Stationary profiles of dimensionless density (left) and velocity (right) perturbations from k_y modes. On the right, red, blue, and black lines show the simulation results for δu_x/c_s at a fixed y coordinate corresponding respectively to the peak, trough, and node of δρ/ρ₀ oscillations. Dotted and dashed lines correspond to the analytical predictions of Eq. (20). Top: No magnetic fields. Bottom: Magnetic field perpendicular to the shock normal.