The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

We explain the emergence of organised structures in two-dimensional turbulent flows by a theory of equilibrium statistical mechanics. This theory takes into account all the known constants of the motion for the Euler equations. The microscopic states are all the possible vorticity fields, while a macroscopic state is defined as a probability disruption of vorticity at each point of the domain, which describes in a statistical sense the fine-scale vorticity fluctuations. The organised structure appears as a state of maximal entropy, with the constraints of all the constants of the motion. The vorticity field obtained as the local average of this optimal macrostate is a steady solution of the Euler equation. The variational problem provides an explicit relationship between stream function and vorticity, which characterises this steady state. Inertial structures in geophysical fluid dynamics can be predicted, using a generalisation of the theory to potential vorticity.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112091003038

Statistical equilibrium states for two-dimensional flows

Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge

Hydrodynamic and hydromagnetic stability

Laboratory experiments on barotropic vortices in a rotating fluid revealed that the instability behaviour of cyclonic and anticyclonic vortices is remarkably different. Depending on its initial vorticity distribution, the cyclonic vortex has in a number of experiments been observed to be unstable to wavenumber-2 perturbations, leading to the gradual formation of a stable tripolar vortex structure. This tripole consists of an elongated cyclonic core vortex adjoined by two anticyclonic satellite vortices.In contrast, the anticyclonic vortex shows a rather explosive instability behaviour, in the sense that it is observed to immediately split up into two dipoles. Under somewhat different circumstances the higher-order mode-3 instability is observed, in which the anticyclonic core has a triangular shape, with three smaller cyclonic satellite vortices at its sides.A modified version of Rayleigh's instability criterion offers a qualitative explanation for this apparent difference between unstable cyclonic and anticyclonic vortices.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112091001301

An experimental study of unstable barotropic vortices in a rotating fluid

THE emergence of coherent flow structures is a well-known feature of quasi-geostrophic or two-dimensional turbulence, and because of their relevance to large-scale geophysical flows the dynamics of these structures have been studied increasingly over the past decade1–5 The most common coherent structures are the axisymmetric (monopolar) vortex, with circular streamlines, and the vortex dipole, both of which have been found to arise in a variety of situations under different (sometimes nondescript) forcing conditions. The emergence of vortex dipoles, for example, has been observed in turbulence in soap films3, in electrically forced magnetohydrodynamic flows5 and in collapsing turbulence in a continuously stratified fluid6. There is growing evidence4,7–9 that, in addition to the monopolar and dipolar vortices, a tripolar coherent flow structure exists. Here we describe a laboratory experiment in which a tripolar structure is found to emerge from an unstable cyclonic vortex in a homogeneous rotating fluid. The tripole seems to be a very stable structure, even persisting in a highly sheared fluid environment, and might therefore be found in natural geophysical flows.

Tripolar vortices in a rotating fluid

Within the framework of the study of coherent vortex structures as emerging in rotating, quasi-two-dimensional flows, the tripolar vortex is a relatively novel feature. It consists of a symmetric, linear arrangement of three patches of distributed vorticity of alternate signs, and the axis of this configuration rotates about the centre of the core vortex. This paper describes an experimental study of the formation of a tripole from an unstable axisymmetric vortex in a solidly rotating, homogeneous fluid. The flow is visualized by addition of dye, and is measured by streak photography of tracer particles. After digitization, the spatial distributions of the vorticity ω and the stream function ψ are calculated numerically, and 'scatter plots’ of ω versus ψ are presented for the various stages in the tripole formation process. Owing to viscous effects (spin-down by the bottom Ekman layer and lateral entrainment of ambient fluid) the tripole shows an exponential decay, both in its rotation speed and its internal, relative flow. The comparison of the observed flow characteristics with a simple point-vortex model shows reasonable quantitative agreement.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112091002069

Laboratory experiments on the tripolar vortex in a rotating fluid

A small-scale cyclonic vortex in a relatively broad valley tends to climb up and out of the valley in a cyclonic spiral about the centre, and when over a relatively broad hill it tends to climb toward the top in an anticyclonic spiral around the peak. This phenomenon is examined here through two-dimensional numerical simulations and rotating-tank experiments. The basic mechanism involved is shown to be the same as that which accounts for the northwest propagation of cyclones on a β-plane. This inviscid nonlinear effect is also shown to be responsible for the observed translationary motion of barotropic vortices in a free-surface rotating tank. The behaviour of isolated vortices is contrasted with that of vortices with non-vanishing circulation.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112091000411

Propagation of barotropic vortices over topography in a rotating tank

Laboratory observations and numerical simulations reveal that, in addition to monopoles, dipoles and tripoles, yet another stable coherent vortex may emerge from unstable isolated circular vortices. This new vortex is the finite-amplitude result of the growth of an azimuthal wavenumber-3 perturbation. It consists of a triangular core of single-signed vorticity surrounded by three semicircular satellites of oppositely signed vorticity. The stability of this triangular vortex is analysed through a series of high-resolution numerical simulations and by an investigation of point-vortex models. This new compound vortex rotates about its centre and is stable to small perturbations. If perturbed strongly enough, it undergoes an instability in which two of the outer satellites merge, resulting in the formation of an axisymmetric tripole, which subsequently breaks down into either a pair of dipoles or a dipole plus a monopole. The growth of higher-azimuthal-wavenumber perturbations leads to the formation of more intricate compound vortices with cores in the shape of squares, pentagons, etc. However, numerical simulations show that these vortices are unstable, which agrees with results from point-vortex models.

/pdf/emergence-and-evolution-of-triangular-vortices-1t4ehj5nyq.pdf

R. C. Kloosterziel

Papers

An experimental study of unstable barotropic vortices in a rotating fluid

Tripolar vortices in a rotating fluid

Laboratory experiments on the tripolar vortex in a rotating fluid

Propagation of barotropic vortices over topography in a rotating tank

Emergence and evolution of triangular vortices