Evaluating Tidal Eigenvalues¶
This appendix describes the eval_lambda executable, which evaluates the eigenvalue \(\lambda\) appearing in Laplace’s tidal equations (see the Rotation Effects section). This executable is used for the calculations presented in Townsend (2020).
Installation¶
eval_lambda is automatically compiled when GYRE is built,
and installed in the $GYRE_DIR/bin
directory (see the main
Installation chapter).
Running¶
Unlike most other GYRE executables, the parameters for eval_lambda are supplied directly on the command line, with the syntax
./eval_lambda l m q_min q_max n_q log_q rossby filename
This evaluates \(\lambda\) for harmonic degree \(\ell\) and
azimuthal order \(m\) on a grid
\(\{q_{1},q_{2},\ldots,q_{N}\}\) in the spin parameter, writing
the results to the file filename
. If the flag log_q
has the value T
then the grid is logarithmically spaced:
where
Alternatively, if log_q
has the value F
, then the grid
is linearly spaced:
As a special case, when \(n_{q}=1\), \(q_{\rm min}\) and \(q_{\rm max}\) must match, and the single \(q\) point is set to equal them.
If the flag rossby
has the value T
, then the Rossby
\(\lambda\) family is evaluated; otherwise, the gravitoacoustic
family is evaluated.
The table below summarizes the mapping between the userdefinable controls appearing in the expressions above, and the corresponding commandline parameters:
Symbol 
Parameter 

\(\ell\) 

\(m\) 

\(q_{\rm min}\) 

\(q_{\rm max}\) 

\(N\) 

Interpreting Output¶
The output file created by eval_lambda is in GYRE’s HDF Format, with the following data:
l
(integer scalar)Harmonic degree \(\ell\)
k
(integer scalar)Meridional order \(k\) (see Townsend, 2003a)
l
(integer scalar)Azimuthal order \(m\)
rossby
(logical scalar)Rossby family flag
q
(real array)Spin parameter \(q\)
lambda
(real array)Eigenvalue \(\lambda\)