Thermal storages are components used in energy systems, such as district heating networks or thermal power plants, in order to decouple the supply of heat from its use. Usage rate of monophasic thermocline storages is highly dependent on the thermal gradient zone inside the fluid, also named thermocline. While thermal stratification results of a formation phase followed by a degradation phase, the early stages of thermocline establishment is primarily responsible for its thickness. CFD allow to consider the multiple physical phenomena involved during the thermocline formation, in particular the buoyancy effects. These effects are usually considered by selecting either a variable density with respect to the temperature or a constant one by using the commonly used (first-order) Boussinesq approximation. However, the former approach implies an increased computational cost, and the latter is only valid for an unclear validity range of temperature difference. Hence, this article suggests the use of a second-order Boussinesq approximation, coupled with a RANS turbulence approach, to better account for buoyancy effects in a turbulent water flow submitted to a large temperature differences. CFD results obtained with a quadratic Boussinesq approximation are similar to the one obtained with a variable density but with a computation time reduced by half. This approach is applied to the issue of reducing the thermocline thickness during its creation and the impact of linear flow rate ramps is assessed on both a uniform and initially stratified storage. On an initially cold tank, results show that the longer the ramp time, the thinner the thermocline. In contrast, on the initially stratified tank tested, a gradual injection shows no significant reduction of the thermocline thickness. This can be relevant when performing storage management enhancement.