Turbulent Lengthscales in Asymmetric Shear Instabilities Subject to Subharmonic Vortex Pairing

Shear-driven mixing in the upper ocean can be modeled using different varieties of stratified shear instabilities. These mixing events can be described in terms of various key turbulent lengthscales, which characterize the physical state and properties of the turbulent flow. However, there has been a relative lack of work exploring how the relationships between such lengthscales evolve for asymmetric shear instabilities, both with and without subharmonic vortex pairing. To explore this, we use direct numerical simulations of flows subject to either asymmetric Kelvin-Helmholtz or Holmboe instability, where the shear and density interfaces are vertically offset. We examine the evolution of three major lengthscales: Thorpe, Ozmidov, and Corrsin scales in both single- and double-wavelength domains. Our findings show that pairing induces a relatively sustained large overturn, indicated by the Thorpe scale, and significantly modifies the temporal evolution of the Ozmidov and Corrsin scales. We also investigate how asymmetry and pairing influence other turbulent energy and mixing quantities related to these lengthscales.