Fig. 8

Frontogenesis by turbulent thermal wind (TTW). The buoyancy field b (left), ageostrophic secondary-circulation streamfunction \(\Phi\) (center), and Lagrangian, velocity-gradient frontogenetic tendency, \(T^\mathbf{u}\ = \ D|\nabla \mathbf {u}|^2/Dt\) [10\(^{-13}\) s\(^{-3}\)] (right), for an idealized 2D surface front with vertical mixing (McWilliams 2017). The thick black line, pointed to by the arrow on the left panel, is the boundary-layer depth, and the curved line in the center panel indicates the direction of the secondary circulation. The horizontal convergence on the dense side near the surface (i.e., the upper left region in the buoyancy b(x, z) in left panel induces frontogenesis in both \(\nabla b\) and \(\nabla \mathbf {u}\)