Skip to main content Accessibility help
×
Home
Hostname: page-component-7ccbd9845f-hl5gf Total loading time: 0.32 Render date: 2023-01-30T02:04:37.941Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Dynamics of roll waves

Published online by Cambridge University Press:  24 August 2004

N. J. BALMFORTH
Affiliation:
Departments of Mathematics and Earth & Ocean Science, University of British Columbia, Vancouver, Canada Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA
S. MANDRE
Affiliation:
Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA

Abstract

Shallow-water equations with bottom drag and viscosity are used to study the dynamics of roll waves. First, we explore the effect of bottom topography on linear stability of turbulent flow over uneven surfaces. Low-amplitude topography is found to destabilize turbulent roll waves and lower the critical Froude number required for instability. At higher amplitude, the trend reverses and topography stabilizes roll waves. At intermediate topographic amplitude, instability can be created at much lower Froude numbers due to the development of hydraulic jumps in the equilibrium flow. Second, the nonlinear dynamics of the roll waves is explored, with numerical solutions of the shallow-water equations complementing an asymptotic theory relevant near onset. We find that trains of roll waves undergo coarsening due to waves overtaking one another and merging, lengthening the scale of the pattern. Unlike previous investigations, we find that coarsening does not always continue to its ultimate conclusion (a single roll wave with the largest spatial scale). Instead, coarsening becomes interrupted at intermediate scales, creating patterns with preferred wavelengths. We quantify the coarsening dynamics in terms of linear stability of steady roll-wave trains.

Type
Papers
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
91
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Dynamics of roll waves
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Dynamics of roll waves
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Dynamics of roll waves
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *