A supersonic base flow is computed to investigate the effect of the eddy viscosity coefficient to the linear ${kappa}-{varepsilon}$ turbulence models. Slight modifications to the eddy viscosity coefficient, which are based on the realizability condition, are given to the Launder-Sharma turbulence model so that present models satisfy the realizability condition. Numerical results for supersonic base flow show that turbulence models with the weaky-nonlinear eddy viscosity coefficient can lead to reasonable enhancements in the prediction of the velocity and turbulent kinetic energy profiles.