Pete Bosler

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Modeling Geophysical Fluid Flows

• Pete Bosler

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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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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

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Data Input

• Over Land
• Satellites
• Airports and automated stations
• Maritime very sparse data
• Satellites
• Ship observations
• Islands

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600 nm
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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

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Jump Example
Warm Eddy
North Wall
Cold Eddies
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Convection in a slab
Stream Function Temperature perturbation
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Lorenz Attractor
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Shock Example
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Precipitation vs. Updraft
Updraft Velocity Rainwater Mixing
Ratio Virtual temperature excess Generation
Parameter Downward velocity of raindrops
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Burgers Equation
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Singularity Example
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Where to go next?

• Level Set Methods
• http//physbam.stanford.edu/fedkiw/

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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