# Demo

Some results, which are got by using programs in "demo" directory, are shown in this page.

## poisson

The program to solve a two-dimensional Poisson equation by the Jacobi iteration method.

A forcing in the Poisson equation is given by a shape of a circle.

- Result
- using subroutine : Ellip_Jacobi (use Ellip_Slv)

## cov

The program to calculate correlation coefficient in a distribution and draw the result.

- Result
- using subroutine : Reg_Line_1d, Cor_Coe_1d (use Statistics)

## wind

The program to calculate a geostrophic wind, vorticity and stream line for an analytic pressure distribution.

- pressure field
- geostrophic wind
- using subroutine : grad_1d (use analy)

- vorticity
- using subroutine : curl (use analy)

- stream line
- using subroutine : Forward_Trajectory (use Trajectory)

## matrix_test

By using the data in the "data.dat", the program to

- solve a simultaneous equation
- using subroutine (use Algebra) :
- gausss, LU_devs, Gau_Sei, Jacobi_algebra, SOR_Gau_Sei, SOR_Jacobi_algebra

- using subroutine (use Algebra) :
- invert a matrix
- using subroutine : invert_mat (use Algebra)

- solve an eigenvalue problem
- using subroutine : eigenvalue_power (use Algebra)
- the program calculates the maximum eigenvalue and the eigenvector correponding to the eigenvalue by using the power method.

When you run this program, select one from some single digits. The digits correspond to some calculating methods.

## adjust

A one-dimensional, linear and shallow-water model to simulate processes of geostropic adjustment and radiation of gravity wave.

- using subroutine (use Derivation)
- grad_1d

- Initial condition
- At rest, a discontinuous distribution for the height of the fluid, whose state is unstable.

- some parameters
- Rossby deformation radius : 300 m.
- propagating speed of gravity wave : 30 m/s.

- Results
- Time series of fluid height
- Black bold line denote the Rossby deformation radius.

- Time series of geostrophic wind
- In the steady state, the fluid height, the geostrophic wind which is induced by the adjustment process.
- During the early period of the simulation, outward radiations of the gravity wave.

- Time series of fluid height
- The Rossby deformation radius and propagating speed are consistent with the linear theory.

## Karman

A two dimensional, incompressible fluid model to simulate Karman vortex sheets.

- Detail
- using subroutine : Ellip_Jacobi (use Ellip_Slv)

## WK04

A two dimensional, incompressible fluid model to simulate cold pools and gravity currents.

- Detail
- using subroutine : Ellip_Jacobi (use Ellip_Slv)

## SEQ

A two-dimensional model to diagnose the transverse circulation induced by diabatic heating and surface friction associated with an axisymmetric tropical cyclone (referring to Pendergrass and Willoughby (2009).

- Detail
- using subroutine : Ellip_Gausei (use Ellip_Slv)

## NM01

A two-dimensional, shallow-water model to simulate a vortex Rossby wave embedded in an axisymmetric cyclonic circulation (Nolan and Montgomery 2001).

The model performs the time integration by a hybrid method for spacial derivations which use a spectral method by FFT for the azimuthal direction and a central finite difference method.

- Detail
- using subroutine : ffttp_1d (use ffts), grad_* (use derivation)

## BAROVOR

A two-dimensional, barotropic, non-divergent vorticity model to simulate any vortex behaviors.

The model performs the time integration by a full spectral method for spacial derivations.

This model includes non-linear terms which is (more accurately than any psedo-spectral methods) evaluated by a method to translate the terms between real and spectral space.

- Detail
- using subroutine : ffttp_2d (use ffts)