Waves 3.5 - Rossby Waves
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- What happens when a parcel of fluid is displaced north or south in an environment where the background vorticity is varying ? The planetary vorticity (or Coriolis parameter) increases northwards and the flow compensates to conserve absolute vorticity, resulting in Rossby waves. We derive the dispersion relation from the vorticity equation and discus some of the properties of the waves.
This video was extremely helpful. You are a skilled lecturer
Your explanation is amazing. I am watching your videos from Saudi Arabia. (Ph.D. student) Thank you very much!!!
Thank you ! I'm glad it's useful for you.
Professor Nick, may I know how can the Kelvin waves be identified in the cross section of the water column?
@@linaaleyouni5771 Good question, no simple answer. All waves have their own kinematic properties (like phase speed) and spatial structures, so that's what you need to check. For a Kelvin wave for example: non-dispersive, propagating in one direction, and with a 2-d velocity structure in the vertical plane.
@@NickMJHall Thanks for your reply. so what I understand is I might see an increase in the sea level from the horizontal view and high velocity from the veritcal view.
Thanks for the great lecture Nick. Could I ask what you meant by "y does not change locally". Does y not refer to the position of the particle?
Yes it does. The context is that I'm talking about a partial derivative with respect to time. So other coordinates are fixed. So the term beta y must vanish because beta is independent of time and the y coordinate is fixed because it's a partial derivative. That's what I meant !
Hi Nick, excellent demonstration, i really filling the gap of my knowledge. could please tell what do you mean by quadratic?
I mean any second degree term in the equation: so a square term or a product of two variables (or their derivatives). Cheers, Nick
Wow
Hello,
The restoring force that leads to Rossby waves takes place in the north-south direction (beta effect). Thus, if what gives rise to these waves depends on the y-related variations, how to explain that we observe meridional propagations (for the phase and the group velocities)? There is no restoring force in the zonal direction (beta is constant).
Waves don't just propagate perpendicular to their "restoring force". I know it looks that way in some of the simple diagrams we draw. But think of a wave front in space. It can propagate in any direction. Sound waves propagate in the same direction as the restoring force. Gravity waves can propagate vertically. Rossby waves can propagate meridionally and vertically. That's the way it is ;)
Thank you for your reply. Isn't there an explanation similar to the meridional displacement of an air parcel conserving AV or PV to explain the meridional propagation ? The reasoning based on the conservation of absolute or potential vorticity does not work for zonal displacements, so I have a hard time getting an intuitive understanding of this phenomenon.
Similar to how angular momentum conservation doesn't "explain" the Coriolis force for meridional movement. Some simple explanations are not easy to generalise ! But in this case it should be possible to construct a general explanation where the basic flow has a vorticity gradient with a zonal component. Just tilt your basic state vorticity contours and forget about latitude and longitude. Alternatively - it's probably easier to think of wave fronts and how they can be tilted if there is a phase shift with latitude. That'll do it for you. Check out the diagram that shows vertical propagation of internal waves.
Hi Nick. Thanks for the lecture. It is really helpful! I have some questions about Rossby wave: (1) You didn't mention the propagation in the y direction. Why? And according to my poor knowledge, the weather systems in midlatitudes mostly travels zonally (from west to east) rather than meridionally which may support our focus on the x direction. But why the nature works this way? I mean, mathematically, Rossby wave can propagate in the y direction. Why we choose to omit it (and the nature supports our choice)? (2) Can I understand in the way that the weather systems in midlatitudes are transported by Rossby wave? If it's right, I guess this transportation should be associated with group speed (rather than phase speed).
A quick reply to your question: The fundamental asymmetry here is that the Earth rotates in the east-west direction ! But north-south propagation of Rossby waves is important, especially for interactions between the tropics and the extratropics.
@@NickMJHall Yeah Thanks Nick! I'm reading literatures about attributing regional heatwave events to Rossby wave trains. In this case, what affect local weather system should be the group propagation of Rossby wave packets, right? After all, it's the group speed that is transporting information and energy.
@@NickMJHall Talking about group speed. I'm curious and confused about the practical application value of our group speed formula: cg=dw/dk. If I remember correctly, this formula is derived by assuming two waves with only infinitesimal difference between their frequency. However, all the differences in the real world are finite (such as the frequencies of different Rossby waves). So, how can this cg=dw/dk formula be helpful to us? Thanks!
@@qinqinkong8330 Yes I'd go along with that. Often what you see is a Rossby wave emanating from the tropics with almost no phase propagation. So its a stationary structure which gains amplitude outwards from the source. Pure group propagation.
@@qinqinkong8330 Consider a continuous spectrum of wave frequencies. At any given frequency you can calculate the group speed. For a dispersive wave it's a continuous function of frequency.