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pigna
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Helmotz decomposition definitions.
- Thread starter pigna
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- Decomposition Definitions
In summary, the conversation is discussing the Hodge-Helmholtz decomposition of a flow field and the confusion surrounding the terms used in the decomposition. The conversation also addresses the issue of posting images in the forum and the guidelines against it. The poster apologizes for the poor quality of the uploaded image and offers to upload a PDF version instead.
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BvU
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Hello Pigna, 
From the guidelines:
Did you do that too ? I can read approximately 40% of it.pigna said:
From the guidelines:
Do not simply post images of the problem statement or your work.
While posting images may be convenient for you, it's actually one of the most effective ways of getting your request for help ignored. Images are often too big, too small, rotated, upside down, out of focus, dimly lit, or of otherwise poor quality, and your handwriting probably isn't as easy to read as you think it is. Images are a hindrance to the helpers as portions of the problem statement or your work can't easily be quoted. Using images also doesn't qualify as filling out the homework template, so your post may be deleted.
While posting images may be convenient for you, it's actually one of the most effective ways of getting your request for help ignored. Images are often too big, too small, rotated, upside down, out of focus, dimly lit, or of otherwise poor quality, and your handwriting probably isn't as easy to read as you think it is. Images are a hindrance to the helpers as portions of the problem statement or your work can't easily be quoted. Using images also doesn't qualify as filling out the homework template, so your post may be deleted.
- #3
pigna
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I'm sorry the upload of the image have made its quality Dim. Now I'm using a Phone and is difficult for me to write code lines. I try to upload a pdf version of the pic. Forgive me for the unproper Way I'm posting. The quality should be better.
FAQ: Helmotz decomposition definitions.
What is the Helmholtz decomposition?
The Helmholtz decomposition is a mathematical technique used to break down a vector field into its component parts: a solenoidal or divergence-free part and a potential or curl-free part. It is named after the German physicist Hermann von Helmholtz.
Why is the Helmholtz decomposition important?
The Helmholtz decomposition is important because it allows us to analyze and understand complex vector fields in physics, engineering, and other fields. It also provides a useful tool for solving differential equations and developing numerical methods.
How is the Helmholtz decomposition calculated?
The Helmholtz decomposition is calculated using vector calculus equations. The solenoidal part is found by taking the curl of the original vector field, while the potential part is found by taking the divergence of the original vector field. The two parts are then combined to reconstruct the original vector field.
What is the difference between the solenoidal and potential parts in the Helmholtz decomposition?
The solenoidal part of the Helmholtz decomposition represents the rotational or curl-like aspect of the vector field, while the potential part represents the irrotational or divergence-like aspect. The solenoidal part is important for understanding fluid flow and electromagnetism, while the potential part is important for understanding gravity and electrostatics.
Are there any limitations to using the Helmholtz decomposition?
Yes, there are some limitations to using the Helmholtz decomposition. It can only be applied to vector fields that are well-behaved and have continuous partial derivatives. It also cannot be used for non-physical vector fields, such as those with singularities or discontinuities.