What is Euler's Momentum Theory and how does it relate to tornado dynamics?

[ProxRB]

Thank you for taking a look at my hopeless plight. As a part my Calculus project, I am trying to define tornados, or any particular feature of a tornado, using calculus, or basically linking tornados and calculus any way I can. In my research, I came across Neil B. Ward’s The Exploration of Certain Features of Tornado Dynamics Using a Laboratory Model. Ward states:

“3. Application of Euler’s Momentum Theory

“The interpretation of the observations of vortices produced with laboratory system is facilitated through an application of the momentum theory (Milne-Thomson, 1960) which pertains to fluid flow into and out of a volume, V, enclosed by a surface, S. The theorem states that:


<img src='http://img.villagephotos.com/p/2005-5/1014872/1.JPG' width=436 height=46 >

“Where
<img src='http://img.villagephotos.com/p/2005-5/1014872/n.JPG' width=17 height=18 > is the inward unit vector normal to the surface,
<img src='http://img.villagephotos.com/p/2005-5/1014872/p.JPG' width=18 height=19 > is the static pressure*,
<img src='http://img.villagephotos.com/p/2005-5/1014872/ro.JPG' width=18 height=19 > is the fluid density,
<img src='http://img.villagephotos.com/p/2005-5/1014872/f.JPG' width=18 height=19 > is the external force per unit mass, including gravity,
<img src='http://img.villagephotos.com/p/2005-5/1014872/t.JPG' width=15 height=14 > is the time and <img src='http://img.villagephotos.com/p/2005-5/1014872/q.JPG' width=17 height=22 > is the fluid velocity

*Static pressure p as in the Bernoulli equation,


<img src='http://img.villagephotos.com/p/2005-5/1014872/2.JPG' width=258 height=51 >” (pg 3, The Exploration of Certain Features of Tornado Dynamics Using a Laboratory Model)

Now, my question is essentially, what does Euler’s Momentum Theory mean, what is it referring to, and what is Ward describing in the use of this theorem, what does it describe in terms of tornados?

Thank you again

 

[Doc Al]

It looks like those are meant to be images of symbols used in some equation. Either take a crack at writing the symbols directly or just give the link where you found the original statement.

 

[charng]

for your time.

Euler's Momentum Theory is a mathematical theorem that describes the flow of fluids into and out of a specific volume. It is based on the concept of conservation of momentum, which states that the total amount of momentum in a system remains constant unless acted upon by an external force.

In the context of tornado dynamics, this theory can be applied to understand the movement and behavior of air within a tornado. The volume, V, in this case, would be the area inside the tornado, and the surface, S, would be the outer boundary of the tornado. The theorem helps to explain how the air flows into and out of the tornado, and how external forces, such as gravity, may affect its movement.

Ward's use of this theory in his laboratory model of tornado dynamics suggests that he is trying to understand how the air is moving within the tornado and how external forces may be influencing its behavior. By studying the flow of air using this mathematical theorem, he may be able to gain insight into the mechanics of tornado formation and development.

In summary, Euler's Momentum Theory is a mathematical tool that can be used to analyze the movement of fluids, such as air in a tornado. It provides a framework for understanding the forces at play and how they may affect the behavior of the system. Ward's use of this theory in his research on tornado dynamics highlights the importance of mathematical models in studying and understanding complex natural phenomena.