Abstract

The properties of large amplitude vortices are numerically investigated using a set of two-layer primitive equations. Numerical experiments are systematically conducted for the f and β plants, quasigeostrophic (small amplitude) and frontal-geostrophic (large amplitude) dynamics, cyclone and anticyclone, and vortex sizes comparable to the radius of deformation and larger. In particular, the evolution and migration of frontal-geostrophic vortices are discussed with reference to the evolution equations in a two-layer ocean. It is shown that the anticyclonic vortex with large amplitude displacement evolves differently from the quasigeostrophic vortex and that it is extremely long-lived.

The evolution of anticyclonic vortices, in which interfacial displacement is large and the size is greater than the radius of deformation, is different from that of cyclonic vortices. While the shapes of anticyclonic vortices change from circle to ellipse because of instability, the large amplitude effect of interfacial displacement restores the vortices' shape and causes them to vacillate based on the conservation of potential verticity and angular momentum. On the other hand, while the shapes of cyclonic vortices change from circle to ellipse, the effect makes their shape more slenderly elliptical. The splitting phenomenon of anticyclonic vortices is also different from that with cyclonic vortices. The anticyclonic vortices are robust in their cores, although they divide their marginal part into several vortices. The cores of cyclonic vortices stretch slenderly and split several into vortices whose size is the radius of deformation. The structure of potential vorticity causes this different behavior between cyclonic and anticyclonic vortices due to the large amplitude of interfacial displacement in the vortices.

An upper-ocean vortex generates a tripolar vortex in the lower ocean through baroclinic instability while changing its shape from circular to elliptical on the f plan. Generating a tripolar vortex in the lower ocean, upper-ocean vortex moreover, releases the available potential energy to the lower ocean as Rossby waves on the β plane. The generated vortex in the lower ocean affects the migration of the upper-ocean vortex due to the dispersion of Rossby waves and nonlinear modal coupling. These result show that the two-layer vortex with large amplitude evolves differently from the reduced-gravity vortex. Finally, same arguments are presented to explain the observation of splitting cyclonic eddies and the robustness of large anticyclonic eddies.

Abstract

The properties of a new equation governing the evolution of planetary eddies larger than the radius of deformation are numerically investigated. Two types of dynamical balances showing remarkable solitary behavior are found. The first is the balance between the weak dispersion due to the planetary beta-effect and the weak nonlinearity due to the continuity equation. Only anticyclonic eddies are extremely long-lived due to this balance. The second is the balance between weak lateral advection due to a particular westward flow and weak planetary dispersion. The collision experiment shows robustness of the two-dimensional solitary eddy, suggesting the existence of a two-dimensional soliton of the latter type.

Also discussed is the relevance of our results to the evolution of the anticyclonic eddies off the Pacific coast of Central America reported by Stumpf and Legeckis (1977).

Abstract

A stratified fluid response to barotropic oscillatory now over a large-amplitude obstacle is examined on the basis of the results of laboratory and numerical experiments. It is demonstrated that, when the obstacle height is fixed relative to the water depth (δ), the type of fluid response is dependent on two dimensional parameters, that is, the maximum internal Froude number at the top of the obstacle (Fr _m ) and the oscillatory period normalized to the time interval an internal wave travels over the horizontal length scale of an obstacle (T ^d ).

For the parameter range 0.5 ≤ Fr _m ≤ 1.75 and 1.5 ≤ T ^d ≤ 2.5, a detailed comparison is made between the results of laboratory and numerical experiments and shown to be in very good agreement. First and second mode internal waves are specifically identified over the leeside slope of the obstacle. When the value of Fr _m is greater than one, in particular, internal waves of large amplitude occur because the elementary waves converge at the vicinity of the critical point (where Froude number ∼1), these waves propagate upstream when the flow decreases and eventually reverses. Depending on the value of T ^d they interact with the waves being formed over the other side slope of the obstacle. These observed features are successfully interpreted in terms of the method of characteristics.

Although temporal and spatial scales are quite different between natural and laboratory situation the evolving internal wave field actually observed over Stellwagen Bank in Massachusetts Bay can be well simulated in the present laboratory and numerical experiments where Fr _m ,T ^d and δ are nearly adjusted to correspond to the observed values. This shows that these parameters indeed play a crucial role for the classification of the stratified fluid responses over a large amplitude bottom topography.

Abstract

A two-layer shallow-water model is used to investigate the transition of wind-driven double-gyre circulation from laminar flow to turbulence as the Reynolds number (Re) is systematically increased. Two distinctly different phases of turbulent double-gyre patterns and energy trajectories are exhibited before and after at Re = 95: deterministic and fully developed turbulent circulations. In the former phase, the inertial subgyres vary between an asymmetric solution and an antisymmetric solution and the double-gyre circulations reach the aperiodic solution mainly due to their barotropic instability. An integrated kinetic energy in the lower layer is slight and the generated mesoscale eddies are confined in the upper layer. The power spectrum of energies integrated over the whole domain at Re = 70 has peaks at the interannual periods (4–7 yr) and the interdecadal period (10–20 yr). The loops of the attractors take on one cycle at those periods and display the blue-sky catastrophe. At Re = 95, the double-gyre circulation reaches a metastable state and the attracters obtained from the three energies form a topological manifold. In the latter, as Re increases, the double-gyre varies from a metastable state to a chaotic state because of the barotropic instability of the eastward jet and the baroclinic instability of recirculation retrograde flow, and the eastward jet meanders significantly with interdecadal variability. The generated eddies cascade to the red side of the power spectrum as expected in the geostrophic turbulence. The main results in the simulation may indicate essential mechanisms for the appearance of multiple states of the Kuroshio and for low-frequency variations in the midlatitude ocean.

Abstract

In an oceanic double-gyre system, nonlinear oscillations of the ocean under seasonally changing external forcing are investigated using a 1.5-layer quasigeostrophic model and a simple model related to energy balance of the oceanic double gyre. In the experiments, the variable parameter is the amplitude of external seasonal forcing and the Reynolds number is fixed as 39, at which periodic shedding of inertial subgyres occurs. The authors found that entrainment (at 2 times the period of the forcing) and intermittency (on–off type), phenomena that are often seen in nonlinear systems, emerge with increasing amplitude of the forcing. They seem to be related to the generation mechanism and characteristics of long-term (from interannual to decadal) variations in the strong current region of subtropical gyres such as the Kuroshio and its extension region.