# How can I interpret the 2D advection equation?

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• jones1234
In summary, the conversation is about modeling the advection of a debris rock layer with a thickness hd on top of a glacier through ice flow with velocity components u and v. The discussion also includes questions about the physical differences between two equations and whether the rock layer is moving as a rigid layer or deforming. The speaker also mentions the importance of understanding the physics behind the equations and references a diagram that will aid in this understanding.
jones1234
TL;DR Summary
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

Delta2
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

Delta2

## 1. What is the 2D advection equation?

The 2D advection equation is a partial differential equation that describes the transport of a conserved quantity, such as mass or energy, in a two-dimensional space. It is commonly used in fluid dynamics and can also be applied to other fields such as meteorology and oceanography.

## 2. How is the 2D advection equation different from the 1D advection equation?

The 2D advection equation is an extension of the 1D advection equation, which describes the transport of a conserved quantity in a one-dimensional space. The 2D advection equation takes into account the transport in both the x and y directions, while the 1D advection equation only considers the transport in one direction.

## 3. What are the variables in the 2D advection equation?

The variables in the 2D advection equation are the conserved quantity being transported (represented by the variable u), the velocity of the fluid or medium (represented by the variables u and v in the x and y directions, respectively), and time (represented by the variable t).

## 4. How can I interpret the solution of the 2D advection equation?

The solution of the 2D advection equation represents the evolution of the conserved quantity in the two-dimensional space over time. It can be interpreted as the movement and spreading of the quantity due to the velocity of the fluid or medium. The shape and behavior of the solution can also provide insights into the underlying physical processes.

## 5. What are some applications of the 2D advection equation?

The 2D advection equation has many applications in various fields, including weather forecasting, pollution dispersion, and ocean currents modeling. It is also used in computer graphics and image processing to simulate the movement and diffusion of visual elements. Additionally, the 2D advection equation is an essential tool in studying and understanding the behavior of fluids and other transport phenomena.

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