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Modeling Geophysical Fluid Flows

Modeling Geophysical Fluid Flows. Pete Bosler. Overview. “Geophysical Fluid Flow” Ocean & Atmosphere Physical oceanography and meteorology Across spatial scales of O(10 m) to O(1000 km) Modeling Deriving & Simplifying Numerical solutions Application and use of modeling Forecasts.

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Modeling Geophysical Fluid Flows

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  1. Modeling Geophysical Fluid Flows Pete Bosler

  2. Overview • “Geophysical Fluid Flow” • Ocean & Atmosphere • Physical oceanography and meteorology • Across spatial scales of O(10 m) to O(1000 km) • Modeling • Deriving & Simplifying • Numerical solutions • Application and use of modeling • Forecasts

  3. State of models today • Global Models • World Meteorological Association • Ex: NOGAPS, GFS • Regional Models • Better resolution • Can resolve smaller scale phenomena • More realistic topographic interaction • Boundary conditions are an added issue

  4. Data Input • Over Land • Satellites • Airports and automated stations • Maritime: very sparse data • Satellites • Ship observations • Islands

  5. 600 nm

  6. Mathematics • Physics of these fluids can turn out to be “not nice.” • Sensitive dependence on initial conditions • Chaotic dymanics • Discontinuities may arise • Jumps • Shocks • Singularities

  7. Jump Example Warm Eddy North Wall Cold Eddies

  8. Convection in a slab = Stream Function =Temperature perturbation

  9. Lorenz Attractor

  10. Shock Example

  11. Precipitation vs. Updraft Updraft Velocity Rainwater Mixing Ratio Virtual temperature excess “Generation Parameter” Downward velocity of raindrops

  12. Burgers Equation

  13. Singularity Example

  14. Where to go next? Level Set Methods http://physbam.stanford.edu/~fedkiw/

  15. References/Additional Reading • Davis, 1988, “Simplified second order Godunov-type methods” • Gottleib & Orszag, 1987, “Numerical Analysis of Spectral Methods” • Lorenz, 1963, “Deterministic Nonperiodic Flow” • Leveque, 2005, “Numerical Methods for Conservation Laws” • Malek-Madani, 1998, “Advanced Engineering Mathematics” • Rogers & Yau, 1989,“A Short Course in Cloud Physics” • Saltzman, 1962, “Finite amplitude free convection as an initial value problem” • Smoller, 1994, “Shock Waves and Reaction-Diffusion Equations” • Srivastava, 1967, “A study of the effect of precipitation on cumulus dynamics”

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