u_s = the x-component of the surface velocity,Chestermiller said:
Is the rock moving as a rigid layer or is it deforming?jones1234 said:
The rocks are not deforming. They are on top of the ice and get transported by the ice.Chestermiller said:
Then u and v do not vary with x and yjones1234 said:
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 ?Chestermiller said:
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.
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.
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).
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.
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.