Abstract
Waves in fluids are ubiquitous, from the outward propagation of pond ripples, ocean waves crashing ashore, sound and shocks in the air, and so many others that to list them all would be impossible.
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.
We do not deal as yet with boundary and/or initial conditions which are necessary to find a particular solution of a PDE.
- 2.
Here we ignore any additive constants in the solution, determining that they are zero, owing to the initial condition.
- 3.
This is a prerequisite for the use of Laplace transforms. In particular, it means that the long time behavior of \(\boldsymbol{\psi }\) could have exponential divergences associated with it \(\propto e^{at}\) for a > 0, but not worse. Functional behavior like (for instance) \(e^{at^{2} }\) cannot be formally handled by the given definition of the Laplace transform.
- 4.
There is considerable mathematical worry over the formalness of Dirac’s δ as a true function per se. A useful conceptualization is to treat it as a distribution, familiar in probability theory.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Regev, O., Umurhan, O.M., Yecko, P.A. (2016). Linear and Nonlinear Incompressible Waves. In: Modern Fluid Dynamics for Physics and Astrophysics. Graduate Texts in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3164-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-4939-3164-4_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-3163-7
Online ISBN: 978-1-4939-3164-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)