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Abstract

The stability, dynamics and energetics of an auroral shear layer are considered in the framework of incompressible, one‐fluid magnetohydrodynamics, under conditions where current flow through the system is limited by the finite Pedersen conductivity and an enhanced field‐aligned resistivity. The model includes a magnetospheric region where currents resulting from polarization electric fields and viscous forces are important, an ionospheric substrate of uniform conductivity, and a force‐free acceleration region, characterized by a linear current‐voltage relation and located at an intermediate altitude between the magnetospheric viscous/polarization layer and the ionosphere. It is assumed that the Alfvén wave transit time across the viscous/polarization layer is small compared with the eddy time. Neutral stability of the model system is determined for a class of one‐dimensional equilibria in which a specified current distribution at the upper boundary of the viscous/polarization layer produces a potential structure with convergent, localized reversals in the transverse (E×B) electric field. The calculated neutral curves depend on three nondimensional parameters related to the intensity of the imposed field‐aligned current, the shear layer scale size, and the ratio of resistive to viscous drag at equilibrium. Numerical simulations of unstable configurations show that (1) two‐dimensional quasi‐steady rotational states arise when the equilibrium is weakly unstable; (2) eddy shedding turbulent states can arise when the equilibrium is strongly unstable; and (3) the flow kinetic energy and energy input/dissipation rates in the model system are reduced as a consequence of the instability. Power spectral densities for the electric and magnetic fields are also evaluated along sample “satellite” cuts through the shear layer. An application to postnoon auroral forms confirms the tendency for 2D rotational motion and periodic bright spots, although the observed intensity of the upward field‐aligned current suggests that the effective resistivity of the system is not sufficient to suppress inductive fields in the vortex dynamics.

This paper proposes a criterion for initiation of leading edge vortex (LEV) formation on a finite wing in unsteady motion. Previous research has shown that a criterion called Leading Edge Suction Parameter (LESP) can predict the time of LEV formation in unsteady 2D airfoil flows. This research aims at extending the criterion to a 3D wing. An approach has been developed to calculate the spanwise variation of LESP using an unsteady vortex lattice method. Higher-order RANS CFD has been used to study a pitch-up motion for a large range of unswept finite-wing geometries to determine the time instant for LEV initiation. Correlation of the results from the UVLM and CFD analyses is used to study the effectiveness of the LESP criterion for predicting the time instant and spanwise location of LEV formation on the wings. It is shown that, for any given airfoil and Reynolds number, the maximum LESP on a finite wing at LEV initiation is largely independent of wing geometry and pitch-pivot location. Thus the LESP concept holds promise as an LEV initiation criterion for finite wings.

A new large-eddy simulation / Reynolds-averaged Navier-Stokes (LES/RANS) turbulence model is described in this work. In common with other such models developed at NCSU, the RANS-to-LES transition is facilitated by a flow-dependent blending function based on estimates of outer-and inner turbulence length scales. In contrast to prior work, the outer scale is a function of an eddy viscosity specifically used for this purpose. A transport equation for this eddy viscosity is solved, with excessive growth of eddy viscosity due to fluctuating strain rates controlled by a destruction term based on the von Kármán length scale. The new model is completely local and is capable of adjusting to the changing state of a boundary layer. The model is tested for incompressible and compressible flat-plate boundary layers at low and moderate Reynolds numbers and for flow over an airfoil with trailing-edge separation. The model is shown to be capable of predicting the composite structure of a boundary layer with minimal log-law mismatch.The model also possesses additional degrees of freedom that may enable improved predictions for strongly nonequilibrium turbulent flows.