Abstract
AbstractIn this paper, we study two‐dimensional Euler equations in a domain with small depth. With this aim, we introduce a small non‐dimensional parameter ε related to the depth and we use asymptotic analysis to study what happens when ε becomes small.We obtain a model for ε small that, after coming back to the original domain, gives us a shallow water model that considers the possibility of a non‐constant bottom, and the horizontal velocity has a dependence on z introduced by the vorticity when it is not zero. This represents an interesting novelty with respect to shallow water models found in the literature. We stand out that we do not need to make a priori assumptions about velocity or pressure behaviour to obtain the model.The new model is able to approximate the solutions to Euler equations with dependence on z (reobtaining the same velocities profile), whereas the classic model just obtains the average velocity. Copyright © 2007 John Wiley & Sons, Ltd.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
