ETF/CEF Discussion: For the third day there were no picks from RSI. No surprise considering the sharp drop, not only today, but the trend over the past few days. As I have been urging, now has been the time to go defensive. Today I sold my positions in IGM, IYW, JGT, PIV, PBW, PXJ, XLK, and XRO, and I bought TIP. Yesterday my stop for BCF was also hit and sold. So you can see my portfolio has been reduced to 25% equities and 75% cash and income holdings. And if the market continues to fall, my equity percentage may drop further.

Personally, I believe holding for the long term is the best portfolio strategy. However, if a portfolio holding doesn’t behave as intended, such as when you first bought it, I believe in selling it. I would rather take a small loss rather than see a small loss turn into a big loss. I had a friend call me earlier and he accused me of becoming a swing trader. I don’t think this label is accurate; however if avoiding losing money is rule #1, then call me a swinger. Rule #2 is always remembering rule #1!

Como tenho vindo a reparar, pelo menos no meio dos delegados e pessoas relacionadas com a Convenção, Portugal possuí excelente imagem aqui nos Estados Unidos. Mas quando digo que temos um Primeiro-ministro socialista, logo tenho que explicar que não é bem socialista, mas sim da esquerda democrática, uma espécie de Partido Democrata. A palavra socialismo assusta muita gente por estes lados. Mas a simpatia tem sido a nota dominante do tratamento que tenho recebido.

EUA impõem novas regras de entrada a portugueses, DN:

Vai ser mais difícil viajar para os EUA. A partir de 12 de Janeiro de 2009 os cidadãos portugueses que pretendam entrar naquele país terão que preencher um pedido de autorização, via Internet, e deverão ser portadores de passaportes electrónicos com chip.

[...]

Ao DN, o secretário de Estado das Comunidades Portuguesas reconhece que o Governo está a seguir com muita atenção esta situação: "Estamos a acompanhar do ponto de vista político e por isso temos equipas de alto nível a negociar a transição. Neste momento ainda não há uma posição final dos países do PIV, apesar de o programa até já ter sido aprovado pelo Senado americano".

ETF/CEF Medium Volatility:

• IYM - Basic Matls iShares
• PXJ - PowerShares Dynamic Oil & Gas Services Portfolio

ETF/CEF Catch a Falling Knife on the Road to Recovery (FKRR):

• BEP - S&P 500 Covered Call Fund
• EWC - Canada iShares
• EWW - Mexico iShares
• FGF - Sun America Focused Alpha Growth Fund Inc.
• IXC - iShares S&P Global Energy Sector Index Fund
• JKH - iShares Morningstar Mid Growth Index Fund
• PIV - PowerShares ValueLine Timeliness Select Portfolio
• PWJ - Powershares Dynamic Mid Cap GR
• UTH - Utilities Holders
• XLU - Utilities Select Sector SPDR

ETF/CEF Discussion: Today we have a lot of picks; many of them are repeats from my past blogs. Showing up are out neighbors represented by EWC & EWW. Maybe RSI is predicting a turnaround in the US translating to our neighbors. Also there is a prediction of returned strength in the energy markets. Plus a strong vote in the utility sector; also predicting an economic rebound? Finally mid-cap growth runs throughout the past few blogs.

BEP hasn't been covered before, so let me spend a minute on it. It is a CEF and has a P/Y/E of -4.11/14.29/1.06...not too shabby. This fund plays the covered calls on the S&P500 and earns yield on this strategy (a healthy 14.29% at that!). This fund will perform well as long as the market goes up. So this is a bet on the overall market.  And as all bets, it's a crap shoot.

Catch you tomorrow.

ETF/CEF Catch a Falling Knife on the Road to Recovery (FKRR):

• EVG - Eaton Vance Short Duration Diversified Income Fund buy now
• EVV - Eaton Vance Limited Duration Income Fund buy above $13.80

ETF/CEF Discussion: Again, RSI is going the conservative route and picking high yielding closed end funds (CEF).  EVG pay a yield of 8.70% and EVV pays 10.59%. As the chart illustrates, these two are not high flyer, but I think you can buy this dip, gather the monthly dividends and wait for the price recovery. They look as if they can book a 10% or so capital gain. Just a thought.

My apology for posting at such a late hour last night. I try to get this blog out in early evening and rarely do I publish later than 10:00PM Mountain Time (midnight Eastern).  Last night was one of my few exceptions.

While I have been shifting my investing style and emphasis on this blog, I have been putting this methodology to good use in my own personal account.  In the past few weeks I have purchased the following:

BEO - Enhanced S&P 500 Covered Call Fd Inc, 15.10% yield

EVG - Eaton Vance Sht Duration Diversf Incm Fd, 8.67% yield

IGM - iShares S&P GSTI Technology Index Fund

IJJ - iShares S&P Midcap 400 value index Fund

IYW - iShares Trust Dow Jones US Tech Sector

PBW - PowerShares WilderHill Cln Energy Portf

PFN - PIMCO Floating Rate Strategy Fund, 9.14% yield

PIV - PowerShares Value Line Tmlnss Slct Prtfl

PWB - PowerShares Dynamic Lg Cap Gwth Portf

SJT - San Juan Basin Royalty Trust, 10.16% yield

TLT- iShares Tr Lehman 20+ Year Treasury Bd, 4.66% yield

VGT - Vanguard Information Technology ETF

XLK - Technology Select Sector SPDR Fund

XRO - Claymore Zacks Sector Rotation

As you can see, I have invested in ETFs and CEFs that RSI has recently selected. I eat my own cooking, so to speak. Since I am retired, I like to have some of my holdings generate income. Likewise I want portfolio growth to counter the ravages of inflation.  Yes, I did bet on the two "trickery" funds for the reason that I believe the methodology behind the funds will outperform passive index funds. What did I sell in order to purchase these funds? For months I have been lightening up on gold, energy, materials and foreign funds and stocks that have served me well in the past, but whose time has come to an end.

Well that's it for tonight...have a great weekend.

ETF/CEF Medium Volatility:

• IYM - Basic Matls iShares close above $76.50

ETF/CEF Catch a Falling Knife on the Road to Recovery (FKRR):

• EVV - Eaton Vance Limited Duration Income Fund close above $14.00*
• NCV - Nicholas Applegate Conv&Income Fund close above $11.50*
• PGH - Pengrowth Energy Trust buy now
• PIV - PowerShares ValueLine Timeliness Select Portfolio buy now
• XRO - Claymore/ZAcks Sector Rotation buy now

ETF/CEF Discussion:   Let me start with the trickery first...the last two ETF funds on the list, PIV and XRO, follow an unusual methodology.  They follow a dynamic "index" of sorts, one based on ValueLine timeliness and the other on sector rotation methodologies. Rather "tricky" sort of in indices, eh what?  Anyway, they are interesting methodologies that RSI has selected, but beware. They trade thinly and are not very popular.  Maybe they will catch on with the public, who knows.  We may be seeing more of these kinds of funds. There are several "managed" ETFs coming to market too.  RSI will track them as data becomes available and they have a one year track record.

PGH isn't either an ETF nor a CEF but it is an energy trust that is currently trading at a 16% yield. Canadian energy trusts have a potential for unfavorable government tax treatments, so do your homework on this one.

Finally the two income funds have quite high yields; EVV 10.51% and NCV 13.72%. Remember, with high yields come high risk.  With that said, they sure beat the heck out of money market rates.

* previously recommended at this buy level

(Michele Catanzaro, el "Le Scienze" n. 479, itala eldono de Scientific American)

Tio memorigis mi pri mia lastatempa legado de La bona lingvo, interesa libreto de Claude Piron, kie la verkisto pli-malpli envortigas la samajn ideojn pri malmultenombreco de vortoj (fakte, de radikoj) kiuj necesas enkonduki en nia verdstela lingvo. Laŭ sinjoro Piron, elstara esperantisto nun bedaŭrinde forpasinta, ne taŭgas enigi senlime novvortojn ("neologismojn"?) en esperanton, kiam la samaj konceptoj povas esti priskribataj per kombinaĵo de kutimaj, jam ekzistantaj radikoj. Li elstarigas, ke kunmetitaj vortoj ne devas iĝi difinojn: kiam la signifo de kunmetaĵo sufiĉe kompreneblas, ne gravas, ke ĝi enhavu ĉiujn la necesajn radikojn por plene difini ĝian signifon.

Bedaŭrinde multaj esperantistoj ankoraŭ ne komprenis tion... :-(

PS. Tie legeblas interesa respondo al la libreto de Piron, verkata de Jorge Camacho, same interesa. Ĝia titolo? "La mava lingvo". Mava estas PIV-a samsencaĵo por "malbona"... :D

PPS. Mi malĉeestis dum unu monato, ĉare de ekzamenoj kaj aliaj aferetoj. Nun espereble mi estos pli libera, do povos skribi pli ofte ĉi tie. Ĉiukaze, mi ne malaperis :)

This episode starts off with Naruto playing soccer with clones (using the cloning jutsu of course) He runs through defense and blocks his own shots (as he is the clones) He lays down and feels bored and wants a mission. A person named, Kiba, comes and says "I guess someone beat me here" as he was going to train jutsus where Naruto was. Akamaru was acompanied by his dog and, Hinata.

[gallery]

Umm.. I forgot what happened, but I think either Hinata or Kiba told Naruto the new mission is in. So, all 3 went to Naruto's Grandma (I think thats who it was) and introduced them to the client, and told them the mission.

The mission was to find something in a limestone cave near the mountains. Not any ordinary ninja could go, it had to be a Shinobi.

They went to near the mountains. They kept coming across short-cuts, and long ways. Naruto and Hinata took the short-cuts, Kiba took the long way. Naruto and Hinata finished without Kiba in sight. Kiba was behind the giant boulder they were racing to. It kept happening over and over until they reached a limestone cave.

Naruto said this is the cave to find the treasure in, Kiba not so sure. Naruto and Hinata once again went in. What they didn't know was 2 disguised ninjas that were see-through were behind trees outside of the cave, and 1 was hanging from the top above them.

They went near the end of the cave and saw it was a dead end. The shadow ninja hanging up top saw his chance and threw a kunai at the wall, sending rocks straight @ Naruto and Hinata. Naruto got away safely, Hinata was injured on her leg. Kiba tells them to stay behind and wait for him. Naruto and Hinata did so.

Kiba traveled some more with his dog. He reached a limestone cave. As he did another scene came up with Naruto waking up and tied up in a cave. Hinata asks Naruto if he was awake. ANOTHER Hinata also asks him if he was awake. He was confused and kept asking questions about them.  Next...

The client of the mission came out, and told Naruto what was going on. He said that he didn't want the treasure for the mission. He wanted there faces. Naruto asked for what.. He replied telling them about an acient cloning Jutsu, not an ordinary cloning, a face one. It was very detailed and hard to tell the clone apart from the real Naruto or whoever. One of the Hinata's was a clone as well.

It went back to the scene with Kiba in the cave. He used a Jutsu to get through the ground in the cave and found the treasure. Naruto and Hinata's clones came up.. They were talking about the treasure and heading back. Kiba was suspicious.. -How did they find this cave with no map, and naruto is bad with directions- -How did Hinata come so quick with an injured leg- Those were going through his mind.

Then Kiba is tied up in the cave as well. He woke up, and the client told him what was going on again. He cloned him, and then threw him in a hole with Hinata, Naruto, and his dog.

They asked what are you doing with our faces? They replied saying "We're going to get into the Hidden leaf village, and mess it up, BIG TIME!" Naruto and his friends had shocked faces, and the clones and the client had sinister faces...

To be continued, Saturday @ 10:00 for a re-run 10:30 for the new episode, Run, Chase, Zig Zag (part 2)

---

Pivots

Pivots are one more of my interests. Pivot is an animation system with Stick Figures. Stick figures may seem like no big thing.. but you can make them so good, it looks like you can't do them on pivot.

Here see yourself, watch this video!

http://youtube.com/watch?v=lXA4vT8tFRg <-- Click here, PivotElite's Awesome Pivot Animations

Wanna see another famous set of Pivots on YouTube made by PivotMasterDX.

Click here for a playlist of "Stick Figures on Crack" --> http://youtube.com/view_play_list?p=062352A164B7FC9A

BTW, That playlist was made by me. :)

Well, right now i'm making a video response of a Pivot Collab organized by PivotJunkie

Click here: http://youtube.com/watch?v=qMkICGKh0jQ

This isn't mine, its the rules etc.. Mine isn't out yet.

---

In other news.. I will make a word of the day, music pick, and random video pick daily. :)

Starting today..

Soz today's WOD is: Chugger

Urban Dictionary Definition (#1 def) http://urbandictionary.com -Charity Mugger. One of those people who stands in the street with a big brightly-coloured bib and quite possibly a clipboard soliticing donations to the Feline Liberation Army or some other worthy cause.

hello, friends. this blog kind of died while i was in missouri last week, enjoying the universe's slowest internet connection. glad all two of you are still here, riveted to the screen.

you will never guess what was waiting for me when i returned to work on monday: orders to receive my very own PIV card.

so this morning i slunk down to the security office, where they took my fingerprints and a vector-based mug shot so that only me, jason bourne, mr. spock and other technologically inclined adventure-types will be able to log onto my computer. because you know, i work on a lot of top-secret ptydepe here in my beehive of an office. and also, there are a lot of people out there trying to impersonate me and get a piece of my new cube.

that's right. not only did i get my PIV picture taken, but i got a NEW CUBE. no longer are we in the moldy semi-cave of the seventh floor. we have moved on up to the spacious 8th floor: a place of real plants, broad hallways, and a strange illusion of light. it's weird. i don't think it has any more windows or florescent lights than the 7th floor did, but the 8th floor seems a great deal more suited for human, rather than bat, habitation. it's very nice. i spent monday unpacking my papers, re-filing my files, and re-mounting my kafka shrine. then i set up my mary-and-jesus icon, lit the candle, and tuned pandora to the diana krall station. ahhhh. very human. very non-bat.

on the home front, the babies are getting chubby. i returned to the oakie house on sunday night to discover that Baby Blue looks almost nothing like he did seven days prior: his face is chubbier, his eyes are more alert, and he delights in smiling and squealing. it's very fun. and Lil L is getting more and more verbal -- she can almost say Baby Blue's proper name, although she still insists on calling ben "mem" and herself "yeti," as in the abominable snowman. very cute, and very funny.

Circuito serie

I = misma para todo el circuito

tensión total = Σ tensiones parciales

Pt = Σ Pi = P1 + P2 + P3 + ... + Pn

Rt = Σ Ri = R1 + R2 + R3 + ... + Rn

Circuito paralelo

Intensidades diferentes para cada circutio

It = Σ Ii = I1 + I2 + I3 + ... + In

tensión total = única = V

Pt = Σ Pi = P1 + P2 + P3 + ... + Pn

1/R = 1/R1 + 1/R2 +1/R3 + ... + 1/Rn

EJERCICIO SERIE

Qué resistencia hay que colocar en serie con la conocida (20W, 0.2A) para que el circuito cumpla con los datos establecidos. Hallar su valor (en Ω) y su potencia.

Ante un problema siempre dispondremos de, como mínimo, dos datos conocidos; en este casoo, potencia y amperaje. Por lo que, de momento, no podemos aplicar la Ley de Ohm.

P = I · V =› V = P / I = 20 / 0.2 = 100V

Podemos considerar las tensiones como el esqueleto del circuito, por eso serán lo primero que calcularemos.

tensión total = Σ Vi

230 = 100 + V =› V2 = 230 - 100 = 130V

Ahora, ya por loa Ley de Ohm...

R = V / I = 130 / 0.2 = 650Ω

Y con el "Producto Interior Bruto"...

P' = I · V2 = 0.2 · 130 = 26W

En este ejercicio la resistencia adicional gasta más que la original...

La Ley de Ohm está basada en el conocimiento de dos magnitudes cualesquiera.

EJERCICIO PARALELO

Hallar el valor de la potencia y del valor resistivo (R) de la carga que podemos disponer para consumir los 25A reglamentarios.

Hallamos la Intensidad I' para poder aplicar el PIV:

I = Σ Ii =› I' = 25 - I1 - I2

Necesitamos saber las intensidades parciales...

I1 = P1 / V = 100W / 230 = 4,34A ; I2 = V / R = 230V / 200Ω = 1.15A =› I' = 25A - 4.34A - 1.15A = 19.51A

Calculamos la potencia P disipada:

P = I · V = 19.51A · 230V = 4485W

R = V / I = 230V · 19.51A = 11.78Ω

La R es inversamente proporcional a la P; por eso las resistencias que se usan en electrónica son mucho mayores que en electricidad.

EJERCICIO SECCIONES

Disponemos de una línea de 40 metros de s = 2 x 6 + T(6). Su función es alimentar un posible aire acondicionado. Calcular a) la potencia máxima admisible; b) la potencia disipada (efecto Joule) al utilizar la Pmáx.

El tierra (amarillo-verde) no debe contarse a efectos de calculo de secciones. Es un cable de seguridad.

Existen 2 procedimientos para el calculo de secciones:

1. por caída de tensión
2. por calentamiento

A1.- Calculo de la Pmáx por caída de tensión:

s = 2 · l · P / (K · w · V) =› P = s · k · w · V / (2 · l)

Como el enunciado no decía nada, se asume que la conducción se hará con cobre.

u = 3 / 100 · 230 = 690 / 100 = 6.9V =› P = 6 · 56 · 6.9 · 230 / (2 · 40) = 6665W

Potencia máxima por caída de tensión = 6665W

A2.- Calculo de la potencia máxima por calentamiento

Suponemos que se trata de un cable directo sobre la pared y consultamos la tabla...

para s = 6 → Imáx = 37A =› Pmáx = V · I = 230V · 37A = 8510W

Potencia máxima por calentamiento = 8510W

Siempre nos quedamos con el más restrictivo, luego por comparación: Pmáx = 6665W

B.- Potencia disipada por el efecto Joule

P = R · I² = ζ · 2 · l · I² ; I = 6665W / 230V =› P = 0.017 · 2 · 40 / 6 · 28.9² = 189W

Multiplicamos la lóngitud por dos, porque necesitamos la longitud geométrica del cable ("ida" y "vuelta").

La notación para cable monopolar sería: s = 2 x 1 x 6

Pyh! Og god søndag til dig også! :-)

ETF/CEF Low Volatility:

• FXS - Currency Shares Swedish Krona Trust
• PID - PowerShares International Dividend Acheivers Portfolio
• PIV - PowerShares ValueLine Timeliness Select Portfolio
• VAW - Vanguard Materials VIPERs
• XLB - Materials Select Sector SPDR

The Krona ETF is a repeat from yesterday, in fact all but PIV have been cited by RSI in the past, especially XLB which has been repeatedly picked.  PIV is most unique.  It is based on a proprietary index that reflects the Valueline timeliness methodology.  As you can see, it hasn't been a barnburner, but this method has an impressive historical record.  Look it up if you are unfamiliar with Valueline.

ETF/CEF Medium Volatility:

• FXC - Currency Shares Canadian Dollar Trust
• IXC - iShares S&P Global Energy Sector Index Fund
• MXI - iShares S&P Global Materials Sector Index Fund

RSI has picked all three of these in the past and still likes them today and going forward.  It is interesting that we have two currency picks today meaning RSI expects the dollar will continue to fall.

ETF/CEF High Volatility:

• none

Stocks Low Volatility:

• none

Stocks Medium Volatility:

• PCP - Precision Castparts Corp.
• SINA - sina.com
• SJR - Shaw Communications, Inc.

SINA & SJR are prior RSI picks.  Precision Castparts is a new pick for RSI.  Precision Castparts Corp. manufactures metal components and products for aerospace, power generation, general industrial, and automotive markets.  All three of these picks have had a great year but have fallen from their highs (especially SINA which has gone from up +70% to pare that gain in half).  Will these fly high again??

Stocks High Volatility:

• BHP - BHP Billiton Ltd.
• BTM - Brasil Telecom SA
• FLR -Fluor Corp.
• GGB - Gerdau Usa
• ICA - Empresas Ica Soc Control
• KOP - Koppers Holdings Inc.
• MDR - Mcdermott Intl, Inc.

Brasil Telecom and Gerdau Usa are new picks.  Brasil Telecom S.A., through its subsidiaries, provides fixed-line telecommunications services.  Gerdau S.A. engages in the production and sale of crude steel and related long rolled products, drawn products, and long specialty products.  Certainly a tilt towards foreign companies or U.S. companies doing global business.

Catch a Falling Knife:

• BGT - Blackrock Global Floating Rate Income Trust
• HGT - Hugoton Royalty Trust
• PWE - Penn West Energy Trust

Again we see energy trusts in this falling group.  Time for a closer look at these bargains?  They may still have potential.

A few words about volatility...I'm defining the volatility levels as less than 5%, between 5% and 15%, and greater than 15% of the one year standard deviation of closing prices for low, medium and high volatility respectively.  Thus far I use these same levels for funds as stocks.  It is interesting to see the lower volatility in ETF/CEFs as compared to stocks.  I hope this volatility discrimination helps you in your deliberations.  Remember that risk equates to volatility which relates to reward.

Everyday observations allow us to describe turbulence loosely as a rushed, gushed, mixed, swirling, twirling, frothing, bubbling, "confused" flow. That description would classify as turbulent the rain water celerities on the road, the hot coffee jet traveling from one cup to another, the cold air that coats and flows around our naked face while traveling in a bike, the smoke from the factory chimney, the clouds and ocean currents, the atmosphere of the Suns and their planets, the blood flow in our arteries - the list is endless.

Science is less romantic but better in description with a systematic study.

Water flow inside a pipe, as observed by Leonardo, is a daily affair. At a sedate pace (determined by the pipe and fluid configuration) such internal pipe flows are termed laminar - modeled as if, laminae of fluid sliding over each other. Fully developed laminar flow inside pipes with circular cross section exhibit a parabolic velocity distribution with zero at the walls and maximum velocity at the axis. Fully developed flow means, the flow retains its radial velocity profile while flowing along the length of the pipe. This render the longitudinal pressure drop linear. This parabolic velocity profile of flow was analytically deduced and experimentally observed independently by Hagen (1839) and Poiseuille (1841). Given an infinite length of the pipe, such a parabolic profiled laminar flow of any fluid is inevitable inside a pipe. The analytical solution could be vindicated.

But laminar flow runs inside the beautiful confines of analytical viscous fluid mechanics, useful to model flows in carefully constructed laboratory experiments by hardworking fluid mechanist. When they step out of work, turbulent cold air gushes in through the opened door to upset their notes of laminar analytical labor. Unlike what our introductory fluid mechanics books suggest, turbulence is the norm, not an exception like laminar flow.

Turbulent flow results when the instabilities in a flow are not damped persistently by the viscous action. The ensuing turbulence in the flow exhibit rapidly varying velocity fluctuations with respect to space and time. If we plot the measured local velocity of a fluid flow as a continuous function of time, for a laminar flow that curve is smooth. The curve develops many random kinks and wiggles when the flow is turbulent as can be seen in the picture below. Similar is the velocity plot when done in space in many location of the flow at a particular instant. The plot resembles the graphed fluctuating fortunes of the SENSEX (SENSitive indEX of the Bombay stock exchange) or the hackneyed ECG of a person about to die in the Indian movies.

Intriguingly, when the kinks are resolved in higher magnification (i.e. plotting measurements done at shorter time or spatial intervals), we see more kinks of smaller scale. Analogously the SENSEX graph shows similar kinky behavior when done for a day (shorter time) or for several months (longer time) as shown in the inset. This behavior of velocity fluctuations doesn't extend endlessly for all further finer scales. Before we jump to spot a fractal, at very high resolution a smooth function for velocity versus time or space is reached.

The physical nature of turbulence is understood using the concept of an eddy. In fluid mechanics, an eddy (or a vortex) is understood to be a macroscopic fluid element in which the microscopic elements composing the eddy behave in some ways as a unit. Macroscopic means a region of fluid and microscopic means the smaller sub-regions within the macroscopic fluid region considered. A turbulent flow is understood to comprise many such eddies (or vortices) of different sizes. Groups of smaller sized eddies of differing behavior can congregate within a larger eddy. Fully turbulent flow means eddies of all shapes and sizes exist.

These eddies are continually formed in fully turbulent flow by drawing on the kinetic energy from the mean flow. The large eddies also keep breaking down into smaller ones, which break down further into smaller ones, and so on. One of the features of a turbulent flow that accompanies this cascade of eddies is the energy cascading or the transfer of energy in an average sense from large scale eddies to progressively smaller scales. At small enough sizes, the eddies die out by dissipating their kinetic energy as heat through local viscous action of the fluid. The British meteorologist Lewis F. Richardson described this process in a now famous verse:

Big whorls have little whorls,
Which feed on their velocity,
And little whorls have lesser whorls,
And so on to viscosity.

Turbulent flow is intrinsically three dimensional and random in space and time. Observe the experimental measurement of instantaneous velocity distribution in a turbulent flow field inside a square cross sectioned duct in the accompanying picture below. These data were recorded using Holopgraphic Particle Image Velocimetry systems developed in the Laboratory for Experimental Fluid Dynamics by Prof. J. Katz and co-workers. For clarity, the experimenters [3] have subtracted the center-line mean velocity, U = 2.1 m/s, from each vector. The colors indicate the magnitude of the velocity (from red high to blue low) and the red arrow indicates the direction of the flow. In a sense, over the centuries,we are now in a position to do better descriptive drawings of turbulence when compared to the drawing of Leonardo in the first picture. However, no two experiments reproduce exactly all the details of a particular turbulent flow.

This is because of the sensitive dependence of the flow to small disturbances in the initial and boundary conditions, which an experimentalist cannot control with any required precision. The randomness has prompted researchers to wonder whether it makes sense to try for a precise mathematical analysis of such flows. In theoretical analysis one assumes a multitude of almost identical experiments to have been performed and deals with the "ensemble" of collected data of the measured parameters. Averaging data from several (in principle, infinite) such ensemble realizations leads to the statistical description of turbulent flows. The mean flow in the above second picture $latex \bar{u} $ is understood to have been arrived at by averaging the measurements over a large number of almost similar experiments in a turbulent flow configuration. The fluctuations (the kinks in the curve) are understood to be the variations from the mean caused by the turbulence itself [4]. For laminar flow, these fluctuations die out considerably.

The advantage of the above approach is statistics of flow is reproducible, while the result from an individual experiment (contained as a data point in the statistics) is not. The turbulent flow field, when analyzed in a length scale that is smaller than the length scale of the flow configuration but big enough when compared to the length scale of the smallest eddy in that flow, exhibit a statistically uniform behavior. However, the basic dynamical equations, the Navier and Stokes equations [5] of momentum conservation for a fluid flow, should hold unequivocally for both laminar and turbulent flows. This means turbulence is a consequence of these equations rather than a breakdown of such a momentum conservation model. Compared to the statistical description from experiments then, the solution of Navier Stokes equations suggest possibility of predicting the results from the individual instances of experiment. A caveat is of course, the general solution for the Navier Stokes equations is yet to be found. Even the existence of a solution, barring some brave attempts [6], is yet to be proved. This is where fast computers come in.

In computational fluid dynamics (CFD) turbulent flow researchers usually solve the Navier Stokes equations in a particular turbulent flow configuration and from the individual results, calculate the statistical properties of the flow enabling comparison with the statistical results of analogous experiments. Another theoretical approach is to work straight with the statistical equations, with suitable hypotheses or "closure models" about the involved unknowns. I am not an expert to write more about this approach.

Some of the physical features of turbulent flows are their inherent randomness and three dimensionality, comprising of features of different scales (like eddies of many sizes), random variations of vorticity in the small scale and their nature to dissipate energy. However, turbulence is essentially a continuum phenomenon (one need not describe turbulence using fluid molecules). Major applications of turbulence hinges on the fact that it enhances the dispersal and transport of material, momentum and energy when compared to simple diffusion or laminar flows. More on each of these in follow-up essays. This is as far I can go without equations.

At the start, we refrained from the customary quoting of scientists on how difficult turbulence is. Citing the frustrations of some of the giants of Science is not the best way to encourage young researchers to pursue the field of turbulence. To illuminate this point I quote here from the starting paragraphs of an excellent recent review article [7]

One need not apologize for or despair over the difficulty of turbulence. For one thing, turbulence has contributed several ideas and tools of lasting value to neighboring areas of physics. A sampling includes negative temperature, anamalous diffusion, and the concept of power-law scaling in many-body problems. The powerful notions of scale invariance and universality were first proposed in the context of turbulence. In general, turbulence is a playground for solutions that are non-unique or that depend sensitively on initial conditions [...]

[...] turbulence is not a single problem but rather a huge field with pivotal applications in engineering, geophysics, astrophysics, and cosmology. It is also an excellent source of problems of pure mathematics. Applied mathematicians, meteorologists, and engineers often focus on particulars like drag and pressure drop, mean velocity distributions, mixing efficiencies, and dispersion rates. Indeed, by considering the totality as "the problem of turbulence," one can justify the claim that the problem remains unsolved. In like manner, the insistence on a complete first-principles understanding of the structure of complex atoms and molecules might lead to the conclusion that quantum mechanics is an unsolved problem.

Along with the above encouragement, to convey the uncertainties that charm the field of turbulence, let us end this essay with a quirky quote alluded to a noted expert [8] on turbulence. To a question that went something like "How to recognize a flow is turbulent?", his answer was

"Turbulence is like pornography. You will know it when you see it."

Related Notes

• Pipe Turbulence
• Turbulence in Flow around Bodies
• Simple Method to Detect Pipe Turbulence

References and End Notes

1. "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." said Werner Heisenberg once. Source: Dr. Brian Thurow.
2. A possible derivative of the above quote is ascribed to Sir Horace Lamb, author of the seminal Hydrodynamics, who in 1932 while addressing the the British Association for the Advancement of Science said, "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic." I read this in Prof. Parviz Moin's Scientific American Article, a good, equation-free, general introduction to how computers are used in tackling turbulence.
3. PIV image is from the paper "Geometry and scale relationships in high Reynolds number turbulence determined from 3-D holographic velocimetry," by B. Tao, J. Katz and C. Meneveau, Phys. Fluids 12, p. 941, (2000). Abstract and pdf of the article from author's website.
4. this is discussed in the 1st Chapter of An Introduction to Turbulent Flow by Jean Mathieu and Julian Scott (2000, Cambridge Uty. Press), a good book that I am using to learn some of the key ideas in turbulence.
5. I am deliberately keeping this post equation free. Read the Wikipedia page for Navier Stokes equations for an introduction or check here just for the equations and a feline perspective.
6. See the post "Analytical Solution to the Navier Stokes Equation Reported" at this blog for a recent attempt. If you can handle comfortably some mathematical language, read the excellent post titled "Why Global Regularity for Navier Stokes is Hard" by Terrence Tao.
7. Falkovich, Gregory and Sreenivasan, Katepalli R. "Lessons from hydrodynamic turbulence," Physics Today, vol. 59, no. 4, pages 43-49 (April 2006). This article is a good review of where the field is. Some sections of the review is accessible to all of us.
8. From academic discussions (i.e. college gossip) I know the name of this scientist but couldn't authenticate hence refrain mention.

Nu har jeg ikke noget alkoholproblem - udover dét, de fleste unge danskere har - så det med alkoholen er nu ikke noget problem for mig. Jeg har f.eks. overhovedet ikke drukket i denne uge, og da vi allerede har nået fredag aften, og lørdag for mit vedkommende bliver en hjemmeaften, skal jeg nok overholde det med nul alkohol.

Men denne uge har været en streng én alligevel! Jeg havde egentlig besluttet, ikke at nævne det videre (mest pga. Lind, der i forvejen synes jeg er en smule ynkelig ;-) ), men det er simpelthen kommet så langt ud på et skråplan nu, at jeg er nødt til at få mine frustationer ud i cyberspace og væk fra mit hoved:

Mandag: Ugen startede godt! Havde fri kl. 15 og var helt oppe at køre over det! Havde en rigtig god dag - lige indtil jeg tjekkede min mail! Der erfarede jeg, at Tones og mit dansehold er blevet lukket fordi vi var for få! (Hvilket i øvrigt er noget pjat!) ØV! (Nr. 1) (Desuden fik vi at vide at Joachim Boldsen havde fået en fibersprængning i maven og at han og Vicky Jo derfor måtte udgå fra Vild med dans - ØV! (Nr. 2)

Tirsdag: Fik fjernet skønhedsplet hos lægen. (Av!) Og da det også er en lidt nederen ting kommer her ØV! (Nr. 3) Da jeg kom hjem fra gruppemøde hos Sarah blev jeg syg! Var på kanalrundfart med Kennis venner og måtte forlade dem til fordel for min seng og influenza-lignende symptomer. ØV! (Nr. 4)

Onsdag: Er syg! Slæber mig alligevel i skole til vigtige fremlæggelser, men må droppe arbejdet til fordel for at sove til middag i 3 timer. Goodbye løn! ØV! (Nr. 5)

Torsdag: Skal læse op på KUA fredag og må derfor sætte dagen af til teorilæsning og oplæsning. Tone og jeg har besluttet at se, hvad det er for noget dans, USG har foreslået os at komme til istedet for vores højtelskede Show. Derfor mødes vi omklædte på KUA kl. 18.25... Alene! Efter at have ledt og ledt og ledt i 15 min finder vi en computer og opdager at dansen er aflyst denne torsdag! Thank you, USG! ØV! (Nr. 6). Intet er selvfølgelig så skidt at det ikke er godt for noget! I stedet for dans tager vi en iste i Nye KUAs Kantine. Jeg går herefter hjem og forbereder mig ganske grundigt til min oplæsning fredag.

Fredag: Natten til fredag vågner jeg kl. 3.30 med smerter i halsen. ØV! (Nr. 7) Det er ret trist, men ender faktisk lykkeligt. Det forholder sig nemlig sådan at Kenni netop er kommet hjem fra byen (lettere beruset godt nok, men stadig!) og han tager mig kærligt under sin vinge. Jeg får således serveret varm te med honning, bliver aet på hovedet og får synget godnatsange. Det var nu meget rart! Da jeg vågner kl. 7.00 står det rigtig skidt til med halsen. Jeg kan ikke snakke! (hvilket er noget skidt, når man skal læse op!) Men jeg synes i hvert fald det er dumt at blive hjemme i sengen fra 3 gode timer blot fordi min hals ikke virker. (Ørene fejler jo intet!) Afsted med mig - og tju hej hvor det går. Stemmen får efter morgensangen "I østen stiger solen op" det på mærkværdig vis bedre og jeg får læst min novelle op - mere eller mindre godt.

Om morgenen ringede jeg til min læge for at få hende til lige at kigge på min hals. Gider simpelthen ikke endnu en nat med søvnbesvær og synkesmerter. Lægen sagde jeg kunne komme mellem kl. 13-14. Da jeg tager fra skole er jeg sikker på, jeg skulle være hos lægen fra 12-13. Denne fejltagelse opdager jeg efter 1 times ventetid hos lægen kl. 13.10 (Flot, Helle!) ØV! (Nr. 8) Nå, men efter 1½ times ventetid kommer jeg endelig til. Det tager lægen 2 minutter at konstatere at jeg IKKE har halsbetændelse, men blot halsvirus. Det kan man ikke kurere. Lægens ord lød: "Tag en panodil"(!) ØV! (Nr. 9)

Men så er det i hvert fald weekend og den har jeg tænkt mig at fejre. Jeg er alene hjemme og skal bare ligge under dynen og spise lidt chokolade og se fjerner. Nej, nej! Sådan skal det ikke gå - og her må du jo huske på, at det er uge 40, vi snakker om. Den er ikke sådan lige at komme udenom! For bedst som jeg har spist mine lækre fiskedeller og skal til at putte under dynen opdager jeg til min store skræk en kæmpe gul plamage i mit ene øje! Adr! Og ØV! (Nr. 10). Piller den væmmelige klat ud og ringer til min mor (som er sygeplejerske!). Efter en kort snak med hende ringer jeg til vagtlægen, som konstaterer at jeg har fået øjenbetændelse i det venstre øje! Jeg bliver herefter sendt hen på Sønderbro Døgnapotek for at hente øjendråber. Inden jeg når derhen, når jeg dog at smitte mit raske højre øje, så jeg nu har 2 gule øjne. ØV! (Nr. 11) På apoteket køber jeg lige nogle hexokain med til halsen, som stadig er i uorden.

Og nu sidder jeg her... Med dryppede øjne, sprayet næse og med en sugetablet i munden.

Må jeg godt have lov at sige: LORTEUGE?!

Men misforstå mig nu ikke! Er faktisk (på besynderlig vis) stadig i ret godt humør! For det er jo som sagt i svære tider man finder sine virkelige venner. Og så bliver man jo lige mindet om, at man har en dejlig, dejlig kæreste, der vil synge "Perhaps love" hele natten og ae blidt på hovedet, mens man luller i søvn, en chef, der ikke bliver sur over at man ikke kan komme på arbejde hele 2 dage på en uge, men bare har medlidenhed med en og nogle dejlige venner, der står parat med hønsekødssuppe, hvis det kan hjælpe på ens hals. :-)

Når man bare tænker på det, så er det faktisk ikke helt så slemt at have opnået hele 11 ØV!'er fredag aften...