Assignment/Reading 10, Physics 426 Fluid Mechanics
Reading (Participation only, very short answer)
Assignment
A1: Two-layer Flow (/15)
Consider a two-layer flow, hydrostatic, with an upper layer that has a resting thickness $d_1=4$ and density $\rho_1=1000$, and a lower layer with resting thickness $d_2=6$ and density $\rho_2=1010$.
As an initial condition, suppose the upper interface is flat, and the interface between the two layers is deformed as a sine wave with amplitude $\zeta_0=0.1 m$, wavelength $k_0$. The fluid is otherwise at rest (i.e. $u(t=0)=0$). The displacement is small enough that the wave satisfies the linear constraint.
- There are four waves possible, what are their phase speeds and directions? How good is the approximation for the phase speeds given in class? (if good, go ahead and use the approximation below)
- What is the amplitude of the surface displacement and interface displacement for each wave?
- Plot a Hovmoller diagram of the surface displacement and interface displacement covering a few wavelengths and periods. Identify the surface and interface waves in the diagram.
- What is the energy flux of each wave? Use the approximate forms of the phase speeds and reasonable approximations to get as physically simple results as you can
Last Modified: 28 April 2024 Licence: Creative Commons Attribution required, non-commercial uses (CC BY-NC 4.0)