Dynamics of the Coastal Transition Zone jet: 2. Nonlinear finite amplitude behavior
Authors: Allen J. S. , Walstad Leonard J. , Newberger P. A. 
Published: February 2008

The finite amplitude nonlinear behavior of the coastal transition zone (CTZ) jet, assumed to be governed by quasi‐geostrophic dynamics, is studied utilizing numerical experiments in an idealized geometry. Finite difference solutions to initial value problems are obtained for a stratified, six‐layer fluid in a periodic, flat bottom, ƒ plane channel. The initial flow field in all experiments includes a uniform along‐channel jet with horizontal and vertical structure obtained from CTZ hydrographic and current measurements made in May 1987. The maximum velocity in the jet is about 0.5 m s−1, the vertical shear is such that the velocities below 500 m depth are small, and the jet width is about 60 km. The Rossby radius for the first baroclinic mode is 24.6 km. An analysis of the linear stability of the jet flow field in part 1 shows that the jet is linearly unstable to disturbances with along‐jet wavelengths greater than 50 km. The largest growth rate is found for a wavelength around 260 km. The objectives here are to find the characteristics of the finite amplitude nonlinear jet instabilities and to examine local dynamical balances for signatures of instability processes that would help with the physical interpretation of results from limited‐area CTZ data assimilation models. Experiments are run with periodic channels of different length L(x), where the initial flow includes the basic jet and a small perturbation in the form of the most unstable linear mode for a wavelength equal L(x). In the basic experiment (BC) L(x) = 250 km. One experiment (LC) is run in a long channel L(x) = 1280 km with initial disturbances forced by application of a weak wind stress curl for three days. For times less than about 70 days, experiments BC and LC show the growth and development of finite amplitude meanders in the CTZ jet with spatial variations similar to those observed in spring 1987. During this early time period, the amplitudes of the meanders grow at rates of 1–4 km d−1, increasing with meander amplitude, and the meanders propagate in the direction of the jet upper layer flow at phase velocities of 5–3 km d−1, decreasing with meander amplitude. Initially, at small amplitudes the instability involves comparable contributions from barotropic and baroclinic processes in agreement with linear theory, but for large amplitude meanders the baroclinic energy conversion processes dominate. The vertical velocity field develops a characteristic spatial structure in relation to the jet meanders as do terms in the kinetic energy balance corresponding to the time rate of change of kinetic energy following fluid particles and to the rate of conversion from potential energy. The spatial structure of the latter field may provide a useful indication for jet baroclinic instability processes in limited‐area models. At later times in experiment BC (days 90–110), the meander growth is limited by a pinching‐off process that results in the formation of detached eddies on both sides of the jet. This process is characterized by a large relative increase of the kinetic energy in the lower layers and in the depth‐independent component of the flow. Experiments with L(x) = 180 and 150 km give qualitatively different behavior than that found in experiments BC and LC. The meander growth is bounded, and the jet flow field exhibits time‐dependent variations in the volume integrated kinetic and potential energies. For large time the flow may asymptotically approach a nearly steady state or states with irregular or nearly periodic oscillations in the integrated kinetic and potential energies.