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Are granules good tracers of solar surface velocity fields

Are granules good tracers of solar surface velocity fields
Are granules good tracers of solar surface velocity fields

a r X i v :a s t r o -p h /0108284v 1 17 A u g 2001

1

https://www.doczj.com/doc/ba8513168.html,ing a numerical simulation of compressible convection with radiative transfer mimicking the solar photosphere,we compare the velocity ?eld derived from granule motions to the actual velocity ?eld of the plasma.We thus test the idea that granules may be used to trace large-scale velocity ?elds at the sun’s surface.Our results show that this is indeed the case provided the scale sepa-ration is su?cient.We thus estimate that neither velocity ?elds at scales less than 2500km nor time evolution at scales shorter than 0.5hr can be faithfully described by granules.At larger scales the granular motions correlate linearly with the underlying ?uid motions with a slope of <

~2reaching correlation coe?cients up to ~0.9.Key words:Convection –Sun:granulation –Sun:pho-tosphere

A&A manuscript no.

(will be inserted by hand later)

ASTRONOMY

AND ASTROPHY SICS

Send o?print requests to:M.Rieutord tion and radiative transfer

originally developed by two of the authors(for a description see Stein&Nordlund, 1998).For this particular run,which aims at simulating supergranulation,certain trade-o?s have been made be-tween physical realism and computational demands:the radiative transfer was treated in grey approximation(with frequency independent opacity,with a dependence on tem-perature and pressure similar to that of the solar contin-uum opacity)and the horizontal resolution was chosen to be a rather coarse95km.The restrictions made it a?ord-able to study a large volume(30×30Mm2wide and3Mm deep represented by315×315×82grid points)which con-tained several hundred granules at any given instant in time.

In section2of this letter we shall present a global view of the velocity?eld,following Euler’s viewpoint while in section3we try to characterize the granules in their ability at tracing the?ow?eld,thus adopting Lagrange’s viewpoint.Our conclusion is that granules are able to trace statistically the large-scale?ows but lead to a systematic underestimation of the actual velocities.

2.Euler’s view

As granules are extended test particles,the measured ve-locity?elds are much less resolved than the one issued from the simulation.Typically,our granule tracking tech-nique yields a velocity?eld on a45×45grid,i.e.seven times coarser than the original315×315pixels.Hence,for comparison,simulated velocity?elds are rebinned(aver-aged)to this coarser resolution.Granules also decrease the time resolution and velocity?elds issued from granule tracking are usually averaged over a time window longer than5min;here,we shall consider three time-windows with durations of1000s,1h,and2h.

But granules are also three-dimensional structures and therefore they“feel”the large-scale velocity?elds aver-aged over some range of depths.The approximate depth

Rieutord et al.:Are granules good tracers of solar surface velocity ?elds?3

Fig.1.Correlations between the velocity ?eld obtained from granule tracking and the actual velocity ?eld as a function of depth and time-window;both methods (LCT and CST)give very similar results.A layer 78km thick has been used.

Fig.4.For three length scales (20,21,22),we represent the actual velocity (v which is either v x or v y )as a function of the measured velocity u for a two-hours average.The clouds represent the 452grid points.The best ?ts (dashed line)show that granules underestimate actual velocities by a factor which varies from 2.1at small scales (20)to 1.6at large scales (22).

and thickness of the contributing layer need to be deter-mined.

Using the three above mentioned time-windows,we plotted in Fig.1the linear correlation between veloc-ity ?elds issued from granule tracking u (for a descrip-tion of how this ?eld is derived,see Roudier et al.1999or Rieutord et al.2001)and the “original”ones v as a function of depth;this correlation is de?ned by C v = u ·v /

4Rieutord et al.:Are granules good tracers of solar surface velocity

?elds?

Fig.2.Optimal depth for di?erent thicknesses (line type)of the contributing layer as a function of the time-window.We see that the depth at which correlation is maximum,remains around 250±30km.

relation when small spatial scales

are ?ltered out.This is indeed the case,as shown by https://www.doczj.com/doc/ba8513168.html,ing the decompo-sition of the velocity ?eld onto the di?erent scales yielded by a MultiResolution Analysis with Daubechies’wavelets,using the scaling function φ4(Daubechies,1992),we show that the correlation reaches ~0.9at the largest scale avail-able.

In Fig.4,we plotted the actual velocity as a function of the measured velocity for various length scales.The clouds of points clearly show that granules motions sta-

Fig.3.Dependence of the correlations with the spatial scale for the three time averages;the depth used is the optimal depth and the thickness is 78km.The 20scale corresponds to a resolution of 7×7pixels or 667×667km 2;we understand the saturation of the 23scale as a conse-quence of the very few resolution elements left for this scale (~5×5).Line type have the same meaning as in Fig.1.

tistically underestimate the actual plasma velocity by a factor which (likely)tends to unity as the scale increases.When no ?ltering is made,measured velocities miss “real”velocities by roughly a factor 2.This quantitative dis-agreement is of course even more pronounced in derivative quantities (divergence or vorticity).

This behaviour is of course no surprise because gran-ules are far from being passive lagrangian tracers:on the contrary they are active vortical structures which can move in the background ?uid thanks to their own vor-ticity or the one of their neighbours.Their motion may be compared (but just qualitatively)to the random motion of molecules in a gas:only long time averages or large-scale averages are able to raise the signal of the mean motion above the noise of random motions.

Finally,let us mention that we have done these tests using the two presently known methods of granule track-ing,namely LCT and CST.As illustrated in Fig.1,both methods give remarkably close results (within a few per-cent in correlation),a fact which gives con?dence in the robustness of the results.CST,however,o?ers additional informations on the way individual granules follow the background ?ow;namely,we can appreciate which gran-ules are the most faithful tracers and characterize them by some property (size or lifetime for instance).We discuss this issue in the next section.

Fig.5.Maximum correlation (solid line)between the ac-tual velocity ?eld and the granule displacement at the place of the granule versus the surface area of the https://www.doczj.com/doc/ba8513168.html,rge granules are only slightly more correlated than smaller ones.The dashed line indicates the depth at which correlation is optimum.

https://www.doczj.com/doc/ba8513168.html,grange’s view

To see which granules are good or bad lagrangian tracers we computed the correlation between the mean velocity of

Rieutord et al.:Are granules good tracers of solar surface velocity?elds?

5 Fig.6.Maximum correlation(solid line)between the ac-

tual velocity?eld and the granule displacement at the

place of the granule versus the lifetime of the granule.

The dashed line indicates the depth at which correlation

is optimum.

individual granules(i.e.the velocities issued from granule

tracking which yield the45×45dataset)and the actual ve-

locity at the place of the granule.We did this computation

for di?erent granular sizes(Fig.5)and lifetimes(Fig.6).

Fig.5clearly shows that the size is a poor criterion

for selecting granules whose motions represent the plasma

?ow.This?gure,however,shows that large granules are

sensitive to’deep’undercurrents.The depth for optimal

correlation increases with the size of the granules.

On the other hand,the life-time is a good criterion for

sampling the plasma velocity?eld.The motion of long-

lived granules can reach0.9correlation with the actual

?ow?eld as shown in Fig.6.Besides,the layer sampled by

these granules is not precisely de?ned and oscillate around

theτ=1level.

4.Conclusions

We have used a simulation of compressible convection with

radiative transfer in grey approximation to test the ability

of granules at tracing the actual plasma?ow.The box used

for this simulation is30×30Mm2wide and3Mm deep,

resolved by a315×315×82grid.The results of these tests

show that

–Granules tend to be lagrangian tracers when the time

and length scales of the?ow tend to in?nity:it shows

that scale separation is a necessary condition for using

granules at representing plasma?ows.Quantitatively,

we?nd that the length scale needs to be larger than

2.5Mm and the time scale longer than1h for the cor-

relation to be higher than0.9.

–They underestimate the velocity?eld,all the more that

scale separation is weak.

–Statistically,they probe a layer300-400km beneath

theτ=1surface.

–Long-lived granules are good tracers.

Hence,we see that granules can be used as tracers to

reveal?ows at meso-and supergranular scale.At smaller

scales their own velocity?eld has a too strong interaction

with the background velocity?eld.However,it may well

be that velocity?elds associated with exploding granules

or with‘strong positive divergences’(see Rieutord et al.,

2000),which are near the lowest(allowed)scale,are cor-

rectly represented by granules motions,at least qualita-

tively,since they are strong advective motions in nature.

Finally,let us note that the situation in the real sun

may not be better than that of the simulation for the

Reynolds number is much higher:nonlinear interactions

are indeed stronger and thus real granules are less pas-

sive.On the other hand,the drift of the thermal structure

with respect to pure advection,which is another pitfall

of granule tracking,is likely correctly represented by the

simulation since it depends on the P′e clet number which

is modeled accurately by the simulation in the layers of

interest.

Acknowledgements.Calculations have been carried out on the

CalMip machine of the CICT which is gratefully acknowl-

edged.R.F.Stein acknowledges?nancial support by NASA

grant NAG5-9563and NSF AST grant98-19799.?A N acknowl-

edges support by the Danish Research Foundation,through its

establishment of the Theoretical Astrophysics Center.

References

Daubechies,I.1992,Ten lectures on wavelets(SIAM)

November,L.J.1989,in High Spatial Resolution Solar

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November,L.J.&Simon,G.W.1988,Astrophys.J.,333,

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Rieutord,M.,Roques,S.,Roudier,T.,&Ducottet,C.

2001,to be submitted to A&A,1,1

Rieutord,M.,Roudier,T.,Malherbe,J.M.,&Rincon,F.

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Roudier,T.,Rieutord,M.,Malherbe,J.,&Vigneau,J.

1999,Astron.&Astrophys.,349,301

Stein,R.F.&Nordlund,?A.1998,Astrophys.J.,499,914

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16.你决意离职的动机是什么? 思路: 1、最重要的是:你要使航空公司相信,你在过往的单位的“离职原因”在这里不存在。 2、避免把“离职原因”说得太详细、太具体。 3、不能掺杂主观的负面感受,如“太幸苦”、“人际关系复杂”、“管理太混乱”、“公司不重视人才”、“公司排斥我们某某的员工”等。 4、但也不能躲闪、回避,如“想换换环境”、“个人原因”等。 5、不能涉及自己负面的人格特征,如不诚实、懒惰、缺乏责任感、不随和等。 6、尽量使解释的理由为应聘者个人形象添彩。 7、如“我离职是因为这家公司倒闭。我在公司工作了三年多,有较深的感情。从去年始,由于市场形势突变,公司的局面急转直下。到眼下这一步我觉得很遗憾,但还要面对显示,重新寻找能发挥我能力的舞台。”同一个面试问题并非只有一个答案,而同一个答案并不是在任何面试场合都有效,关键在于应聘者掌握了规律后,对面试的具体情况进行把握,有意识地揣摩面试官提出问题的心理背景,然后投其所好。 18.你认为自己的英语实力如何? 34.你的英语水平如何? 如未取得4、6级证书 A.I still have any difficulties in listening because of the limited vocabulary B.I don’t think I have problem in the daily conversation, And if I could have a good environment I could improve fast 21你的优点和缺点是什么? 这里只对缺点作一些提示 思路: 1、不宜说自己没缺点。 2、不宜把那些明显的优点说成缺点。 3、不宜说出严重影响所应聘工作的缺点。 4、不宜说出令人不放心、不舒服的缺点。 5、可以说出一些对于所应聘工作“无关紧要”的缺点,甚至是一些表面上看是缺点,从工作的角度看却是优点的缺点。 23.你喜欢什么俱乐部活动? 32.大学时做过什么活动? 35.你在休息日做什么?

(完整版)the的用法

定冠词the的用法: 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...

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具体而言,主要有两种做法要特别注意避免。首先是要避免使用过于生僻的单词,或是地方俚语之类接受群体相对比较小的表达方式。因为这种表达方式很有可能造成听者的困惑与曲解。 其次则是要避免过多,过于主观地谈及宗教文化或时事政治方面的问题。不少面试者出于第一项提到的急于展示英语水平的目的,或是想给面试官留下深刻印象的目的,常常会犯这个错误。 与英语考试的口试不同,面试人员通常是由航空公司的人事主管,空乘部门主管或公司高层组成,他们更关心和器重的是你的专业知识和工作能力,而英语此时只是一种交流工具,或者说是你要展示的众多技能中的一种,因此要切忌为说英语而说英语,有些人就怕自己的英语减分,为了希望给面试官留下英语水平高的印象,常常会大量的使用事先准备好的花哨的词汇及句式,而真正针对面试官所提问题的、与工作有关的'个人见解却很少。最后除了得到一句英语不错的夸奖之外,恐怕很难有理想的收获。无论是到中国的国际航空公司还是国外的航空公司应聘,公司都要求空中小姐不仅有高挑的身材和甜美的长相,而且要具备优雅的气质,会讲一口流利的英语。口试内容主要分为中英文面试、中英广播词、航空状况题、时事题、个人问题等。每一家公司会有不同的考试流程,初复试的难易度也不同,要多方面收集资料,知己知彼,再配合临场应

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幼儿园英语教学方案 一、教学目标: 本学期我们将多组织富有趣味性的英语游戏,让小朋友在游戏中掌握了一些英语单词、对话、儿歌、歌曲等。以游戏的形式开展英语教学活动旨在培养孩子学习英语的积极主动性。 二、教学重点: 让幼儿对学习英语有初步兴趣,并对日常的用语有一定的了解和掌握,做到结合生活场景学以致用。我们将多采用生动有趣的教具,在班级中帮助学校布置英语角,采用游戏化的教学形式及利用现代化的工具,让孩子在多种感官刺激下增强学习英语的兴趣,使幼儿的英语教学真正落到实处。 1、继续培养幼儿学习英语的兴趣,并能注意英语的发音。 2、让孩子多说、多听,结合一日活动的各个环节,继续学习一些日常用语,礼貌用语,愿意在日常生活中加以运用。大胆地说。 3、继续学习单词(动作、玩具、生活用品、文具、食品、星期等),掌握一些简短的儿歌、歌曲、故事,并乐意和主动参加一些英语的情景和故事表演。 4、尝试欣赏一些有趣的故事,了解其中的内容。 5、愿意运用所学的对话、句型和同伴、老师进行交流。 6、对教师的常规用语可以快速准确的做出反应。 三、教学措施 1、在班中布置英语角,增加墙面也说话的作用,粘贴各种相关的英语单词,让孩子置身于学习英语的良好氛围中。 2、充分挖掘教材的作用,以游戏为基本组织形式,充分调动幼儿学习的积极性。

3、面向全体幼儿,注重个体差异,因人施教,使每位幼儿在原有水平上得到一定程度的提高。 四、课程设置 1、选用《幼儿英语点点通 0-3岁》作为本课程教材,根据幼儿的年龄特点及发展水平,科学有序的合理安排英语活动。 2、准备多种教学具,配合教材的图片、卡片、实物、木偶等灵活运用,以更好的让幼儿掌握教学内容。 3、课次:29次。课程时间:周二、周三,9:00-9:30 总之,在今后的工作中,我们必定努力将英语特色教学活动开展得更好。 Unit 1 Hello Unit 2 Goodbye Unit 3 Girls and boys Review 1 Unit 4 Numbers Unit 5 Fruits Unit 6 Toys Review 2 Word List 课次学习内容 第一课次学习单词nose、 mouth、 eye、 ear 感知单词one to five 与数字1-5的对应

“the way+从句”结构的意义及用法

“theway+从句”结构的意义及用法 首先让我们来看下面这个句子: Read the followingpassageand talkabout it wi th your classmates.Try totell whatyou think of Tom and ofthe way the childrentreated him. 在这个句子中,the way是先行词,后面是省略了关系副词that或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1.the way之后,引导定语从句的关系词是that而不是how,因此,<<现代英语惯用法词典>>中所给出的下面两个句子是错误的:This is thewayhowithappened. This is the way how he always treats me. 2.在正式语体中,that可被in which所代替;在非正式语体中,that则往往省略。由此我们得到theway后接定语从句时的三种模式:1) the way+that-从句2)the way +in which-从句3) the way +从句 例如:The way(in which ,that) thesecomrade slookatproblems is wrong.这些同志看问题的方法

不对。 Theway(that ,in which)you’re doingit is comple tely crazy.你这么个干法,简直发疯。 Weadmired him for theway inwhich he facesdifficulties. Wallace and Darwingreed on the way inwhi ch different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way(that) hedid it. I likedthe way(that) sheorganized the meeting. 3.theway(that)有时可以与how(作“如何”解)通用。例如: That’s the way(that) shespoke. = That’s how shespoke.

空姐面试英语口语的例句都有哪些

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空乘专业面试技巧

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way 用法

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Teachi ng Summ ary Through this unit learning,students can understand the preschool education.Students can write down the right answers by repeatly listening.They can speak the dialogue fluently.Can read the text and understand the meaning .

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