K.E. of turbulence
How do we define K.E. of turbulence? How is this effected by viscous heat dissipation effect? How are pressure and density effected by viscous heat dissipation? Thanks, Daniel (pl. answer in detail)

Re: K.E. of turbulence
I need immediate answer to my questions . Waiting for a quick response, Daniel

Re: K.E. of turbulence
I want to know the general method to calculate about k & e value for boundary conditions which are according to control volume, inflow velocity and pressure. I think, it could be formal function of various boundary conditions.

Re: K.E. of turbulence
Please help me out of this difficult situation.

Re: K.E. of turbulence
If I understand your question correctly, you want to know how to define the turbulent kinetic energy of your flow. Well, first of all you need to actually define what is the "turbulent" flow field. Generally, out of an unstationary flow you extract a statistical mean flow (trhough local or other averaging methods). Substracting this mean flow from the instantaneous flow field will give you a fluctuating flow field which can be thought of as a description of turbulence levels. You can then define your turbulent kinetic energy (TKE) as .5*uprime*uprime where uprime is the fluctuating component of velocity. This is of course a onedimensional example. I would suggest however, that instead of eagerly waiting for answers here you get a good textbook and read all about it. I could suggest Tennekes and Lumley's First Course in Turbulence. There's hundreds of books on the subject of turbulence.

Re: K.E. of turbulence
I am really thankful for your answer but my question is whether viscous dissipation effects static pressure, density and K. E. of turbulence. Yours Daniel

Re: K.E. of turbulence
Dear Daniel,
I think that you understand the meaning of k.e. of turbulence. this is of course elated to the the fluctuating component of the velocity. The interesting thing to note is that the effect of viscous dissipation in turbulence prevades all the velocity scales in turbulence. An ideal example is to look at the energy spectra of the flow which involves the total k.e. of the fluid and not the fluctuating component alone. Essentially, when plotting the k.e decay in turbulence in a simulation you relate to the flutuating velocity. However, when talking of viscous dissipation you study the energy spectrum, the transfer function etc. which relate to the fourier decomposition of the total velocity vector resolved into its Fourier Components. Please make sure that you distinguish between the two. Finally, yes the viscous dissipation effects the k.e. It does not effect the pressure and density in incompressible flow since th energy equation can be shown trivially to relate to the transfer of energy between scales (the convective term in the N.S. equations) and the viscous dissipation. That is only the total fluid velocity is modified by the viscous dissipation inherent in the fluid. Ravi 
instability of flows
The flow issuing out off a cigarrete is unstable at a very low velocity but the same smoke if passed through a parallel plate channel would become unstable at a higher velocity.
Please explain the role of surrounding medium in causing instability of flows. Bipin. 
Re: instability of flows
Dear Bipin,
Essentially, you are looking at the onset od diffusion rather than instabilities in the flow. The first case being a diffusion dominated flow and the latter a convection dominated flow. Don't you think that the onset of what you call instabilities is related to diffusion in the first case and turbulence in the latter ? Ravi 
Re: instability of flows
Dear Ravi, Thanks for replying my querry.
As far as the flow of cigarrete smoke is concerned it comes in the category of thermal plumes. What I think is that in this category of flow the smoke gets diffused after it becomes turbulent. Can we compare it with the dispersion of drop of ink in a water ?. Another think is that the surrounding boundary in which flow is taking place may also be responsible for onset of turbulence. For e.g. in a channel flow the noslip boundary condition gives rise to a viscous layer near a wall which could damp the fluctuations that create instabilites. In the case of plumes this is not the condition as there's no such viscous layer present beacause of interation with the air and so result in instability at a very early stage.This is what I feel. 
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