Chanel: Science of Fluids,    / scienceoffluids  
Playlist: Fluids made easy: 02 Fluid motion descriptions
   • Fluids Madeeasy Courses: 02  Fluid ...  

As we are all told in classrooms or read in the textbooks, the streamlines and pathlines in unsteady flows would be different, but what is the difference and how different they could be? in most textbooks, there are no good examples to show the difference. Here in this talk, I will use an example to give you the theoretical solutions and the relevant drawings and show you how different they are.
To show the difference between the streamline and pathline equations in an unsteady flow, an example of a linear ocean wave would be studied, for which the flow itself can be regarded as a 2D potential flow, such that we could have an analytical solution to the flow, and thus the velocity field. As such, it would allow us to build the streamline and pathline equation mathematically for such a flow, and the solutions of the streamline equation and the pathline equation could show and prove: the streamlines and pathlines in an unsteady flow are actually very different!
The following contents are discussed in the talk:
A target to mathematically calculate the streamlines and pathlines in an unsteady flow
An introduction of a linear ocean wave: an unsteady flow
Building streamline equation: the solution and streamlines
Building pathline equation: the solution and pathlines
To illustrate why the streamlines and pathlines are so different in unsteady flows?