of the drop quantitatively, we will compute and present the time-dependent spectral coefficients, obtained from the decomposition $$\zeta(\theta,\phi,t) = \sum_{\ell=0}^\infty \sum_{m=-\ell}^{m=\ell} \zeta_\ell^m(t)Y_\ell^m(\theta,\phi)
\label{eq:defint}$$ where $\zeta$ is the distance from the domain center. We compute both $|\zeta_\ell^m(t)|$ and $$\zeta_\ell(t) \equiv \left[\sum_{m=0}^\ell |\zeta_\ell^m(t)|^2\right]^{1/2}
\label{eq:coeffylm}$$ We note that, according to the normalization convention we use, $$\zeta_0(t)=\zeta_0^0=\int_0^{2\pi} d\phi\int_0^{\pi} d\theta\: \sin\theta \:\zeta(\theta,\phi,t) \,Y_0^0(\theta,\phi)
\label{eq:zeta0}$$ i.e. $\zeta_0(t)$ is $\sqrt{4\pi}$ times the spherically averaged distance of the interface from the origin.

We calculate the spherical harmonic transform as follows. The three-dimensional Lagrangian interface consists of triangles composed of points $\left(x_i, y_i, z_i \right)$ on the fixed Cartesian grid. We transform each of these points to spherical coordinates $\left(\zeta_i, \theta_i, \phi_i\right)$ and interpolate the function $\zeta(\theta_i,\phi_i) = \zeta_i$ onto a regular spherical grid $(\theta_j,\phi_k)$, discretizing the latitudinal interval $[0,\pi]$ and longitudinal interval $[0,2\pi]$ with $N_\theta = 80$ and $N_\phi = 80$ points. Using the discrete data $\zeta(\theta_j,\phi_k)$ and truncating the series at four times the dominant value of $\ell$, we compute the spherical harmonic coefficients $\zeta_\ell^m$ by the method of least squares [@Politis; @politis_phd]. This procedure is carried out for each sampled temporal snapshot of the interface. We note that the spherical harmonic coefficients are weighted averages of 