A Two Dimensional Shock Capturing, Hydrodynamic Model of the Venus
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GEOPHYSICALRES•RCH •S, VOL.18, NO. 5, PAGES801-804, MAY 1991 A TWODIMENSIONAL SHOCK CAPTURING, HYDRODYNAMIC MODEL OF THE VENUS IONOSPHERE A. F. Nagy,A K6r•Ssmezeyl,J.Kim and T. I. Gombosi SpacePhysics Research Laboratory, TheUniversity of Michigan • A two-dimensional,time-dependent, shock capturing ModelDescription single-sp•ies(O+) hydrodynamicmodel of the Venus ionosphere, Govemin• Eouations whichsolves the coupledcontinuity, momentum and energy v _ _,•ons forthe altitude range of 150- 500km and the solar zenith The time-dependenttwo-dimensional continuity, momentum and anglerange of 0O - 180ø has been developed and is presented inthis energyequations for O+ ions and electronsare solvedself- paper.It was again demonstrated thatthe introduction oftopside consistently.Quasi-neutrality is assumed,i.e. ni = ne, wheren heat inflows leads to calculated dayside electron ,red ion denotesnumber density. Furthermore, the ion and electronsare temperatures,which are consistent with the measured values. In assumedto havethe samevelocity, i.e. Uion= Uelectmn,in other orderto reproducethe measured electron temperatures, which are words the cunvmtis assumedto be zero. Knudsen et al. [1981] have roughlyconstant over all SZA's,the heat inflows had to be reduced shownthat the transterminator flow is not stronglyinfluenced by the significantlyoverthe nightside compared tothe dayside values. The magneticfield; therefore,the use of a hydrodynamicapproach, calculatedtransterminator ion flowsare supersonic and relatively assumedin this model, is sufficient to elucidate the important •ose to the observedaverage values. The modelpredicts a aspectsof thehigh speed ion flow. The bulkmotion of theneutral dec•lerationshock at a SZAof about135 ø, consistent with the ion atmosphereis neglected. This is a reasonableassumption, because, tempe• andvelocity observations. in general,the ion velocities are significantly larger than the neutral ones.The assumptionof only a singleion species,O +, was Introduction necessaryin order to make the numerical solution "feasible". Howeverthis is a reasonablygood assumption,because above Our understandingof the coreroilingphysical and chemical about190 kin, O+ is thedominant ion speciesand the mainaim of processesin the ionosphere of Venushas advanced significantly thesecalculations is to establishthe ion flows and their effect, which sincethe launch of the PioneerVenus Orbiter (PVO) [Colin,1980]. becomesignificant only above about 200 kin. The chemical Thediscovery of the transonicflow directedfrom the dayside reactionsincluded in themodel are listedin Table 1. In calculating towardthe nightside of theVenus ionosphere was one of themany thechemical source for O+ fromreaction (R1), the [CO2 +] density -surp•ngfacts that PVO established[Knudsen et al., 1980].The wasapproximated from the photochemical equilibrium relationship: typicalhigh altitude transterminator ion velocitieswere found to be ofthe order of 2-3 km/sand are supersonic across the terminator at P(CO•) highaltitudes. The ion flow is drivenpredominantly by thelarge (k 1+ k2)[O] + k3[ne] lXe•-• gradient,which is presentacross the terminator[Knudsen (1) et al., 198!]. The rapid rise in ion temperaturesand whereP(CO2 +) is the photoionization rateof CO2 +. drop/mdomizationin ion velocities beyond a zenithangle of about Thecontinuity equation is: 150ø, led Knudsen et al., [1980]to suggesta shock deceleration of thesupersonic flow deepon the nightside. 1 J 1 3(AoPu0)=Sc_S1 A numberof modelshave been developed to studyand establish rAo B0 themechanisms responsible for thesesupersonic ion flows,but all ••t+••(Arpur) +----- (2) ofthese previous transport models had some limitations (e.g. use of The ion momentumequation in the radialdirection is: assumedvelocity components, limited spatialcoverage, lack of shock"capturing" ability). The need for a full-scale,two- dimensional,shock capturing model has been obvious for many •t[@Ur]+13 2 •1•[AoPurUo] years.However two dimensionalmodels capableof such calculationsarevery complex and computer intensive and have only = + + + beguntobe employed in the field of spaceplasma physics relatively A r (3) recently[e.g. Gombosi et al., !985]. A two-dimensional,time- Theion momentumequation in theangular direction is: dependent,shock capturing single-species (O+) hydrodynamic modelof the Venusionosphere, which solves the coupled cmtinuity,momentum and energy equations forthe altitude range of I 150- 500 km and the solar zenith angle range of 0 ø - 180ø has been developedandis presentedin this paper. This two-dimensional modelwill help us to evaluate the importance ofsupersonic day-to- = + +uSS- uo% + rA0 + aA__o•0 nightflows and, for the first time address, ina quantitative way, the (4) probabilityofshock formation inthe nightside ionosphere ofVenus. Table !. Ion chenfical reaction rates Reaction Rate constant .... (cmS,s,e, c'1 ) 1on leave from Central Research Institute forPhysics, Budapest, !525,Hungary (R!) CO2+ + O ..... > O+ + CO2 1.0xl 0'!ø (R2) CO2+ + O ..... > 02 + + CO 1.64xl 0'1ø Copyright1991 by the AmericanGeophysical Union. (R3) CO2+ + e ..... > CO + C 1.!4x10-agrc (R4) O+ + CO2 ..... > 02+ + CO 9.4x104ø Papernumber 9!GL00362 0094-8534/ 91 / 91GL-003 62 $03. O0 (.R5)... O. + + H ..... ,--.:>..H+ + O ...... 2.5X10-!1 Tn 1/2 ' 801 8O2 Nagyet al.: A 2D,Shock Capturing, HDModel of the Venus Ionosphere B9undaryand Initial Conditions Theion energy equation is: The upperboundary is setat 500 km altitude,and the lower boundaryis setat 150kin. Thetwo sideboundaries are at solar zenithangles (SZA) of 0ø and180 ø. The verticaland horizontal resolutionis5 kmand 5 ø SZA, respectively. For ion densities (@), 7t arr + chemicaland diffusiveequilibrium conditions are appliedat the lowerand upper boundaries, respectively. For verticalvelocities (Ur),the conditions Ur=0 and 3u•/3r=-0, are imposed atthe upper boundaryon the day and nightside respectively, but no flows into +-rA0 " A0u0• •i •lpi +Ur• +u0r• thesystem are allowed. Vertical (Ur) and horizontal velocities (u0) arekept equal to zero at the lower boundary. The floating boundary 3 K condition,3u0/3r=-0 is imposedat the upperboundary for the =Qi + •r(F•+F•) +u0(F• +F$) +•3( K•3Ti• W)+ r•( •3T• horizontal velocities (u0). _For ion and electron temperature cri,Te) ' theheat fluxes, • = -KOT/3r,are set at theupper boundary. Ti and Te areset equal to theneutral temperatures (Tn) at thelower u•2 +u 0 + - _ • boundary.The floating boundary conditions (3p/r30--0; 3Ur/rO•-0; +-( 2 o2•i-1)miJkT n•S c (u3 +u•2 +(•i p•l)P[•S1 3Ti/r30=0;3Te/r30=0) are set at theside boundaries (SZA = 0ø, O) 180ø),except that the horizontalvelocities (u0) havereflective boundaryconditions (u0 i,n+ 1 = -u0i n) atSZA= 180 ø. •e electronener• equationis: In orderto establisi•confidence' in our model, a numberof differenttest runswere cardedout. In one casewe droppedall • 1 • 1 • sourceterms and perturbed the density to checkif thepropagation speedis equal to the sonic speed. A testmn with all the source terms ••YPe: i•+••[Arur Ar • L Y•:•Pe•+ r• •[A0u0 •e - t J includedwas alsocarried out for the caseof no horizontalvariatior• of the inputdata (photoionization rates, neutral densities, and photoelectronheating rates) to comparewith previous 6ne. dimensional model results. The results of these pseudoone- Pe dimensionalcalculations areused as the initial conditions forthe =Qe +•• ea% + O K r•) kTn- 1)m•Sc- (7e' 1)pc S1numericaltwo-dimensional method calculations.can be foundin A Kimmore [1991].detailed description ofthe (6) InputParameters. where All inputparameters for the model are for solar cycle maximum r radial component; conditions(F10.7 =200). The neutral densities are from Hedin et 0 angularcomponent; al., [1983]except for the H densities,which were taken from subscripti ions; VIRA(VenusInternational Reference Atmosphere) [Keating etfl., subscripte electrons; 1985]and extrapolated (VIRA only gives densities forF10.7 =15,0 subscriptn neutrals; conditions).The presenceof hot oxygenis neglected. p massdensity (=Pi = Pemi/rne ) Photoionizationrates and electron heating rates are calculated Ar,A0 areafunction in radialand angular every5ø SZA and 5 kmaltitude grids using the two-stream model direction,respectively, Nagyand Banks [1970]. Ion production rates were arbitrarily (Ar= r2; A0= sin0); decreasedfrom 90 ø to 100ø SZA by a factorof 100and remaiv•l Sc,S1 ionproduction andloss rate, respectively; constant after 100ø SZA in orderto removethe effectof Ur,U0 plasmavelocity photoionizationonthe nightside. Onthe nightside, theelectron p pressure; heatingrates are set to thevalues at theterminator inorder to ¾. specificheat ratio; approximatetheheating due to the transported photoelectrons ard Frl,F0i ionforce term precipitatingenergetic electrons. Fre,F0e electronforce term k Boltzmann constant; Results and Discussions m mass; T temperature; Thecomputer intensive nature ofthis model allowed only alimit• K thermalconductivity; numberoftest cases tobe run, therefore theinput parameters and Qi netion heating rate, boundaryconditions could not be "tuned forthe best" results, in Qe netelectron heating rate, termsofan overall agreement withobservations. However thei•Jtial urO,u0o bulkvelocity ofthe newly created species. useand purpose ofthis model isto establish thenature of transterminatorionflow and related energetics ina quantitative a• Sphericalgeometry isused and axial symmetry around the sun- selfconsistent manner, rather than fit the observed values exactly. Venusaxis is assumed.The use of these"five moment"