This paper presents results from a three-dimensional numerical model analyzing turbulence and entrainment in mixed layers capped by stratocumulus clouds, with or without parameterized cloud-top radiative cooling. The model eliminates many assumptions from previous theories but has limitations in resolution and truncation errors in and above the capping inversion. For thick mixed layers with thick capping inversions, cloud-top radiative cooling is mostly within the capping inversion and does not significantly contribute to buoyancy flux or turbulence in the well-mixed layer below. The optimal way to correlate entrainment rate or mixed-layer growth rate is through a functional dependence on an overall jump Richardson number, using the standard deviation of vertical velocity at the top of the mixed layer (near the capping inversion) as the scaling velocity. This velocity is a fraction of the generalized convective velocity, which is greater for cloud-capped mixed layers than for clear ones. The study discusses the difficulties in understanding the structure of turbulence in stratocumulus-capped mixed layers compared to clear layers. Theories of these layers have lacked reliable data, but three-dimensional numerical results are presented to provide guidance. Lilly (1968) proposed a theory with several assumptions, including the well-mixed boundary layer, negligible capping inversion thickness, and no precipitation. Schubert (1976) used a closure assumption compatible with Lilly's theory to predict reasonable structures of stratocumulus-capped mixed layers. Deardorff (1976a) revised Lilly's theory, allowing a fraction of cloud-top divergence to occur in the capping inversion and the rest in the mixed layer below, enhancing turbulence and cooling. The paper highlights the importance of these models in understanding the dynamics of stratocumulus-capped mixed layers.This paper presents results from a three-dimensional numerical model analyzing turbulence and entrainment in mixed layers capped by stratocumulus clouds, with or without parameterized cloud-top radiative cooling. The model eliminates many assumptions from previous theories but has limitations in resolution and truncation errors in and above the capping inversion. For thick mixed layers with thick capping inversions, cloud-top radiative cooling is mostly within the capping inversion and does not significantly contribute to buoyancy flux or turbulence in the well-mixed layer below. The optimal way to correlate entrainment rate or mixed-layer growth rate is through a functional dependence on an overall jump Richardson number, using the standard deviation of vertical velocity at the top of the mixed layer (near the capping inversion) as the scaling velocity. This velocity is a fraction of the generalized convective velocity, which is greater for cloud-capped mixed layers than for clear ones. The study discusses the difficulties in understanding the structure of turbulence in stratocumulus-capped mixed layers compared to clear layers. Theories of these layers have lacked reliable data, but three-dimensional numerical results are presented to provide guidance. Lilly (1968) proposed a theory with several assumptions, including the well-mixed boundary layer, negligible capping inversion thickness, and no precipitation. Schubert (1976) used a closure assumption compatible with Lilly's theory to predict reasonable structures of stratocumulus-capped mixed layers. Deardorff (1976a) revised Lilly's theory, allowing a fraction of cloud-top divergence to occur in the capping inversion and the rest in the mixed layer below, enhancing turbulence and cooling. The paper highlights the importance of these models in understanding the dynamics of stratocumulus-capped mixed layers.