Boundary Layer Climatology Fundamentals of Turbulence (Arya CH 8) + supplemental material Theodore  von Kármán  1881-1963 ...
<ul><li>Big whorls have little whorls, </li></ul><ul><li>Which feed on their velocity, </li></ul><ul><li>And little whorls...
Turbulent development from laminar flow through a grid after Frisch (1995)
Laminar to Turbulent in Surface Layer (Oke, 1987)
The Reynolds Number <ul><li>dimensionless ratio of the inertial force to the viscous force in the Navier–Stokes equations ...
The “Butterfly effect” <ul><li>sensitive dependence on initial conditions </li></ul><ul><li>in 1960s, computers were slow,...
40 years later, Hollywood discovers the butterfly effect.
Shear instability Animation: U California Irvine Source: Turner J.S., 1973, Buoyancy effects in fluids Cambridge Universit...
from (Stull, 1988)
Reynolds Decomposition <ul><li>Fluctuating winds include mean (u-hat) and fluctuating (u’) components. </li></ul>from (Stu...
from Fritsch (1995) Turbulence, Cambridge Univ. Press
Mean and Turbulent Kinetic Energy
Types of ‘Instabilities’ <ul><li>Buoyant or ‘gravitational’ instability </li></ul><ul><ul><li>i.e.,   v  decreasing with ...
Turbulence generation and maintenance <ul><li>Hydrodynamic instability (H) </li></ul><ul><li>Buoyancy Production (B) </li>...
Review of concepts <ul><li>The butterfly effect </li></ul><ul><li>Types of instabilities in turbulence </li></ul><ul><li>T...
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Choas Theory1

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Choas Theory1

  1. 1. Boundary Layer Climatology Fundamentals of Turbulence (Arya CH 8) + supplemental material Theodore von Kármán 1881-1963 Osborne Reynolds 1842-1912 Lewis Fry Richardson 1881-1953 Lecture 14 Universität Stuttgart
  2. 2. <ul><li>Big whorls have little whorls, </li></ul><ul><li>Which feed on their velocity, </li></ul><ul><li>And little whorls have lesser whorls, </li></ul><ul><li>And so on to viscosity. </li></ul><ul><li>Lewis Fry Richardson (1922) </li></ul><ul><li>‘ energy cascade’ from higher to lower order, from low to high entropy, ending in viscous dissipation. </li></ul>A whorl or swirl
  3. 3. Turbulent development from laminar flow through a grid after Frisch (1995)
  4. 4. Laminar to Turbulent in Surface Layer (Oke, 1987)
  5. 5. The Reynolds Number <ul><li>dimensionless ratio of the inertial force to the viscous force in the Navier–Stokes equations </li></ul><ul><ul><li>U is velocity </li></ul></ul><ul><ul><li>l is length (length scale) </li></ul></ul><ul><ul><li> is the kinematic viscosity of the fluid </li></ul></ul><ul><li>R e is of great importance in the theory of hydrodynamic stability and the origin of turbulence. </li></ul><ul><li>The inertia force generates vortex stretching and nonlinear interactions and hence creates randomness. </li></ul><ul><li>Turbulence occurs when the inertial term dominates the viscous term, that is, when the Reynolds number is large. </li></ul><ul><li>For many engineering flows, turbulence occurs when R e > R ec , where the critical Reynolds number is roughly R ec = 2100. </li></ul>Adapted from AMS glossary of meteorology
  6. 6. The “Butterfly effect” <ul><li>sensitive dependence on initial conditions </li></ul><ul><li>in 1960s, computers were slow, so MIT meteorologist Edward Lorenz made a shortcut and discovered the butterfly effect </li></ul>
  7. 7. 40 years later, Hollywood discovers the butterfly effect.
  8. 8. Shear instability Animation: U California Irvine Source: Turner J.S., 1973, Buoyancy effects in fluids Cambridge University press. pp 368
  9. 9. from (Stull, 1988)
  10. 10. Reynolds Decomposition <ul><li>Fluctuating winds include mean (u-hat) and fluctuating (u’) components. </li></ul>from (Stull, 1988)
  11. 11. from Fritsch (1995) Turbulence, Cambridge Univ. Press
  12. 12. Mean and Turbulent Kinetic Energy
  13. 13. Types of ‘Instabilities’ <ul><li>Buoyant or ‘gravitational’ instability </li></ul><ul><ul><li>i.e.,  v decreasing with height </li></ul></ul><ul><li>Shear instability </li></ul><ul><li>Dynamic or hydrodynamic instability </li></ul><ul><ul><li>Stable if perturbations are found to decay with time (or distance) in the direction of the flow. </li></ul></ul><ul><ul><li>Unstable if the perturbations grow in space or time. </li></ul></ul><ul><ul><li>In unstable case, perturbations continually grow no mater how small they were initially. </li></ul></ul><ul><li>These instabilities are Irreversible </li></ul>
  14. 14. Turbulence generation and maintenance <ul><li>Hydrodynamic instability (H) </li></ul><ul><li>Buoyancy Production (B) </li></ul><ul><li>shear production (S) </li></ul><ul><li>Dissipation (D) </li></ul><ul><li>Transport (T) </li></ul>
  15. 15. Review of concepts <ul><li>The butterfly effect </li></ul><ul><li>Types of instabilities in turbulence </li></ul><ul><li>Turbulence maintenance </li></ul><ul><li>Meaning of terms in R i equation </li></ul><ul><li>Reynolds Decomposition </li></ul><ul><li>MKE and TKE </li></ul>

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