This paper presents a parameterization of vertical mixing in numerical models of tropical oceans, focusing on the Equatorial Undercurrent and its response to wind stress. The authors propose a Richardson-number dependent parameterization of eddy mixing, which improves the simulation of oceanic responses to wind stress patterns. The parameterization involves coefficients of vertical eddy viscosity (ν) and diffusivity (κ) that vary with the Richardson number (Ri), which is a measure of the ratio of buoyancy forces to shear forces. The parameterization is tested against measurements and simulations, showing that it leads to more realistic results compared to constant values for ν and κ. The study highlights that mixing processes are intense in the surface layers of the ocean but weak below the thermocline, except in the region below the core of the Equatorial Undercurrent where vertical temperature gradients are small and shear is large. The parameterization accounts for these variations, leading to better simulations of the equatorial oceans' response to different wind stress patterns. For eastward winds, the model agrees well with measurements in the Indian Ocean, while for westward winds, the nonzero heat flux into the ocean is crucial as it stabilizes the upper layers and reduces mixing intensity, especially in the east. The authors also discuss the importance of appropriate surface boundary conditions and the sensitivity of model results to the values of ν and κ. They propose a non-constant parameterization for ν and κ, which depends on the Richardson number and the shear of mean currents. This parameterization is tested in simulations, showing that it improves the model's ability to capture features such as a sharper thermocline, a more realistic equatorial thermocline, an eastward equatorial jet with little shear in the mixed layer, and a shoaling of the core of the Equatorial Undercurrent. The study concludes that the proposed parameterization significantly improves the simulation of vertical mixing in tropical oceans, particularly in the context of the Equatorial Undercurrent. The results are sensitive to the values of ν and κ, but with appropriate surface boundary conditions, the model is relatively insensitive to the specific value of ν₀ (the neutral value of ν when Ri = 0). The parameterization is also compared with other schemes, such as the turbulent closure scheme of Mellor and Durbin, showing that the proposed parameterization is more efficient computationally. The study emphasizes the need for further measurements to refine the parameterization and improve the accuracy of numerical models of tropical oceans.This paper presents a parameterization of vertical mixing in numerical models of tropical oceans, focusing on the Equatorial Undercurrent and its response to wind stress. The authors propose a Richardson-number dependent parameterization of eddy mixing, which improves the simulation of oceanic responses to wind stress patterns. The parameterization involves coefficients of vertical eddy viscosity (ν) and diffusivity (κ) that vary with the Richardson number (Ri), which is a measure of the ratio of buoyancy forces to shear forces. The parameterization is tested against measurements and simulations, showing that it leads to more realistic results compared to constant values for ν and κ. The study highlights that mixing processes are intense in the surface layers of the ocean but weak below the thermocline, except in the region below the core of the Equatorial Undercurrent where vertical temperature gradients are small and shear is large. The parameterization accounts for these variations, leading to better simulations of the equatorial oceans' response to different wind stress patterns. For eastward winds, the model agrees well with measurements in the Indian Ocean, while for westward winds, the nonzero heat flux into the ocean is crucial as it stabilizes the upper layers and reduces mixing intensity, especially in the east. The authors also discuss the importance of appropriate surface boundary conditions and the sensitivity of model results to the values of ν and κ. They propose a non-constant parameterization for ν and κ, which depends on the Richardson number and the shear of mean currents. This parameterization is tested in simulations, showing that it improves the model's ability to capture features such as a sharper thermocline, a more realistic equatorial thermocline, an eastward equatorial jet with little shear in the mixed layer, and a shoaling of the core of the Equatorial Undercurrent. The study concludes that the proposed parameterization significantly improves the simulation of vertical mixing in tropical oceans, particularly in the context of the Equatorial Undercurrent. The results are sensitive to the values of ν and κ, but with appropriate surface boundary conditions, the model is relatively insensitive to the specific value of ν₀ (the neutral value of ν when Ri = 0). The parameterization is also compared with other schemes, such as the turbulent closure scheme of Mellor and Durbin, showing that the proposed parameterization is more efficient computationally. The study emphasizes the need for further measurements to refine the parameterization and improve the accuracy of numerical models of tropical oceans.