<p>Did you try to sketch one of those situations? Try a square grid, define x and y, and then put <span class="math-container">$U$</span> and <span class="math-container">$V$</span> components onto one of the grid points, which you choose as starting point.  </p>

<p>Now proceed to implement a). For example, from your starting arrows, go to the next grid point eastwards, and implement <span class="math-container">$\frac{dV}{dx}&lt;0$</span>, 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 <span class="math-container">$U$</span> and <span class="math-container">$V$</span> components into the final, two-dimensional velocity vector <span class="math-container">$\vec v$</span>.</p>

<p>In this way you will possibly self-answer your question. I don't know if I can help you more, because I don't know what you mean with \</p>

<blockquote>
  <p>I would like to know what does it mean to have</p>
</blockquote>

<p>The end result will be the graphical representation of a vector field. The shear tensor simply measure the amount of shear in each vector field. You will discover that some field structures surprisingly possess shear, while others don't.</p>

CC BY-SA 4.0
2019-09-22T02:10:31.663Z
2019-09-22T02:10:31.663Z
AtmosphericPrisonEscape
<p>I have the following equation for the shearing term of the deformation zone in meteorology. The reference is <a href="https://resources.eumetrain.org/satmanu/CMs/Def/navmenu.php?tab=2&amp;page=2.0.0" rel="nofollow noreferrer">here</a>.</p>
<p>Shearing = <span class="math-container">$\frac{dV}{dx} + \frac{dU}{dy}$</span></p>
<p><span class="math-container">${U}$</span> and <span class="math-container">${V}$</span> are the zonal and meridional winds, respectively; <span class="math-container">${x}$</span> and <span class="math-container">${y}$</span> are the longitude and latitude, respectively.</p>
<p>I would like to know what does it mean to have if:</p>
<p>a) <span class="math-container">$\frac{dV}{dx}$</span> &lt; 0 and <span class="math-container">$\frac{dU}{dy}$</span> &gt; 0;</p>
<p>b) <span class="math-container">$\frac{dU}{dy}$</span> &lt; 0 and <span class="math-container">$\frac{dV}{dx}$</span> &gt; 0;</p>
<p>c) both <span class="math-container">$\frac{dV}{dy}$</span> and <span class="math-container">$\frac{dU}{dx}$</span> are less than 0;</p>
<p>d) both <span class="math-container">$\frac{dV}{dy}$</span> and <span class="math-container">$\frac{dV}{dx}$</span> are greater than 0.</p>

CC BY-SA 4.0
2019-09-16T07:40:27.327Z
@gansub i want to know when both are negative and one is larger positive and the other is negative. I'll edit my post.
Lyndz
CC BY-SA 4.0
2019-09-18T08:56:29.260Z
@Lyndz The components ∂u/∂x and ∂v/∂y (c) & d)) don't occur in the shearing term... ??
klanomath
<meteorology><wind>
Question about the sign of the shearing deformation terms
Lyndz
# Question about the sign of the shearing deformation terms

(Asked by: username_0 on 2019-09-16)

I have the following equation for the shearing term of the deformation zone in meteorology. The reference is [here](https://resources.eumetrain.org/satmanu/CMs/Def/navmenu.php?tab=2&page=2.0.0).

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.

**Tags:** meteorology, wind

> **Comments:**
> **username_0**: @gansub i want to know when both are negative and one is larger positive and the other is negative. I'll edit my post.  
> **username_1**: @username_0 The components ∂u/∂x and ∂v/∂y (c) & d)) don't occur in the shearing term... ??  

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## 1 answers

### Answer by username_2 on 2019-09-22. Score: 3

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 $\vec v$.

In this way you will possibly self-answer your question. I don't know if I can help you more, because I don't know what you mean with \

> I would like to know what does it mean to have

The end result will be the graphical representation of a vector field. The shear tensor simply measure the amount of shear in each vector field. You will discover that some field structures surprisingly possess shear, while others don't.


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