Spectral link and wave breaking enhanced dissipation of turbulent kinetic energy

At the ocean surface, the wind shear stress not only drives the ocean currents, but also generates waves and breaks waves. The turbulence in the ocean surface layer (OSL) is much enhanced due to wave breaking. A typical field measurement of this enhanced turbulence is the dissipation of turbulent kinetic energy (TKE) ɛ at a depth y below the ocean surface, which scales as ε∝y−a . However, there is significant uncertainty as to the value of this power law exponent a in different field measurements. Here we consider the dissipation of TKE in the OSL by adding the wave breaking influence into the theoretical framework of the spectral link, originally proposed in sheared flows with no waves (Gioia et al 2010 Phys. Rev. Lett. 105 184501). The expanded theory recovers the power law of ɛ and sheds light on the uncertainty of the power law exponent a by relating it to the variation of the turbulent Prandtl number. In addition, we also apply this theory to oscillating-grid turbulence.