Abstract
Ageostrophic secondary circulation (ASC) in frontal data sets have been previously diagnosed using only adiabatic versions of Omega equations. This study includes the effect of vertical mixing on such diagnostics. Modified quasi‐geostrophic and semigeostrophic balance equations are examined for the existing Azores front data sets and idealized fronts in the presence of diabatic vertical mixing as well as a large‐scale deformation field. The relevant dimensionless parameter representing the relative importance of large‐scale deformation and vertical mixing is the inverse of the Ekman number based on the deformation rate (αH2/Ao), where α is large‐scale deformation rate, H is vertical scale of the front, and Ao is the maximum vertical eddy viscosity; when this parameter is smaller than O(102), the influence of vertical mixing may be important. Other relevant parameters include Burger number, Bu, and Prandtl number, Pr. The vertical velocity in ASCs caused by diabatic mixing in all diagnostics solutions except for large Bu cases shows good agreement with the Garrett‐Loder scaling. The structure of ASCs is found to be sensitive to Pr. The diagnostics of ASCs for the Azores front data set indicates that the vertical mixing intensifies the ASC in the upper ocean (∼100 m) and should not be neglected, when the large‐scale deformation rate, α, is O(10−6 s−1) or smaller. The magnitude of vertical velocity in ASCs due to mixing contributions reaches ∼O(10 m d−1) with downwelling on the dense side and upwelling on the less dense side of Azores front.