Total transmission modes in draining bathtub model with vorticity

TL;DR

This paper studies the total transmission modes in a vorticity-influenced draining bathtub model using spectral methods, revealing complex spectral behaviors and sensitivities.

Contribution

It introduces a numerical approach to analyze TTMs in the DBM with vorticity, highlighting spectral mobility and stability characteristics.

Findings

TTM spectra can have positive or negative imaginary parts.

Higher overtones show pronounced spectral mobility.

Spectral behaviors depend on model parameters.

Abstract

We investigate the total transmission modes (TTMs) in the draining bathtub model (DBM) with vorticity using the Chebyshev-Lobatto pseudospectral method, where the boundary conditions of the total transmission modes are both ingoing at the event horizon and infinity. Numerical results show that the (right) TTM spectra can possess positive imaginary parts, while for certain parameters they acquire negative imaginary parts. The extreme sensitivity of the higher overtones is manifested as their pronounced spectral mobility.