Differences between Homogeneous, Uniform and Isotropic Flow

kayla1994 · May 12, 2017, 04:29

Hello to all,
I have some doubts about theory arguments.
I know the definition that a quantity which is invariant respect to translation is homogeneous and, if invariant respect to rotation, is isotropic. I found these definitions studying on "Turbulent Flows" by Stephen B. Pope.
I also know homogeneous isotrpic velocity field can be obtained downstream a grid in wind tunnel, but i don't understand why the flow in the pic is homogeneous. before that, i had supposed the condition should be no velocity gradient.
And what does "uniform" mean in this context? Can a property imply another? Which is the most strictly?
I would like some flow examples to understant better the definition in a pratical sense.

Thanks very much

piu58 · May 12, 2017, 05:57

As far as I understand not the flow is homogeneous, but the shear.

FMDenaro · May 12, 2017, 09:44

You should consider those definitions in terms of the statistics ...

LuckyTran · May 13, 2017, 12:50

It's a flow with homogeneous shear.

I realize homogeneous shear flow is a bit ambiguous but let's not get into a pedantic argument and just appreciate that there is homogeneous flow, homogeneous shear, & homogeneous lint in my pocket.

The context is clear. Obviously the flow is not homogeneous.
The understanding of the concept (that they're talking about turbulence and not the mean flow) is way more important than the words.

As my mathematical fluids prof would always say when asked for clarification on what a certain symbol means...
"It's whatever it needs to mean to make sense" usually followed by
"You're an engineer, you should have an intuition for these things. Clueless people like me, we don't have the intuition to know any better. But people like you do. You should use it."

May 12, 2017, 05:57		#2
piu58 Senior Member Uwe Pilz Join Date: Feb 2017 Location: Leipzig, Germany Posts: 744 Rep Power: 15	As far as I understand not the flow is homogeneous, but the shear. __________________ Uwe Pilz -- Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)

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LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,678 Rep Power: 66	It's a flow with homogeneous shear. I realize homogeneous shear flow is a bit ambiguous but let's not get into a pedantic argument and just appreciate that there is homogeneous flow, homogeneous shear, & homogeneous lint in my pocket. The context is clear. Obviously the flow is not homogeneous. The understanding of the concept (that they're talking about turbulence and not the mean flow) is way more important than the words. As my mathematical fluids prof would always say when asked for clarification on what a certain symbol means... "It's whatever it needs to mean to make sense" usually followed by "You're an engineer, you should have an intuition for these things. Clueless people like me, we don't have the intuition to know any better. But people like you do. You should use it."