Assignment/Reading 5, Physics 426 Fluid Mechanics
Reading (Participation only, very short answer)
- Sec 3.8, 3.11
- Ch 5, but skim 5.7
R1: Simplifications due to vorticity equation
What variable drops out of the vorticity equation compared to the momentum equations. Practically, can you think why dropping that term is useful?
R2: Circulation
Sometimes we want to know the vorticity. Why might it be easier to measure the circulation than the vorticity, and hence why would we calculate the circulation of a flow?
R3: Method of images
Vortex interactions with a wall can be modelled using the method of images. What is the electrical equivalent?
Assignment
- hydrostatic gravity waves
- non-linear waves and bores
A1: Standing wave in fjord (/15)
Consider a hydrostatic wave being forced at the mouth of a rectangular fjord of depth $H$ and length $L$. The sea-surface height at the mouth of the fjord is prescribed by the sea-surface height in the ocean $\eta(0,t) = \eta_O \cos (\omega t)$, where $\omega$ is the tidal frequency.
- Derive an expression for the the sea-surface height $\eta$ as a function of $x$ in the fjord assuming that there is no energy dissipation in the fjord. Describe the response of sea-surface height at the head of the fjord as a function of the length of the fjord, $L$. Also note that there are sometimes nulls in the response in the fjord. Where are they?
- What is the relationship between $u(x,t)$ and $\eta(x,t)$ in the fjord? What happens to the velocity at the mouth as the fjord length approaches the resonant length?
Last Modified: 28 April 2024 Licence: Creative Commons Attribution required, non-commercial uses (CC BY-NC 4.0)