addGeostrophicStreamfunction

add a geostrophic streamfunction to existing geostrophic motions

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Declaration

 addGeostrophicStreamfunction(psi)

Parameters

• psi function handle that takes three arguments, psi(X,Y,Z)

Discussion

The geostrophic streamfunction is added to the existing values in A0

The geostrophic streamfunction, \(\psi\), is defined such that

\[u= - \frac{\partial \psi}{\partial y}\] \[v=\frac{\partial \psi}{\partial x}\] \[N^2 \eta = \frac{g}{\rho_0} \rho = - f \frac{\partial \psi}{\partial z}\]

Note that a streamfunction also projects onto the mean-density-anomaly (MDA) component of the flow, and thus it is not strictly geostrophic.

Consider a shallow eddy where the density anomaly sits close to the surface. This example was constructed in Early, Hernández-Dueñas, Smith, and Lelong (2024)

  x0 = 3*Lx/4;
  y0 = Ly/2;
 
  Le = 80e3;
  He = 300;
  U = 0.20; % m/s
 
  H = @(z) exp(-(z/He/sqrt(2)).^2 );
  F = @(x,y) exp(-((x-x0)/Le).^2 -((y-y0)/Le).^2);
  psi = @(x,y,z) U*(Le/sqrt(2))*exp(1/2)*H(z).*(F(x,y) - (pi*Le*Le/(wvt.Lx*wvt.Ly)));
 
  wvt.addGeostrophicStreamfunction(psi);