PBL Velocity Profile: Sinusoidal Variation w/ Height

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SUMMARY

The discussion centers on the sinusoidal variation of the planetary boundary layer (PBL) velocity profile with height, as illustrated in Figure 14.10 of "Fluid Mechanics" by Kundu and Cohen, 2nd edition. Participants express confusion regarding the absence of a clear explanation for this undulation in the text, particularly in contrast to flat plate boundary layer profiles. The conversation references the Ekman boundary layer and its characteristics, indicating a need for further clarification on the underlying principles of these velocity profiles.

PREREQUISITES
  • Understanding of planetary boundary layers in meteorology
  • Familiarity with fluid dynamics concepts, particularly laminar flow
  • Knowledge of the Ekman spiral and its implications in boundary layer theory
  • Access to "Fluid Mechanics" by Kundu and Cohen, 2nd edition for reference
NEXT STEPS
  • Research the Ekman boundary layer and its velocity profile characteristics
  • Study the principles of the Ekman spiral and its relevance in atmospheric science
  • Examine additional resources on planetary boundary layers, such as the linked turbulence course notes
  • Explore graphical representations of boundary layer profiles for better visualization
USEFUL FOR

Meteorologists, fluid dynamics researchers, and students studying atmospheric boundary layers will benefit from this discussion, particularly those interested in the complexities of velocity profiles in varying atmospheric conditions.

MOHAMMAD UMAIR
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Why does the planetary boundary layer velocity profile shows a sinusoidal variation with height?
Reference: Fig:14.10 Page 576 Fluid Mechanics - Kundu and Cohen 2nd edition
 
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I don't see any mention of sinusoidal variation with height in the text ? Perhaps you have misinterpreted what is shown in fig 4.10 (b) ?

I think that the general topic is explained quite well by the author .

Please post new questions if you have any specific problems .
 
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Nidum said:
I don't see any mention of sinusoidal variation with height in the text ? Perhaps you have misinterpreted what is shown in fig 4.10 (b) ?

I think that the general topic is explained quite well by the author .

Please post new questions if you have any specific problems .
Thanks Nidum for your reply. I know that the general topic is explained quite well in the text but the author has presented the boundary layer velocity profile in the figure without explaining why there is an undulation of the velocity profile with height. You won't find such undulations in the general boundary layer velocity profiles on a flat plate.
 
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jim mcnamara said:
My apologies if I am making a mess of this question. But. Is Figure 1 in the linked pdf file what you are talking about?

people.atmos.ucla.edu/jcm/turbulence_course_notes/planetary_boundary_layers.pdf

interesting article, thanks :smile:
MOHAMMAD UMAIR said:
Why does the planetary boundary layer velocity profile shows a sinusoidal variation with height?
Reference: Fig:14.10 Page 576 Fluid Mechanics - Kundu and Cohen 2nd edition
I don't have access to that article/book ... it would be good for you to copy and paste the section or if you cannot, scan it or at bare minimum type out the paragraph or two that you are referring to, so that we are all on the same page

As a result, I have no idea which boundary you are referring to ??
Moho ?, upper/lower mantle ?, mantle/outer core ?
MOHAMMAD UMAIR said:
I know that the general topic is explained quite well in the text but the author has presented the boundary layer velocity profile in the figure without explaining why there is an undulation of the velocity profile with height. You won't find such undulations in the general boundary layer velocity profiles on a flat plate.

assuming you are referring to one of my listed ones, and probably the Moho boundary,

Why would you expect to ? the Earth isn't flat and nor are the layers and their boundariesDave
 
Thank you all for showing your keen interest in answering the question I've posed. Davenn I am referring to the Ekman boundary layer profile that you have in your lecture notes on page number 24 figure15 a.
 
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jim mcnamara said:
I believe he is talking about this, which is why I am cautious, cannot see the book he referenced. (meteorology, laminar flow (fluid dynamics) and more intricacies):
https://en.wikipedia.org/wiki/Planetary_boundary_layer

There is a really great graphic there.

ohhh, we are going up, not down, I guessed that wrong ... will do some reading :smile:
 
MOHAMMAD UMAIR said:
Thank you all for showing your keen interest in answering the question I've posed. Davenn I am referring to the Ekman boundary layer profile that you have in your lecture notes on page number 24 figure15 a.
Are you asking why the "Ekman spiral" spirals?
 

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