羟氨苄青霉素引起大疱性类天疱疮样疹

Atmospheric and Oceanic Fluid Dynamics

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.

Fluid dynamics is fundamental to our understanding of the atmosphere and oceans. Although many of the same principles of fluid dynamics apply to both the atmosphere and oceans, textbooks tend to concentrate on the atmosphere, the ocean, or the theory of geophysical fluid dynamics (GFD). This textbook provides a comprehensive unified treatment of atmospheric and oceanic fluid dynamics. The book introduces the fundamentals of geophysical fluid dynamics, including rotation and stratification, vorticity and potential vorticity, and scaling and approximations. It discusses baroclinic and barotropic instabilities, wave-mean flow interactions and turbulence, and the general circulation of the atmosphere and ocean. Student problems and exercises are included at the end of each chapter. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation will be an invaluable graduate textbook on advanced courses in GFD, meteorology, atmospheric science and oceanography, and an excellent review volume for researchers. Additional resources are available at www.cambridge.org/9780521849692.

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Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation

A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competing methods of implicit-explicit differencing, integrating factors, time-splitting, and Fornberg and Driscoll's "sliders" for the KdV, Kuramoto--Sivashinsky, Burgers, and Allen--Cahn equations in one space dimension. Implementation of the method is illustrated by short MATLAB programs for two of the equations. It is found that for these applications with fixed time steps, the modified ETD scheme is the best.

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Fourth-Order Time-Stepping for Stiff PDEs

Forced turbulence in a rotating frame is studied using numerical simulations in a triply periodic box. The random forcing is three dimensional and localized about an intermediate wavenumber kf. The results show that energy is transferred to scales larger than the forcing scale when the rotation rate is large enough. The scaling of the energy spectrum approaches E(k)∝k−3 for k<kf. Almost all of the energy for k<kf lies in the two-dimensional (2D) plane perpendicular to the rotation z-axis, and thus the large-scale motions are quasi-2D with E(k)≈E(kh,kz=0), where kh and kz are, respectively, the horizontal and vertical components of the wavevector. The large scales consist of cyclonic vortices. Possible mechanisms responsible for the two-dimensionalization are discussed. The development of the 2D spectrum E(kh,kz=0)∝kh−3 is analogous to the dynamics of β-plane turbulence leading to the Rhines spectrum E(ky,kx=0)∝ky−5.

Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence

Numerical simulations are used to study homogeneous, forced turbulence in three-dimensional rotating, stably stratified flow in the Boussinesq approximation, where the rotation axis and gravity are both in the zˆ-direction. Energy is injected through a three-dimensional isotropic white-noise forcing localized at small scales. The parameter range studied corresponds to Froude numbers smaller than an O(1) critical value, below which energy is transferred to scales larger than the forcing scales. The values of the ratio N/f range from ≈1/2 to ∞, where N is the Brunt–Vaisala frequency and f is twice the rotation rate. For strongly stratified flows (N/f[Gt ]1), the slow large scales generated by the fast small-scale forcing consist of vertically sheared horizontal flow. Quasi-geostrophic dynamics dominate, at large scales, only when 1/2 [les ] N/f [les ] 2, which is the range where resonant triad interactions cannot occur.

Generation of slow large scales in forced rotating stratified turbulence

Forced rotating turbulence is simulated within a periodic box of small aspect ratio. Critical parameter values are found for the stability of a 2D inverse cascade of energy in the presence of 3D motions at small scales. There is a critical rotation rate below which 2D forcing leads to an equilibrated 3D state, while for a slightly larger rotation rate, 3D forcing drives a 2D inverse cascade. It is shown that inverse and forward cascades of energy can coexist. This study is relevant to geophysical flows, and contains physics beyond the scope of quasigeostrophic models.

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Crossover from Two- to Three-Dimensional Turbulence.

Numerical simulations are used to study a series of reduced models of homogeneous, rotating flow at moderate Rossby numbers Ro 0.1, for which both numerical and physical experiments show the generation of quasi-two-dimensional vortices and symmetry breaking in favour of cyclones. A random force at intermediate scales injects energy at a constant average rate. The nonlinear term of reduced models is restricted to include only a subset of triad interactions in Fourier space. Reduced models of near-resonant, non-resonant and near two-dimensional triad interactions are considered. Only the model of near resonances reproduces all of the important characteristics of the full simulations: (i) efficient energy transfer from three-dimensional forced modes to two-dimensional large-scale modes, (ii) large-scale energy spectra scaling approximately as k -3 h , where k h is the wavenumber in the plane perpendicular to the axis of rotation, and (iii) strong cyclone/anticyclone asymmetry in favour of cyclones. Non-resonances, defined as the complement to near resonances, act to reduce the energy transfer to large scales.

On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number

Steady but generally unstable solutions of the 2D Boussinesq equations are obtained for no-slip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number Ra ≈ 1708 has been calculated up to Ra ≈ 5.106 and its Nusselt number is Nu ∼ 0.143 Ra0.28 with a delicate spiral structure in the temperature field. Another solution that maximizes Nu over the horizontal wavenumber has been calculated up to Ra = 109 and scales as Nu ∼ 0.115 Ra0.31 for 107 < Ra ≤ 109, quite similar to 3D turbulent data that show Nu ∼ 0.105 Ra0.31 in that range. The optimum solution is a simple yet multi-scale coherent solution whose horizontal wavenumber scales as 0.133 Ra0.217. That solution is unstable to larger scale perturbations and in particular to mean shear flows, yet it appears to be relevant as a backbone for turbulent solutions, possibly setting the scale, strength, and spacing of elemental plumes.

Leslie M. Smith

Papers

Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence

Generation of slow large scales in forced rotating stratified turbulence

Crossover from Two- to Three-Dimensional Turbulence.

On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number

Heat transport by coherent Rayleigh-Bénard convection