title: Evolution of energy-containing turbulent eddies in the solar wind

authors: Matthaeus, William H.

abstract: Previous theoretical treatments of fluid-scale 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 quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale 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 two-dimensional 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.

text: Evolution of energy-containing turbulent eddies in the solar wind Previous theoretical treatments of fluid-scale 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 quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale 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 two-dimensional 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.

year: 1994

title: Steady free surface flows induced by a submerged ring source or sink

authors: Stokes, Tim E.

subjects: critical layers

abstract: The steady axisymmetric flow induced by a ring sink (or source) submerged in an unbounded inviscid fluid is computed and the resulting deformation of the free surface is obtained. Solutions are obtained analytically in the limit of small Froude number (and hence small surface deformation) and numerically for the full nonlinear problem. The small Froude number solutions are found to have the property that if the non-dimensional radius of the ring sink is less than ρ=√2, there is a central stagnation point on the surface surrounded by a dip which rises to the stagnation level in the far distance. However, as the radius of the ring sink increases beyond ρ=√2, a surface stagnation ring forms and moves outward as the ring sink radius increases. It is also shown that as the radius of the sink increases, the solutions in the vicinity of the ring sink/source change continuously from those due to a point sink/source (ρ=0) to those due to a line sink/source (ρ→∞). These properties are confirmed by the numerical solutions to the full nonlinear equations for finite Froude numbers. At small values of the Froude number and sink or source radius, the nonlinear solutions look like the approximate solutions, but as the flow rate increases a limiting maximum Froude number solution with a secondary stagnation ring is obtained. At large values of sink or source radius, however, this ring does not form and there is no obvious physical reason for the limit on solutions. The maximum Froude numbers at which steady solutions exist for each radius are computed.

text: Steady free surface flows induced by a submerged ring source or sink The steady axisymmetric flow induced by a ring sink (or source) submerged in an unbounded inviscid fluid is computed and the resulting deformation of the free surface is obtained. Solutions are obtained analytically in the limit of small Froude number (and hence small surface deformation) and numerically for the full nonlinear problem. The small Froude number solutions are found to have the property that if the non-dimensional radius of the ring sink is less than ρ=√2, there is a central stagnation point on the surface surrounded by a dip which rises to the stagnation level in the far distance. However, as the radius of the ring sink increases beyond ρ=√2, a surface stagnation ring forms and moves outward as the ring sink radius increases. It is also shown that as the radius of the sink increases, the solutions in the vicinity of the ring sink/source change continuously from those due to a point sink/source (ρ=0) to those due to a line sink/source (ρ→∞). These properties are confirmed by the numerical solutions to the full nonlinear equations for finite Froude numbers. At small values of the Froude number and sink or source radius, the nonlinear solutions look like the approximate solutions, but as the flow rate increases a limiting maximum Froude number solution with a secondary stagnation ring is obtained. At large values of sink or source radius, however, this ring does not form and there is no obvious physical reason for the limit on solutions. The maximum Froude numbers at which steady solutions exist for each radius are computed.

year: 2012

title: Haere mai rā

authors: Maxwell, Te Kahautu

abstract: Whakaeke (entrance). Lyrics composed by Te Kahautu Maxwell, Musical score composed by Te Whānau Mitai. Performed by Ōpōtiki Mai Tawhiti (Kapa Haka group) (3mins)

Waiata Tira: Aroha
Whakaeke: Haere mai rā
Mōteatea: Te Pātere a Te Turuki
Poi: Iarararararī
Waiata ā ringa: Taku Mana Māori Motuhake
Haka: Waiwharangi
Whakawātea: Āio

text: Haere mai rā Whakaeke (entrance). Lyrics composed by Te Kahautu Maxwell, Musical score composed by Te Whānau Mitai. Performed by Ōpōtiki Mai Tawhiti (Kapa Haka group) (3mins)

Waiata Tira: Aroha
Whakaeke: Haere mai rā
Mōteatea: Te Pātere a Te Turuki
Poi: Iarararararī
Waiata ā ringa: Taku Mana Māori Motuhake
Haka: Waiwharangi
Whakawātea: Āio

year: 2020