1. Pete Bosler Modeling Geophysical Fluid Flows

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

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

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

5. 600 nm

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

7. North Wall Warm Eddy Cold Eddies Jump Example

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

9. Lorenz Attractor

10. Shock Example

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

12. Burgers Equation

13. Singularity Example

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