Housing walls are often designed with a curved shape to improve their appearance and meet functional demands. The creation of a comfortable environment in an indoor space with curved walls poses a new challenge for air distribution design. This paper uses the brachistochrone curved wall as an example to explore the applicability of attachment ventilation mode in buildings with specially shaped enclosures. Experiments and numerical simulations were applied to investigate the airflow characteristics of this particular ventilation mode. For the attached air curtain ventilation based on a brachistochrone curved wall, the semi-empirical equations for the maximum jet velocity decay, maximum jet temperature decay, and jet spreading rate were obtained. The results show that the proposed air supply mode can be applied to the brachistochrone curved wall. The current study motivates further research on the design of ventilation systems in buildings with specially shaped enclosures.