# Question about the sign of the shearing deformation terms

I have the following equation for the shearing term of the deformation zone in meteorology. The reference is here.

Shearing = $$\frac{dV}{dx} + \frac{dU}{dy}$$

$${U}$$ and $${V}$$ are the zonal and meridional winds, respectively; $${x}$$ and $${y}$$ are the longitude and latitude, respectively.

I would like to know what does it mean to have if:

a) $$\frac{dV}{dx}$$ < 0 and $$\frac{dU}{dy}$$ > 0;

b) $$\frac{dU}{dy}$$ < 0 and $$\frac{dV}{dx}$$ > 0;

c) both $$\frac{dV}{dy}$$ and $$\frac{dU}{dx}$$ are less than 0;

d) both $$\frac{dV}{dy}$$ and $$\frac{dV}{dx}$$ are greater than 0.

• You need to clarify if if you want both a and b is less than 0 or just either one of them
– user1066
Commented Sep 16, 2019 at 7:37
• @gansub i want to know when both are negative and one is larger positive and the other is negative. I'll edit my post. Commented Sep 16, 2019 at 7:40
• I am not sure if the individual terms sign has any distinct meaning. But the the net value of shear surely h as some meaning
– user1066
Commented Sep 16, 2019 at 8:28
• @Lyndz The components ∂u/∂x and ∂v/∂y (c) & d)) don't occur in the shearing term... ?? Commented Sep 18, 2019 at 8:56
• @klanomath One is shear and the other is stretch earthscience.stackexchange.com/questions/16990/…
– user1066
Commented Sep 22, 2019 at 5:05

Did you try to sketch one of those situations? Try a square grid, define x and y, and then put $$U$$ and $$V$$ components onto one of the grid points, which you choose as starting point.
Now proceed to implement a). For example, from your starting arrows, go to the next grid point eastwards, and implement $$\frac{dV}{dx}<0$$, i.e. the upwards pointing arrows become smaller as you go eastwards. Do the same for U. Repeat for enough grid points until you see a pattern. Now connect $$U$$ and $$V$$ components into the final, two-dimensional velocity vector $$\vec v$$.