Mathematics in Fluid Mechanics:

A Study of Vorticity in Stochastic Fluid Flow

Mikal Grant Mikal Grant University of Wyoming University of Wyoming

The Rundown Fluids Vorticity Biot-Savart Brownian Motion Biot-Savart…again So What? Where to?

Fluids

Categories Gas or liquid

Restrictions Nonviscous Incompressible

Fluids Velocity field

0 U Density

Zero viscosity

Restrictions of fluid types

Demon

Vorticity Rotation curl U

kji

kji

U

y

U

x

U

x

U

z

U

z

U

y

U

UUUzyx

curl 123123

321

)(

kjiU 321 UUU

Vorticity Prediction variable Numerical Weather

Forecasting Global Climate Models Electromagnetism Turbulent flow patterns

Biot Jean Baptiste Biot

1774 – 1862 Physicist, astronomer,

mathematician

Félix Savart 1791 – 1841 Professor at Collége de

France

-Savart Light polarization Magnetism

Electrical Current

Acoustics Electrical magnetism

Electromagnetics Vector field analysis Vortical fluid flow Inverse curl

2

2

2

ˆ

ˆ

ˆ

r

rqvKB

r

rdKB

r

rKB

m

m

m

I

I

j

Forms

Biot -Savart

T

t

t

t dWWx

WxxU

034

N

ktt

tt

t

N kk

kk

k WWWx

WxxU

13 14

lim

Brownian MotionProperties

1.

2.

3.

100 WP

Tts 0

Tts 0 sWtW stN ,0~

1,0~ NstsWtW

Tvuts 0 uWvWsWtW &

Brownian Motion

N

Tt

Brownian Motion

Brownian Motion in 3-space

Biot -Savart Vortex filament

Biot -Savart Vortex filament

So What?

So What?

Where to Now? Time step/Evolution

3),0[ t ss t

ssuds

dt

t ,

30 xt

Rearview Fluids

Restrictions Macroscopic vs. Microscopic view

Vorticity Mathematical definition

Biot-Savart Original applications Relation to vorticity and velocity fields Forms

Brownian Motion Properties Using to build a vortex filament

Vorticity + Biot-Savart = Demon in a cage

Thank You’s & Hollywood Credits David Anton

Maximillian Cohen Myron Allen

Professor Jones Hakima Bessaih

(Project Advisor)Marcie

Questions

Decoding the Torah:

Mathematics in the Hebrew Language

“Numbers are the language of the universe.”Pythagoras

Mikal Grant Mikal Grant University of Wyoming University of Wyoming

Huh? Decoding the What…Why? Torah Hebrew 5 Books of Moses Gematria Bible Codes

Origin & Methods Soferim Standard

Mispar GadolOrdinalAt BashMispar KaKadmiMisparHaPerati

The Hebrew Language

Gematria & Roots of Popular Superstition

1 2 3 4 6 7 8 1 2 3 4 6 7 8 9 139 13

Trivia

Tell us already!

Recommended Reading The God of Abraham: A Mathematicians

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Recommended Reading The God of Abraham: A Mathematicians

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