Gordillo, JM , Pérez-Saborid, M
No
Phys. Fluids
Article
Científica
1.697
2.454
01/12/2002
000179177800022
We have obtained a uniformly valid asymptotic solution which accounts for the transient effects which take place during the response to the periodic forcing in the linear signaling problem. This solution complements the results of classical references [Huerre and Monkewitz, J. Fluid Mech. 159, 151 (1985); Annu. Rev. Fluid Mech. 22, 473 (1990); Huerre, in Perspectives in Fluid Dynamics (Cambridge University Press, Cambridge, 2000), pp. 159-229] by determining the spatiotemporal limits for the transition region separating the zone where the response has reached the periodic regime from that free of disturbances. The method of solution is based on the well-known steepest descent technique and does not invoke any type of causality arguments of the type resorted to in above-mentioned works. In addition, our technique provides one with a procedure, alternative to that presented in the above-mentioned works, which permits to identify very easily the direction of propagation (downstream or upstream) of the waves associated with the different spatial eigenvalues of the problem. The asymptotic solution obtained using the general procedure described in this paper has been validated with the numerical results for two relatively simple problems: the forced one-dimensional Ginzburg-Landau equation, and the forced Kelvin-Helmholtz problem. (C) 2002 American Institute of Physics.