IC::PerturbedInterface
======================

:bdg-link-secondary-line:`src/IC/PerturbedInterface.H <../../doxygen/PerturbedInterface_8H_source.html>`

Initialize a perturbed interface using Fourier Modes

Notes:
1. \todo Extend this class to allow for 3D perturbations, currently only 2D are allowed
2. \todo Allow for cosine (or complex exponential) expansions rather than just sin.
3. \note This is a **two grain only** initial condition.
4. \note This replaces the depricated "perturbed_bar" initial condition from previous versions

The interface is defined as the :math:`x=0` plane (2D), or the :math:`x=0,z=0` plane (3D).
The equation for the interface is given by
:math:`y(x,z) = \sum_{n\in \{n_1,\ldots,n_N\}} A_n \sin(n\pi x/L_x)`
where :math:`A_n` are the amplitudes (stored in #wave_amplitudes),
:math:`n_1,\ldots,n_N\subset\mathbb{Z}_+` are wave numbers (stored in #wave_numbers),
and :math:`L_x` is the length in the x direction (obtained using the #geom object).

Grain 1 is defined as being above :math:`y(x,z)`, Grain 2 is defined as being below.

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