eval-lambda.rst

Evaluating Tidal Eigenvalues

This appendix describes the eval_lambda executable, which evaluates the eigenvalue λ appearing in Laplace's tidal equations (see the osc-rot section). This executable is used for the calculations presented in :ads_citet: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

bash

./eval_lambda l m q_min q_max n_q log_q rossby filename

This evaluates λ for harmonic degree ℓ and azimuthal order m on a grid {q₁, q₂, …, 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 λ 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
ℓ	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 ℓ

k (integer scalar)

Meridional order k (see :ads_citealp:townsend:2003a)

m (integer scalar)

Azimuthal order m

rossby (logical scalar)

Rossby family flag

q (real array)

Spin parameter q

lambda (real array)

Eigenvalue λ