The Baroclinic Adjustment of Time-Dependent Shear Flows

Abstract

Abstract Motivated by the fact that time-dependent currents are ubiquitous in the ocean, this work studies the two-layer Phillips model on the beta plane with baroclinic shear flows that are steady, periodic, or aperiodic in time to understand their nonlinear evolution better. When a linearly unstable basic state is slightly perturbed, the primary wave grows exponentially until nonlinear advection adjusts the growth. Even though for long time scales these nearly two-dimensional motions predominantly cascade energy to large scales, for relatively short times the wave–mean flow and wave–wave interactions cascade energy to smaller horizontal length scales. The authors demonstrate that the manner through which these mechanisms excite the harmonics depends significantly on the characteristics of the basic state. Time-dependent basic states can excite harmonics very rapidly in comparison to steady basic states. Moreover, in all the simulations of aperiodic baroclinic shear flows, the barotropic component of the primary wave continues to grow after the adjustment by the nonlinearities. Furthermore, the authors find that the correction to the zonal mean flow can be much larger when the basic state is aperiodic compared to the periodic or steady limits. Finally, even though time-dependent baroclinic shear on an f plane is linearly stable, the authors show that perturbations can grow algebraically in the linear regime because of the erratic variations in the aperiodic flow. Subsequently, baroclinicity adjusts the growing wave and creates a final state that is more energetic than the nonlinear adjustment of any of the unstable steady baroclinic shears that are considered.