This paper details a free surface method using an explicit time stepping scheme for use in z-coordinate ocean models. One key property that makes the method especially suitable for climate simulations is its very stable numerical time stepping scheme, which allows for the use of a long density time step, as commonly employed with coarse-resolution rigid-lid models. Additionally, the effects of ...

A two-layer quasi-geostrophic model is used to study the effect of lower boundary Ekman pumping on the energetics of baroclinic waves. Although the direct impact of the Ekman pumping is to damp the total eddy energy, either the eddy available potential energy (EAPE) or the eddy kinetic energy (EKE), individually, can grow due to the Ekman pumping. Growth of EAPE is favored if the phase differen...

This chapter will introduce the phenomenology of vacillation in baroclinic flows based on experimental data, CFD and low-order numerical models. The processes leading to vacillation of a steady baroclinic wave will be discussed in terms of nonlinear interactions between different wave modes and between waves and the azimuthally or longitudinally averaged baroclinic flow. Complementing the revie...

The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-geostrophic, baroclinic flow is investigated. Period doubling cascades and Shil’nikov bifurcations lead to chaos in this model. The low dimension of the chaotic attractor suggests the possibility to reduce the model to three degrees of freedom. In a physically comprehensible limit of the parameters this...

Under the influences of stable density stratification and Earth’s rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics— sometimes called the slow manifold—in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear Balance Equations are a widely successful, approximate model for th...