Scale‐by‐scale budget of turbulence kinetic energy in the convective atmospheric boundary layer: Analysis of structure functions

Abstract We investigate the scale‐by‐scale budget of turbulence kinetic energy in convective atmospheric boundary layers using airborne measurements performed in the shallow trade‐wind regime over the ocean by the ATR 42 aircraft during the Elucidating the Role of Cloud–Circulation Coupling in Climate (EUREC4A) measurement campaign. The simple and repeatable flight pattern sampled four altitude levels: near‐surface, the middle and top of the subcloud layer, and the cloud base. This approach provides acceptable statistical convergence, including mixed velocity–temperature and third‐order velocity structure functions. The scale‐by‐scale budget obtained from the data is approximately closed up to length‐scales of about 200 m at all four levels. At the near‐surface and mid‐subcloud levels, the buoyancy forcing supplies energy to the largest scales and becomes negligible at smaller scales. As a result, Kolmogorov equilibrium is observed over a wide range of scales, from a few to about 100 m. On the other hand, at the top‐subcloud and cloud‐base levels, the budget at scales above 10 m is far from Kolmogorov equilibrium, with a significant contribution of buoyancy forcing and turbulent transport. The contribution to the buoyancy forcing related to humidity variations is substantial and strictly positive at all four levels, even at the cloud base, where it balances the negative contribution related to temperature only.