Pete Bosler Modeling Geophysical Fluid Flows

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

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

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

600 nm

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

North Wall Warm Eddy Cold Eddies Jump Example

= Stream Function =Temperature perturbation Convection in a slab

Lorenz Attractor

Shock Example

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

Burgers Equation

Singularity Example

Where to go next? Level Set Methods Level Set Methods

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”