astrophysical and space plasma turbulence is distributed anisotropically in space relative to the magnetic field direction. The cross helicity, represented by correlations between velocity and magnetic field fluctuations, enters a magnetohydrodynamic description on equal footing with the energy, but its anisotropy has not been examined in the same degree of detail. Here we employ Advanced Coronal Explorer data to examine the rotational symmetry of the cross helicity. We find that the normalized cross helicity is associated more or less equally with all angular components of the fluctuations. This favors turbulence models that allow for cross communication between parallel and perpendicular wave numbers, suggesting that "wavelike" and "turbulencelike" fluctuations are strongly coupled.

Formulation of subgrid stresses for large-scale fluid equations.

A formulation is presented based on a previously derived self-consistent procedure for obtaining subgrid scale models for complex system of equations. Using linear stability analysis and numerical simulations of the one-dimensional Burgers equation the formulation is shown to be very stable numerically and to reproduce accurately the large-scale flow of a high-resolution, direct simulation. Moreover, the resulting equation has a structure very similar to the viscous Camassa-Holm equation recently introduced in the modeling of turbulent flows.