A self-consistent non-evolving two dimensional slab model of a viscous low-latitude boundary layer (LLBL) coupled to the ionosphere was developed by Phan, et al., (1989). Numerical results from the model and possible use of observations to determine the model parameters are discussed. The dynamical model developed by Lotko, et al., (1987) was used by Lotko and Shen (1991) to examine dynamical processes relevant to the LLBL with particular application to post-noon auroral shear layers. Initial results from a magnetohydrodynamic study of flank-side mangetopause boundary configuration are described. Effects of compressibility, scalar viscosity, and electrical resistivity are included in the MHD equations

Lotko, William

Sonnerup, B. U. O.

English

NASA Technical Reports Server

INVESTIGATION OF TURBULENT PROCESSES
IN MAGNETOSPHERIC BOUNDARY LAYERS
/ - c
cYO
r7
Final Technical Report
Grant NAGW- 1169
9/1/87- 2/28/90
National Aeronautics and Space Administration
Office of Space Science and Applications
Space Physics Division
Magnetospheric Physics Branch
submitted by
Thayer School of Engineering
Dartmouth College
Hanover, NH 03755
Principal Investigators:
William Lotko
B.U.O. Sonnerup
(NASA-CR-I_8009) INVFSTIGATI_N OF TURBULENT
PRJCES_ES IN MAGNETOSOHERIC _UNOAAY LAYER_
fin._l Technic:_! _eport, I Sop. 1987 - 28
FeD. 1990 (" tmouth Coll ) 9 p. _:.:r . CSCL 04A
N91-22628
Unclas
G3/_5 0001580
https://ntrs.nasa.gov/search.jsp?R=19910013315 2020-03-19T17:59:51+00:00Z
NASA Final Technical Report
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Final Technical Report
1. Summary of Results
1.1. Self-Consistent Slab Model of a Viscous LLBL
A self-consistent non-evolving two-dimensional slab model of a viscous low-latitude
boundary layer (LLBL) coupled to the ionosphere was developed by Phan et al. [1989]. In the
model, an exact balance is maintained between jxB forces and viscous forces generated by
A
unidirectional shear flow, v = -xV(y), in the layer. Thus the structure and thickness of the layer
do not evolve in the flow direction. The flow velocity V(y) has its maximum value, Vo, at the
magnetopause edge of the layer and then drops to zero or to some magnetospheric sunward
A
convection speed v = +xV,,. at the inner edge. The magnetic field in the layer is determined self-
consistently from the currents, the result being parabolic shapes of the field lines with the vertices
pointing tailward and with the field lines adjacent to the magnetopause having the greatest
curvature, those at the magnetospheric edge of the layer being straight. A qualitative sketch of the
geometry is shown in Figure 1.
z
!
,,,,"
iK
/d ¢'
L I_IB.
3 -t_j.
Figure 1. Model of non-evolving low latitude boundary layer and its connection to
the ionosphere. [Phan et al., 1989]
More precisely, the magnetic field in the layer is found to be of the following exact form: Bx =
(z/Ho)Bxl(Y), By -- 0, Bz - Bz(y), where Bxl(Y) is a maximum at the magnetopause, i.e., at y = 0,
and Bxl(Y) _ 0 as y --->_, i.e., at the magnetospheric, or "inner" edge of the layer. Also, Bz(y) is
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a minimum at y = 0 and approachesits magnetosphericlevel, Bo, asy _ 0-. The variation in
magneticpressureacrossthelayer is balancedpreciselyby theplasmapressurein the boundary
layer. Themagneticpressureis aminimumandtheplasmapressurea maximumin theequatorial
plane(z = 0) adjacento themagnetopause(y -- 0); asy --_** or Izl--_Ho themagneticandplasma
pressuresboth approachtheir magnetosphericlevels,B_,2/2laoandp_, respectively. At Izl= Ho
thecurrentcomponentsjz andjx arecontinuousandaresuchthat theyform a netcurrent thatis
exactlyparallelto themagneticfield ateachy value. Thecurrentcomponentjy(y) which is nonzero
andindependentof z for Izl<Hois switchedto zeroabruptlyat Izl= I4o. Theviscousforce is also
switchedoff at thatlocationsothattheboundarylayermodelterminatesthere. However,thefield
alignedcurrents,Jll,arethenmappedalongB into the ionospherebyuseof appropriategeometrical
mapping factors. Field-aligned potential drops, A_II, governed by a simple conductance
relationship, jll = _A(_II, are allowed for and the field-aligned currents are then deflected into
horizontal Pedersen currents in the ionosphere, which is modelled as a purely resistive substrate.
Numerical results from the model are presented in the paper by Phan et al. [1989] and the
possible use of observations to determine the model parameters is discussed. The general
predictions of the model in terms of region 1 currents and associated ionospheric signatures are
similar to those obtained earlier by Lotko et al. [1987] and by Sonnerup [1980]. Those predictions
are in qualitative and approximately quantitative agreement with a number of observations. The
main new contribution of the study is to provide a better description of the field and plasma
configuration in the LLBL itself and to clarify in quantitative terms the circumstances in which
induced magnetic fields become important. In particular, it appears that for the low values of the
field-aligned conductance expected on the duskside of the magnetosphere, these fields may remain
relatively unimportant, at least in the noon to dusk segment of the LLBL.
1.2. Auroral Shear Layer Dynamics
The dynamical model developed by Lotko et al. [1987] was used by Lotko and Shen
[1991] to examine two-dimensional dynamical processes of relevance to the LLBL with particular
application to post-noon auroral shear layers. In this model, the magnetic field threading the layer
is taken to be uniform. The plasma motion within the layer is incompressible and confined to
planes perpendicular to the magnetic field. The equation of motion includes inertia effects,
pressure gradients, the jxB force, and a viscous force; the current j is determined via coupling to
the ionosphere with allowance for the effects of field-aligned potential drops. The approach taken
by Lotko and Shen is to treat the distribution of field-aligned current generated in the LLBL proper
as given, and ask what are the dynamical consequences of such currents in the lower altitude, low
13region extending along magnetic field lines from the bottom of the LLBL to the ionosphere.
Although the distinction between the LLBL region and the tenuous plasma region below it is
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somewhatartificial in Lotko andShen'sanalysis,thefact that E×B shearflow instabilitiestendto
besuppressedby thestrongmagneticshearthataccompaniesfield-alignedcurrentsin thehigher_,
LLBL region,andthatthegenerationof currentsby anenhancedviscousinteractionis substantial
in theLLBL relative to the tenuousplasmaregion below it, suggeststhat sucha distinction is
qualitatively meaningful. Given this distinction, the stability of the shearlayer canbe readily
evaluated,asshownin thefigure below.
'°°L X_ ' ', + ' ' '_ '/
,o- \ . //
i \_ STABLE
l[ I _ /L t I ' , I J t__ t L
.I I o'/). I0
i
I00
Figure 2. Neutral stability curves for effective Hartmann number M = 0.5, 1.5, 10,
and 105. For a given value of M, the shear layer is linearly stable below the curve
corresponding to that value of M and unstable above it.
The neutral curves depend on three nondimensional parameters related to the amplitude of the field-
aligned current (or ExB velocity amplitude) produced by the LLBL, the scale size of the current
distribution, and the so-called Hartmann number, which is a measure of the relative importance of
resistive drag in the ionosphere proper and viscous drag in the viscous/polarization layer above the
ionosphere. Numerical simulations of unstable cases show that (1) 2D quasi-steady rotational
states arise when the shear layer is weakly unstable, (2) eddy shedding turbulent states can arise
when the shear layer is more strongly unstable, and (3) the flow kinetic energy and energy
dissipation by ionospheric Joule heating, production of field-aligned particle fluxes, and viscous
heating are all reduced as a consequence of the instability. Power spectral densities are also
evaluated along selected "satellite" cuts through the shear layer. The results of the study confirm
the observed tendency for 2D rotational motion and periodic bright spots in post-noon auroral
forms, although an important finding of the study is that typically observed electric current
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densities in post-noon auroral regions are sufficiently large to require a full inductive treatment, in
which Alfv6n waves may play a prominent role.
1.3. Magnetic Field Draping at the Magnetopause Boundary
Initial results from a magnetohydrodynamic simulation study of a flank-side magnetopause
boundary configuration are described in the paper by Richard and Lotko [1990]. Effects of
compressibility, scalar viscosity and electrical resistivity are included in the MHD equations. The
geometry allows 2D variations of all three components of magnetic field and velocity, as well as
the density and pressure, in the plane containing the boundary normal and initial magnetic field
directions, i.e., variations in the downstream direction are not allowed. While dynamical effects
are allowed in principle, the relatively low values of the mechanical and magnetic Reynolds
numbers (300 - 1000) used in the simulations tend to suppress any large amplitude fluctuations that
might arise after the initial transients have died away. Consequently, the results are illustrative of
time-average properties. Boundary normal flows are imposed at the magnetosheath and
magnetopause boundaries (a merging type configuration); a shear in the tangential (downstream)
flow is also imposed by the boundary conditions. The major new finding of this study, as
illustrated in the figure below, is the formation of a substantial "draping" field - the magnetic field
component in the tangential downstream/upstream direction.
Z (NORTH)
B-LINE TOEARTH
TO IMF
Figure 3. Schematic of the simulation geometry and normal field line draping. A
draped, reconnected field line is shown along with its projection onto the yz plane.
Projections of streamlines are drawn on the same plane, while tailward an_
sunward flows are indicated on the equatorial plane (the flow there has a small y
component, hut it has been omitted for clarity. The magnetosheath end of the
reconnected field line is pulled and-sunward relative to the magnetospheric end due
to the shear in Vx. This effect generates a Bx component.
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The currents responsible for the draping field appear to be consistent with the sense of direction of
the region 1 currents that flow into/out of the ionosphere. However, the effects of the ionosphere,
e.g., as represented by current closure in a conducting substrate, are not presently included in the
model. Considerable effort has been expended in demonstrating that the phenomenon is robust, in
particular for a variety of different inflow/outflow boundary conditions.
2. Bibliographic References of Publications (abstracts attached)
Lotko, W. and M. Shen, On large scale rotational motions and energetics of auroral shear layers,
J. Geophys. Res., in press, 1991.
Phan, T.D., B.U.O. Sonnerup and W. Lotko, Self-consistent model of the low-latitude boundary
layer, J. Geophys. Res., 94, 1281, 1989.
Richard, R.L. and W. Lotko, Magnetic field draping at the low-latitude magnetopause, submitted
to J. Geophys. Res., August, 1990.
3. Student Support
Ian Gregory (graduate research assistant), 1/1/88 - 2/28/90.
NASA Final Technical Report 7 Grant NAGW-1169
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On Large Scale Rotational Motions and Energetics
of Auroral Shear Layers
w, Lotko and M.-M Shen
Tharyer School of Engineering, Dartmouth College, Hanover, NH 03755
ABSTRACT
The stability, dynamics and energetics of an auroral shear layer ate considered
in the framework of incompressible, one-fluid magnetohydrodynamies, under condi-
tions where current flow through the system is limited by the finite Pedersen conduc-
tivity and an enhanced field-aligned resistivity. The model includes a magnetospheric
region where currents resulting from polarization electric fields and viscous forces ate
important, an ionospheric substrate of uniform conducuvity, and a force-free accelera-
tion region, characterized by a linear current-voltage relation and located at an inter-
mediate altitude between the magnctospherie vi_r.ou.Vpolarization layer and the iono-
sphere. It is assumed that the Alfv_ 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 distri-
bution at the upper boundary of the viscous/polarization layer pmduoes a potential
structure with convergent, localized reversals in the tran_erse (E x B) electric field.
The calculated neutral curves depend on three nondimensional parameters related to
the intensity of the imix_d field-aligned cta'rent, the shear layer scale size, and the
ratio of resistive to viscom drag at equilibrium. Numerical simulations of unstable
configurations show that (1) 2D qtmsi-sleady rotational states arise when the equili-
brium is w_dy unstable,; (2) eddy shedding tuttmlent states can asise when the equili-
brium is _ocqOy 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 spec-
tral densities for the electric and magnetic fields are also evaluated along sample
'satellite' cuts through the shear layer. An application to post-noon 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 resis-
tivity of the system is not sufficient to suppress inductive fields in the vortex dynam-
ics.
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JOLRN_L OF GEOPHYSICAL RESEARCH. VOL. 94. NO. A2. PAGES i281-1293. FEBRUARY 1. 1989
Self-Consistent Model of the Low-Latitude Boundary Layer
T. D. PHAN, B. U. 6. SONNERUP, AND W. LOTKO
Thayer School of Engineering, Dartmouth Colleo¢, Henover, New Hampshire
A simple two-dimensional, steady state, viscous model of the dawnside and duskside low-latitude
boundary layer (LLBL) hn._ been developed. It incorporates coupling to the ionosphere via field-
aligned currents and associated field-aligned potential drops, governed by a simple conductance
law, and it describes boundary layer currents, ms.eric fields, and pluma flow in a self-cor_sistent
manner. Slab geometry is auumed, with no vn._iatious along the flow direction -_ and with the
layer on closed field lines. The currents in the layer are regulated by coupling to the ionosphere.
The magnetic field induced by these currents leads to two effects: (1) a diamagnetic depression of
the magnetic field in the equatorial region and (2) bending of the field lines into parabolss in the
rz plane with their vertices in the equatorial plane, at z -- 0, and pointing in the flow direction,
i.e., tailward. Both effects are strongest at the magnetopsuse edge of the boundary layer and
vanish at the magnetospheric edge. The diamagnetic depresmon corresponds to an excess of
plasma pressure in the equatorial boundary layer near the magnetopause. This pressure drops
off both with increasing distance z from the equatorial plane and with inere_dng distance y from
the magnetopause. It reaches the magnetospheric level for z _. :k/'/as well ss for y -- oo. The
boundary layer structure is governed by a fourth-order, nonlinear, ordinary differential equation
in which one nondimensional parameter, the Hartm&nn number M, appears. A second parameter,
introduced via the boundary conditions, is a nondimensional flow velocity v o at the mAgnetopatme.
It is shown that for large M values the coupling to the ionosphere is weak; in that limit, or when
v_ is small, the model reduces to that discussed by Lotko et al. (1987) in which induced magnetic
fields are neglected. Numerical results from the model are presented and the possible use of
observations to determine the model parslrtetens is disctumed. The general predictions of the
model in terms of region 1 currents and _socisted ionospheric signstures are similar to those
obtained earlier by Lotko et al. and by Sonnerup (1980). Tho_ predictions are in qualitative and
approximately quantitative agreement with a number of observations. The main new contribution
of the study is to provide a better description of the field and plasma configan'ation in the LLBL
itself and to clarify in quantitative term_ the circumstances in which induced mn4vaetic fields
become important, In particul_, it appears that for the low values of the field-aligned conductance
expected on the dusk.side of the magnetosphere, these fields may remain relatively unimportant,
at least in the noon to dusk segment of the LLBL.
NASA Final Technical Report 9 Grant NAGW-1169
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Magnetic Field Draping at the Low Latitude Magnetopause
R. L. POchard, W. Lotko
Thayer School of Engineering, Dartmouth College
Abstract
The structure of the low-latitude magnetopause is investigated for
IMF conditions with a dominant southward component using magneto-
hydrodynamic simulations. The structure is self-consistentlycalculated
as an initial-valueproblem in which the system is allowed to evolve to
a quasi-steady-state.All components of the three-dimensional velocity
and magnetic fieldas well as compressibility,resistivityand viscosity
are included in the two-dimensional calculation. The boundary condi-
tions sustain inflow from the magnetosheath and the magnetosphere, as
well as a flow tangential to the magnetopause, sunward in the magne-
tosphere and tailward in the magnetosheath. The tangential flow leads
to the draping of magnetic fieldlinesin the magnetopause region. No
draping (tailward or sunward) was included initially,while as the sys-
tem evolved this component of the magnetic fieldbecame comparable in
magnitude to the other two components. The resultingdraping struc-
ture isfound to be dependent sensitivelyon the ratioof the viscous and
magnetic ditfusivities.


Investigation of turbulent processes in magnetospheric boundary layers

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