You need to clarify your question, please! The frequency response of a dynamic system is simply the Fourier transform of the the impulse response function for the system. In other words, there is no difference...

Thanks Luisiana for your response! I am asking this question from flow instability perspective. In Schubauer and Skramstad (J. Aero. Sci., 1947) to study flow transition over a flat plate, the authors vibrated a ribbon near the wall at a single fixed frequency to create what is known as Tollmien-Schlichting wave. This is an example of frequency response. Later, Gaster and Grant (Proc. Royal Soc., A, 1975) excited the flat plate boundary layer by an exciter at the wall, which is given as a delta function in space and time. This can be termed as the impulse response. Results produced in these two experiments display completely different physical phenomenon. So one is not simply a Fourier transform of the other! The same can be done by computing the flow field. These results obtained by us are also representing different physical phenomenon. That is the reason for the posted discussion. I would like to hear from scientists working on dynamical system theory, their opinion with supporting results. Thank you again!

Tapan,

Tollmien-Schlichting waves involve nonlinear responses, hence, would deviate from naive mathematical descriptions. If you transform the equations into codomain, treated coefficients as time dependent, then convolution might be able to recover the missing information.

In the case of thermal distribution, even if it were a dirac delta, there are two distinct geometric spaces to consoder: one being elliptic, the other hyperbolic, see my paper "Spectral analysis of Pennes' bio-heat equation."

The two separate geometric regions are qualitatively different, demarcated by a thin parabolic transition zone, where laminar flow speed and other factors determine the placement of this transition zone. Information is shared throughout the elliptic space, a sort of mixing zone, and information is otherwise isolated in the hyperbolic region...being carried out into the surroundings. Since fluid dynamics depends ultimately on thermal distribution, you can clearly see a reason for a difference.

Another paper of interest, possibly, is "A compact analytic solution describing optoacoustic phenomenon in absorbing fluid," which gives a very nice, compact solution for impulse driven disturbances in a fluid. In this case, the impulse driving force is a nanosecond Q-switched laser pulse. It provides a kernel, to wit, you could make further investigations.

Once again, the initial thermal distribution in the fluid determines the resulting acoustic wave in the fluid media. If you wanted to consider a moving fluid, you would need to use kernel solution and make further computations.

My guess, for Tollmien-Schlichting waves, is that the impulse drive causes orthogonal T-S drives in the elliptic region, which emanate from the parabolic region (i.e. become separated and pronounced), finally, progress into turbulence downstream.

Cheers!