DNS of blasius flow for trasition
I try to do DNS of blasius flow for trasition. I presume I put the correct unstable modes and boundary condition, including the code, and disturbance equations. But I can only see TS waves damping downstream. I follow the work of Fasel. But my question is, since the streamwise velocity magitude along constant y actually decreases in the downstream direction (i.e. as the boundary layer grows), why do the waves grow in the first place.
I am intrigued, and must have missed something. Can someone in this field explain to me about it using simple logic. For instance how do I treat pressure values, i.e. I just use the pressure to enforce divergence free flow. and obviously for bl dp/dx=0. So do I need to enforce p_upstream_edge=p_dowstream_edge?. But already in the base flow u/u_infinity=1 ouside the boundary layer. TAW 
(1) "why do the waves grow in the first place."
I want to ask the same question! 
I am not quite sure why the disturbance grow. But depending on the stability charecteristic of the flow these disturbances can amplify or die down along the flow. When the amplitude of TS waves are small compared to the base flow, you can use linearised stability equation to find the growth characeteristic, since the growth depends on linear characeteristic.

It might be related to the boundary layer instability used in estimating the laminar to turbulence transition zone. This can be mathematically analyzed by linearizing the NS equations for the boundary layer, and then doing a fourier analysis to estimate its stability characteristics. This, I think, will provide the stability characteristics of the boundary layer flow. Please correct me if I am wrong.

Thank you for the above responses,
I do take both replies correct. It is true the LST actually provides the stability of the flow to infintismal amplitude disturbances, and I was able to obtain this result as in the published papers on stability planes. That solution is an eigenvalue solution method, and the result is in wavenumberRe space. My problem, is when I wanted to reproduce this result with FVDNS. Many publications have successfully reproduced this. For instance, in DNS the outflow bc is the source of the problem, as it creates unphysical wave reflections, and I did some absorbing condition for that. But still, I only see a damping wave, for the most unstable frequencies, and I said that is reasonable if the stream wise velocity is decellarating downstream. But it is not the case, and I was wondering what I have missed. Right now I am investigating if the absorbing bc has contribution on the unexpected damping. Regards, TAW 
Correct me if I am wrong, but it is in accelerating flow that you may see dampening of turbulence generation. Positive acceleration in effect increased transition region. In decelerating flow transition is more easily induced. I am speaking in terms of the physics of transition process.

Hi SKK,
Thanks for the reply. I think what you said is correct; that for instance favorable pressure gradient dp/dx<o (flow accelerated), delays flow reversal for a flat plate flow, and in essence turbulence, for subsonic range. In the flat plate flow, flow transition, as you said deceleration (or static pressure increase) would be responsible for the onset of turbulence. Thank you very much for reminding me the basics. I will further look through my simulation, in light of this. Cheers TAW 
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