Appearance Of Multiple States Research Articles

Vortex flows of moist air with non-equilibrium and homogeneous condensation

A small-disturbance model is presented for the complex dynamics of vortex flows of moist air in a straight, circular pipe with non-equilibrium and homogeneous condensation. The model explores the nonlinear interactions among the vortex near-critical swirl ratio and the small amount of water vapour in the air. The condensation rate is calculated according to classical nucleation and droplet growth models. The asymptotic analysis gives the similarity parameters that govern the flow problem. These are the flow inlet swirl ratio , the inlet Mach number , the initial humidity , the number of water molecules in a characteristic fluid element , the inlet centreline super-saturation ratio and the ratio of characteristic condensation and flow time scales . Also, the flow field may be described by an ordinary first-order nonlinear differential equation for the flow evolution coupled with a set of four first-order ordinary differential equations along the pipe for the calculation of the condensate mass fraction. An iterative numerical scheme which combines the Runge–Kutta integration technique for the flow dynamics with Simpson’s integration rule for the calculation of the condensation variables is developed. Specifically, equilibrium states are determined, including the possibility of the appearance of multiple states under the same boundary conditions, and the stability characteristics of these states are described. The model is used to study the effects of humidity and of energy supply from nanoscale condensation processes on the large-scale dynamics of vortex flows as well as the effect of flow swirl on condensation processes in swirling flows.

Two Different Aperiodic Phases of Wind-Driven Ocean Circulation in a Double-Gyre, Two-Layer Shallow-Water Model

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.