Outline for final presentation

Outline of slides for 451 final presentation:

Main takeaway message: The linearized equation sets that I initially set out to use are not well suited to studying the impact of sharpness of topography.

One slide:

• Recap assumptions of linearization Slide 8 lecture 14 Takeaway: Constant N^2. N^2/u^2 is key parameter. Where do boundary conditions come from?

• The dispersion relation: Slide 9: Key parameter.

  • Takeaway: Under highly idealized conditions this gives a simple solution (but how does this generalize?)

• Coming at this from a different angle: long's model

  • maximum 4 equation derivation.
  • Introduce stream function.
  • Assumptions Optional: * Long's notes on existence and uniqueness
  • Main takeaway: tbd
  • The first pin: come back to this.

• Re-deriving what we already know:

  • Without linearizing at the start, assume \partial_z u = 0, N constant.
  • We get the same dispersion relation.

• Boundary conditions:

  • A quick jaunt through fourier transformations (with a dispersion relation)
  • Gives us solution for gravity wave in the absence of wind shear. Very solvable.

• A brief deviation into energy transport and topography in the steady state

  • Weirstrauss mountain. low-pass filtered weirstrauss mountain
  • Mountain with extremely steep gradients
  • Enforcing a non-linear boundary condition (impacts).
  • Low-pass filter the topography

• Returning to the complex equations: Keller's solution

  • Suppose that we have linear wind shear.
  • Derive new equations with Z variable.
  • Scale analysis for complicated scorer parameter

• non-hydrostatic version

  • nonhydrostatic Solutions for different topography
  • Energy transport using same topography.
  • Vertical and horizontal structure.
  • low-pass filtered weirstrauss mountain
  • Potentially indicates decreased dependence on topographic steepness? Promising?

• Conclusions:

  • Impact of wind shear on energy transport.
  • Implications for test case design (compare to DCMIP 2012)