Two incompressible, inviscid fluids occupy the regions 0
Posted: Mon May 09, 2022 10:50 am
- Two Incompressible Inviscid Fluids Occupy The Regions 0 Z And Z 0 Respectively Where Z Is Measured Vertically Up 1 (47.89 KiB) Viewed 32 times
Two incompressible, inviscid fluids occupy the regions 0 <z« and - <z<0, respectively, where z is measured vertically upwards. The upper fluid has density pı, while the lower fluid has density P2, where P2 > P1. In this question, you are asked to investigate the propagation of small-amplitude waves at the interface between the two fluids. The velocity potentials are denoted by 01 (2, z, t) for the upper fluid and 02(1, 2, t) for the lower fluid. Under the assumptions made on page 10 of Unit 12, the following results may be derived. (You are not asked to derive them.) 2202 a02 (1) дот 2202 მ2 + = 0 Әr2 8:2 (-<<0), θοι a62 at z = 0 (to first order), (2) az az a21 pi + 9 at2 az P2 at z = 0 (to first order), (3) at2 +9 az where g is the magnitude of the acceleration due to gravity. (a) Write down a condition on ci similar to that given in Equation (1) for 02, and the conditions on ci at 2+ and on 2 at 2 +-oo, with an explanation. 
= m ( a
Posted: Mon May 09, 2022 10:50 am
- Two Incompressible Inviscid Fluids Occupy The Regions 0 Z And Z 0 Respectively Where Z Is Measured Vertically Up 1 (47.89 KiB) Viewed 32 times
= m ( a