Grass waves Presented by Bulanchuk Pavel. Build a theory of grass waves excitation.
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Transcript of Grass waves Presented by Bulanchuk Pavel. Build a theory of grass waves excitation.
![Page 1: Grass waves Presented by Bulanchuk Pavel. Build a theory of grass waves excitation.](https://reader036.fdocuments.us/reader036/viewer/2022062320/56649d2e5503460f94a062a1/html5/thumbnails/1.jpg)
Grass waves
Presented by Bulanchuk Pavel
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Build a theory of grass waves excitation
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Structure
• Features• Models:
А) Independent cones B) CollisionsC) Thick grass
• Details of “Thick grass”• Demonstration
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Features
• 2 types of waves: “quick small waves” and “slow big waves”
• Weak wind → only quick waves
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Independent cones(quick waves)
• Waves - a consequence of heterogeneity of air flow (turbulence)
• Disturbances propagate at the speed of wind
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Collisions
• Cones collide → disturbances propagate
• Problem: quick dying-out
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Thick grass
• The higher the blade above the rest → → The stronger it is bend → → The grass starts to sway →
→ effect of self-oscillations
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Thick grass: theory
1) 1D model2) Stable wind3) Grass surface is described by
( , ),y y n t t R n Z
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Thick grass: theory
2 21n n n n ny y y y y
Wind elasticity fading
(*)
• Linear approximation
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Thick grass: theory
Separate for sine waves
Solve individually
Sum solutions
2 21n n n n ny y y y y
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Thick grass: theory
• • Dispersion law:
2 21n n n n ny y y y y ( )i kn x ty e
2 2 21( ) 4 4 1
2ik xk e
i
x
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Thick grass: theory
• Disturbance will exponentially rise if
2
2 2
sin( )1
cos( )
k x
k x
2 21n n n n ny y y y y
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Dispersion lawIm( )
k
22 2 No waves
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Conclusion
• Slow and fast waves• Self-oscillations in constant wind• Critical wind velocity
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Thank you for attention!
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Experiment
Artificial Real2 2100 /m с 2 2300с
12 8c
2 2100 /m с 2 2100с
12 4c
4кр m 10кр m
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Thick grass: analysis
• Phase speed:
• Group speed:
1
222 2 4 2 2 214 16 4
2фV k
k
2 2 2 2
4
4 2 2 2 4 2 2 2
4 2
16 ( 4 ) 4 16 ( 4 )гр
kV
k k
tt x ty y y y
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Dispersion lawIm( )
k
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Dispersion lawRe( )
k