mathematics in fluid mechanics: a study of vorticity in stochastic fluid flow
TRANSCRIPT
![Page 1: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/1.jpg)
Mathematics in Fluid Mechanics:
A Study of Vorticity in Stochastic Fluid Flow
Mikal Grant Mikal Grant University of Wyoming University of Wyoming
![Page 2: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/2.jpg)
The Rundown Fluids Vorticity Biot-Savart Brownian Motion Biot-Savart…again So What? Where to?
![Page 3: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/3.jpg)
Fluids
Categories Gas or liquid
Restrictions Nonviscous Incompressible
![Page 4: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/4.jpg)
Fluids Velocity field
0 U Density
Zero viscosity
Restrictions of fluid types
![Page 5: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/5.jpg)
Demon
![Page 6: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/6.jpg)
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
![Page 7: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/7.jpg)
Vorticity Prediction variable Numerical Weather
Forecasting Global Climate Models Electromagnetism Turbulent flow patterns
![Page 8: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/8.jpg)
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
![Page 9: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/9.jpg)
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
![Page 10: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/10.jpg)
Brownian MotionProperties
1.
2.
3.
100 WP
Tts 0
Tts 0 sWtW stN ,0~
1,0~ NstsWtW
Tvuts 0 uWvWsWtW &
![Page 11: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/11.jpg)
Brownian Motion
N
Tt
![Page 12: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/12.jpg)
Brownian Motion
![Page 13: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/13.jpg)
Brownian Motion in 3-space
![Page 14: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/14.jpg)
Biot -Savart Vortex filament
![Page 15: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/15.jpg)
Biot -Savart Vortex filament
![Page 16: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/16.jpg)
So What?
![Page 17: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/17.jpg)
So What?
![Page 18: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/18.jpg)
Where to Now? Time step/Evolution
3),0[ t ss t
ssuds
dt
t ,
30 xt
![Page 19: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/19.jpg)
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
![Page 20: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/20.jpg)
Thank You’s & Hollywood Credits David Anton
Maximillian Cohen Myron Allen
Professor Jones Hakima Bessaih
(Project Advisor)Marcie
![Page 21: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/21.jpg)
Questions
![Page 22: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/22.jpg)
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
![Page 23: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/23.jpg)
Huh? Decoding the What…Why? Torah Hebrew 5 Books of Moses Gematria Bible Codes
![Page 24: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/24.jpg)
Origin & Methods Soferim Standard
Mispar GadolOrdinalAt BashMispar KaKadmiMisparHaPerati
![Page 25: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/25.jpg)
The Hebrew Language
![Page 26: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/26.jpg)
Gematria & Roots of Popular Superstition
1 2 3 4 6 7 8 1 2 3 4 6 7 8 9 139 13
![Page 27: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/27.jpg)
Trivia
![Page 28: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/28.jpg)
Tell us already!
![Page 29: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/29.jpg)
Recommended Reading The God of Abraham: A Mathematicians
View
![Page 30: Mathematics in Fluid Mechanics: A Study of Vorticity in Stochastic Fluid Flow](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649f575503460f94c7b6eb/html5/thumbnails/30.jpg)
Recommended Reading The God of Abraham: A Mathematicians
View
Image courtesy of ianadesign.com
QuestionsQuestions