Time evolution of the maximum Mach number in a 1D atmosphere with an isothermal temperature profile (Eq. (74)) and a linear gravitational potential (Eq. (73)). The colors indicate different well-balancing (WB) methods, the markers different flux functions. CL stands for Cargo–LeRoux. Time is given in units of the Brunt–Väisälä time t_BV = 9.93 s (Eq. (18)) and sound-crossing time t_SC = 3.10 s (Eq. (19)). The curves have been slightly smoothed for better visibility.