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.

Fast Fourier Transform

Natural ventilation of buildings is the flow generated by temperature differences and by the wind. The governing feature of this flow is the exchange between an interior space and the external ambient. Although the wind may often appear to be the dominant driving mechanism, in many circumstances temperature variations play a controlling feature on the ventilation since the directional buoyancy force has a large influence on the flow patterns within the space and on the nature of the exchange with the outside. Two forms of ventilation are discussed: mixing ventilation, in which the interior is at an approximately uniform temperature, and displacement ventilation, where there is strong internal stratification. The dynamics of these buoyancy-driven flows are considered, and the effects of wind on them are examined. The aim behind this work is to give designers rules and intuition on how air moves within a building; the research reveals a fascinating branch of fluid mechanics.

The fluid mechanics of natural ventilation

A quasi-static uncoupled theory of thermoelasticity based on the heat conduction equation with a time-fractional derivative of order α is proposed. Because the heat conduction equation in the case 1≤α≤2 interpolates the parabolic equation (α = 1) and the wave equation (α = 2), the proposed theory interpolates a classical thermoelasticity and a thermoelasticity without energy dissipation introduced by Green and Naghdi. The Caputo fractional derivative is used. The stresses corresponding to the fundamental solutions of a Cauchy problem for the fractional heat conduction equation are found in one-dimensional and two-dimensional cases.

Fractional heat conduction equation and associated thermal stress

In this paper, we study the time-space fractional order (fractional for simplicity) nonlinear subdiffusion and superdiffusion equations, which can relate the matter flux vector to concentration gradient in the general sense, describing, for example, the phenomena of anomalous diffusion, fractional Brownian motion, and so on. The semi-discrete and fully discrete numerical approximations are both analyzed, where the Galerkin finite element method for the space Riemann-Liouville fractional derivative with order 1+@b@?[1,2] and the finite difference scheme for the time Caputo derivative with order @a@?(0,1) (for subdiffusion) and (1,2) (for superdiffusion) are analyzed, respectively. Results on the existence and uniqueness of the weak solutions, the numerical stability, and the error estimates are presented. Numerical examples are included to confirm the theoretical analysis. During our simulations, an interesting diffusion phenomenon of particles is observed, that is, on average, the diffusion velocity for 0<@a<1 is slower than that for @a=1, but the diffusion velocity for 1<@a<2 is faster than that for @a=1. For the spatial diffusion, we have a similar observation.

Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

Elastic mismatching is studied by an impulse technique. Elastic mismatches are created by joining two latex rubber tubes of the same internal diameter but different wall thickness. A short duration pressure impulse is generated at the entrance of the water-filled tube system and the transmission characteristics of the impulse are determined from a series of measurements along the tube system using a catheter-tip pressure manometer. This technique enables the magnitude and phase change of the reflection at the elastic discontinuity to be obtained. A number of tube combinations are examined and in all cases a good agreement is shown between the measured reflection coefficient and the value calculated theoretically.

Reflection from elastic discontinuities

Analogues of arterial stenoses and aneurysms were constructed from latex tubing containing inserts of various lengths, and with diameters and elastic properties that differed from those of the surrounding tube. A pressure impulse (duration <10ms). was generated at one end of the tube and its transmission and reflection were monitored at various points within the system using a catheter-tip manometer. The complex waveforms produced by multiple reflections from either end of the insert were analysed and compared with those generated by a numerical model in which the reflection sites were regarded as isolated junctions between two tubes of infinite length. There was close agreement between the synthesised and measured waveforms.

Impulse propagation in rubber-tube analogues of arterial stenoses and aneurysms.

A theory of wave propagation in liquid filled distensible tubes, which extends the region of validity of the linear long wavelength theory commonly employed in haemodynamics, is presented and tested against experiments on water filled latex tubes. The theory which is linear and involves but a single free parameter provides excellent agreement with the impulse experiments.

Impulse propagation in liquid filled distensible tubes: Theory and experiment for intermediate to long wavelengths

The linear Gurtin-Pipkin theory of heat conduction is invoked to study the problem of an inhomogeneous half space whose boundary is subjected to step inputs of temperature. A ray series approach is employed to reduce the governing integro-differential equation to a set of differential-difference equations which may be solved. Various general properties of the propagation process are derived in a simple and direct fashion and the solution constructed for particular choices of the heat-flux and energy relaxation functions.

On thermal transients with finite wave speeds

A detailed study is presented of cylindrical shear waves in inhomogeneous Maxwellian viscoelastic materials whose parameters depend continuously on a single radial coordinate. A formal asymptotic technique is employed to investigate various impact problems. Rigorous arguments are then used to show that the formal technique gives results that are asymptotic to the exact solution even when boundaries or interfaces are present. Simple termination in the Karal-Keller series is shown to be associated with the Baecklund transformation method.

T. B. Moodie

Papers

Reflection from elastic discontinuities

Impulse propagation in rubber-tube analogues of arterial stenoses and aneurysms.

Impulse propagation in liquid filled distensible tubes: Theory and experiment for intermediate to long wavelengths

On thermal transients with finite wave speeds

Cylindrical impact waves in inhomogeneous viscoelastic media