How can I interpret the 2D advection equation?

Click For Summary
SUMMARY

This discussion focuses on interpreting the 2D advection equation in the context of modeling debris transport on glaciers. The key variables include the x-component of surface velocity (u_s), the y-component of surface velocity (v_s), and the thickness of the debris layer (h_d). It is established that the rocks do not deform and are transported rigidly by the ice flow. Understanding the physics behind the modeling process is essential, particularly the derivation of equations and the significance of the divergence term related to debris height change.

PREREQUISITES
  • Understanding of 2D advection equations
  • Familiarity with glacier dynamics and ice flow mechanics
  • Knowledge of surface velocity components in fluid dynamics
  • Ability to interpret physical models and diagrams
NEXT STEPS
  • Research the derivation of the 2D advection equation in fluid dynamics
  • Study glacier dynamics and the impact of surface velocity on debris transport
  • Explore the concept of divergence in vector calculus as it applies to physical processes
  • Learn how to create and interpret diagrams that illustrate physical models
USEFUL FOR

Researchers in glaciology, environmental scientists, and engineers involved in modeling debris transport on glaciers will benefit from this discussion.

jones1234
Messages
5
Reaction score
1
TL;DR
How can I interpret the 2D advection equation?
I want to model the advection of debris rock layer with a thickness hd on top of a glacier through ice flow with velocity components u and v. Can anybody explain the physical difference between these 2 equations and which one I should take? Thanks

advection.png
 
  • Like
Likes   Reactions: Delta2
Physics news on Phys.org
Please provide a diagram. Are the v's in the equations the averages with respect to z over the thickness of the layer or the values at the top of the layer?
 
Chestermiller said:
Please provide a diagram. Are the v's in the equations the averages with respect to z over the thickness of the layer or the values at the top of the layer?
u_s = the x-component of the surface velocity,
v_s = the y-component of the surface velocity,
h_d = the thickness of the rock layer
 
jones1234 said:
u_s = the x-component of the surface velocity,
v_s = the y-component of the surface velocity,
h_d = the thickness of the rock layer
Is the rock moving as a rigid layer or is it deforming?
 
Chestermiller said:
Is the rock moving as a rigid layer or is it deforming?
The rocks are not deforming. They are on top of the ice and get transported by the ice.
 
jones1234 said:
The rocks are not deforming. They are on top of the ice and get transported by the ice.
Then u and v do not vary with x and y
 
Chestermiller said:
Then u and v do not vary with x and y
The most important part of modeling is actually understanding the physics of the process and then deriving the underlying model. Do you see how eq. (2) can be obtained from eq. (1) with the comments of @Chestermiller ?

If you haven't done so already, it will also be good for your understanding to go back even one step further and ask yourself why the change of debris height in time is given by this divergence term in the first place. The diagram that @Chestermiller asked for will be crucial for this understanding
 
  • Like
Likes   Reactions: Delta2

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 9 ·
Replies
9
Views
3K
Replies
3
Views
3K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 19 ·
Replies
19
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 18 ·
Replies
18
Views
2K