Abstract
Disturbances play an important role in Physics and notably in Fluid Mechanics. Indeed all flows in Nature are constantly subjected to perturbations of various origin: thermal noise, variations of boundary conditions, etc. If the flow is stable, these disturbances are always damped: otherwise, some of them grow, up to the disappearance of the initial flow replaced by, perhaps, more stable one.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
To say it in a simple way, compact (linear) operators are like matrices of finite dimension although the space on which they act is a space of functions and therefore of infinite dimension.
- 2.
For “root mean square”; this is the typical dispersion of molecules velocities in a gas.
- 3.
This is an idealization of course. In reality the fluctuations of pressure do not exactly vanish, but their amplitude is very small compared to the one inside the tube.
- 4.
This doesn’t imply that δ p = 0 because (5.20) doesn’t apply to a superimposition of plane waves.
- 5.
- 6.
As for the shock waves, we use a frame attached to the discontinuity. Upstream and downstream regions are defined similarly.
References
Courant, R. & Friedrichs, K. (1976). Supersonic flow and shock waves. New York: Springer.
Drazin, P. & Johnson, R. (1989). Solitons: An introduction. Cambridge: Cambridge University Press.
Gillet, D. (2006). Radiative shocks in stellar atmosphere: Structure and turbulence amplification. In M. Rieutord & B. Dubrulle (Eds.), EAS Publications Series (Vol. 21, pp. 297–324).
Lighthill, J. (1978). Waves in fluids. Cambridge: Cambridge University Press.
Newell, A. (1985). Solitons in mathematics and physics. The Society for Industrial and Applied Mathematics, 39, 422–443.
van Dyke, M. (1982). An Album of Fluid Motion. The Parabolic Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Rieutord, M. (2015). Waves in Fluids. In: Fluid Dynamics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-09351-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-09351-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09350-5
Online ISBN: 978-3-319-09351-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)