What does pseudo randomness mean in turbulence

Nick R · August 6, 2011, 02:27

I read in a CFD book that the randomness in turbulence is pseudo. I don't understand the meaning of the following statement
" The reason for pseudo-randomness is that small perturbations that are constantly added to the solution are enhanced exponentially in time"

-From CFD essentials by Zikanov

Can someone please explain what that statement means

insane_alien · August 6, 2011, 05:48

pseudo random means it has all the appearences of being random but if you start from the exact same initial conditions and put it through the exact same process then it will be the exactly the same, ie. it is deterministic.

however, if there is even a slight difference then trial n+1 will differ from trial n by an amount proportional to the length of time the simulation has been running for.

a better way of describing turbulence would be that it is deterministic but highly chaotic.

without a way to accurately measure the position and velocity of all the molecules involved and a similarly accurate way to model their behaviour then the simulation will diverge from reality, the averages can turn out the same but down at the small details there can be big differences.

CFD is and probably always will be an approximation, it can be a pretty darn good approximation however so it is still incredibly useful.

Nick R · August 9, 2011, 03:09

I see. Thanks for clarifying it.

August 6, 2011, 02:27	What does pseudo randomness mean in turbulence	#1
Nick R Senior Member Nick Join Date: Nov 2010 Posts: 103 Rep Power: 4	I read in a CFD book that the randomness in turbulence is pseudo. I don't understand the meaning of the following statement " The reason for pseudo-randomness is that small perturbations that are constantly added to the solution are enhanced exponentially in time" -From CFD essentials by Zikanov Can someone please explain what that statement means

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August 6, 2011, 05:48		#2
insane_alien New Member Stephen Lucchesi Join Date: Jul 2011 Posts: 8 Rep Power: 3	pseudo random means it has all the appearences of being random but if you start from the exact same initial conditions and put it through the exact same process then it will be the exactly the same, ie. it is deterministic. however, if there is even a slight difference then trial n+1 will differ from trial n by an amount proportional to the length of time the simulation has been running for. a better way of describing turbulence would be that it is deterministic but highly chaotic. without a way to accurately measure the position and velocity of all the molecules involved and a similarly accurate way to model their behaviour then the simulation will diverge from reality, the averages can turn out the same but down at the small details there can be big differences. CFD is and probably always will be an approximation, it can be a pretty darn good approximation however so it is still incredibly useful.

August 9, 2011, 03:09		#3
Nick R Senior Member Nick Join Date: Nov 2010 Posts: 103 Rep Power: 4	I see. Thanks for clarifying it.