# 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).

eval_lambda is automatically compiled when GYRE is built, and installed in the $GYRE_DIR/bin directory (see the main Installation chapter). ## Running¶ Unlike most other GYRE executables, the parameters for eval_lambda are supplied directly on the command line, with the syntax  span.prompt1:before { content: "$ ";
}
./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:

$q_{i} = 10^{(1 - w_{i}) \log q_{\rm min} + w_{i} \log q_{\rm max}},$

where

$w_{i} \equiv \frac{i-1}{N-1}.$

Alternatively, if log_q has the value F, then the grid is linearly spaced:

$q_{i} = (1 - w_{i}) q_{\rm min} + w_{i} q_{\rm max}.$

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 gravito-acoustic family is evaluated.

The table below summarizes the mapping between the user-definable controls appearing in the expressions above, and the corresponding command-line parameters:

Symbol

Parameter

$$\ell$$

l

$$m$$

m

$$q_{\rm min}$$

q_min

$$q_{\rm max}$$

q_max

$$N$$

n_q

## 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 $$\lambda$$