1 / 5

Assumptions

Inviscid: no term in Navier-Stokes Non-rotating, uniform density atmospheric pressure constant and uniform. Shallow Water Equations Equation of Continuity: Depth Integration:. Assumptions. Equation of Continuity. m = density( ) * h* dx Dx = u*dt

Download Presentation

Assumptions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Inviscid: no term in Navier-Stokes Non-rotating, uniform density atmospheric pressure constant and uniform. Shallow Water Equations Equation of Continuity: Depth Integration: Assumptions

  2. Equation of Continuity m = density( ) * h* dx Dx = u*dt m = *h*u*dt

  3. Pressure increases with depth according to overhead mass per unit area. Pressure at depth h-z: Integrating Hydrostatic Balance

  4. But, => Therefore Net Force => F = Fs + F1 – F2 Thus we get, Depth Integration

  5. => (h)tx= - (uh)xx => (u)tt = - g(h)tx Eliminating (h)tx on both sides, (uh) xx - 1/g*u tt = 0. (u)xx – (1/gh)*utt=0 (Hyperbolic PDE) Wave Equation -> c2(u)xx – utt = 0 Thus, c=root(gh); - Tushar Athawale. Shallow Water Equation

More Related