The design requirements of a high-stability narrowband dye laser with a curved dye cell, pumped by a copper vapor laser, are discussed. The design is simple and easy to fabricate at low cost. It is shown that the curved dye-cell geometry, with hydraulic diameter varying from 23 to 1 mm and curvature ratio varying from 1 to 81, creates flow conditions that meet the requirements of a stable narrowband tunable dye laser. It is shown numerically that the eddy sizes, temperature fluctuations, and associated energies in boundary layer are responsible for the fluctuations in the output. A dye laser based on this geometry was operated from Reynolds number 184 to 1100. The numerical results agree with the experimental results showing better dye laser stability at higher Reynolds number.