The spontaneous generation of inertia–gravity waves during frontogenesis forced by large strain: numerical solutions

Abstract

A fully nonlinear numerical model is used to investigate spontaneous wave generation during two-dimensional frontogenesis forced by a horizontal strain field. The model uses the idealised configuration of an infinitely long straight front and uniform potential vorticity, with a uniform imposed convergent strain across the front. Shakespeare & Taylor (J. Fluid Mech., vol. 757, 2014, pp. 817–853) formulated a generalised analytical model (ST14) for this system that extends the classical Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp. 11–37) model (HB) to large strain rates (${\it\alpha}\sim f$). Here, we use a numerical model to simulate the fully nonlinear problem and compare the results with the predictions of the analytical model for a variety of strain rates. Even for weak strains (${\it\alpha}=0.2f$), the confinement of the secondary circulation and the spontaneous generation of waves, predicted by ST14, are shown to be important corrections to the HB solution. These inviscid predictions are also robust for an equilibrated front where strain-forced frontogenesis is balanced by diffusion. For strong strains the wavefield becomes of leading-order importance to the solution. In this case the frontal circulation is tightly confined, and the vertical velocity is an order of magnitude larger than in the HB model. The addition of a strain field that weakens with time allows the release and propagation of the spontaneously generated waves. We also consider fronts with both large vorticity and strain rate, beyond the validity of the ST14 model.