Stirring and mixing in two-dimensional divergent flow

While stirring and mixing properties in the stratosphere are reasonably well understood in the context of balanced (slow) dynamics, as is evidenced in numerous studies of chaotic advection, the strongly enhanced presence of high-frequency gravity waves in the mesosphere gives rise to a significant unbalanced (fast) component to the flow. The present investigation analyses result from two idealized shallow-water numerical simulations representative of stratospheric and mesospheric dynamics on a quasi-horizontal isentropic surface. A generalization of the Hua–Klein Eulerian diagnostic to divergent flow reveals that velocity gradients are strongly influenced by the unbalanced component of the flow. The Lagrangian diagnostic of patchiness nevertheless demonstrates the persistence of coherent features in the zonal component of the flow, in contrast to the destruction of coherent features in the meridional component. Single-particle statistics demonstrate t2 scaling for both the stratospheric and mesospheric regimes in the case of zonal dispersion, and distinctive scaling laws for the two regimes in the case of meridional dispersion. This is in contrast to two-particle statistics, which in the mesospheric (unbalanced) regime demonstrate a more rapid approach to Richardson’s t3 law in the case of zonal dispersion and is evidence of enhanced meridional dispersion.

Flow-dependent predictability of the North Atlantic Jet

The North Atlantic eddy-driven jet is a major component of the large-scale flow in the northern hemisphere. Here we present evidence from reanalysis and ensemble forecast data for systematic flow-dependent predictability of the jet during northern hemisphere winter (DJF). It is found that when the jet is weakened or split it is both less persistent and less predictable. The lack of predictability manifests itself as the onset of an anomalously large instantaneous rate of spread of ensemble forecast members as the jet becomes weakened. This suggests that as the jet weakens or splits it enters into a state more sensitive to small differences between ensemble forecast members, rather like the sensitive region between the wings of the Lorenz attractor.

Effect of earthworm Eisenia fetida and wetland plants on nitrification and denitrification potentials in vertical flow constructed wetland.

The response of nitrification potentials, denitrification potentials, and N removal efficiency to the introduction of earthworms and wetland plants in a vertical flow constructed wetland system was investigated. Addition of earthworms increased nitrification and denitrification potentials of substrate in non-vegetated constructed wetland by 236% and 8%, respectively; it increased nitrification and denitrification potentials in rhizosphere in vegetated constructed wetland (Phragmites austrail, Typha augustifolia and Canna indica), 105% and 5%, 187% and 12%, and 268% and 15% respectively. Denitrification potentials in rhizosphere of three wetland plants were not significantly different, but nitrification potentials in rhizosphere followed the order of C. indica > T. augustifolia > P. australis when addition of earthworms into constructed wetland. Addition of earthworms to the vegetated constructed significantly increased the total number of bacteria and fungi of substrates (P < 0.05). The total number of bacteria was significantly correlated with nitrification potentials (r = 913, P < 0.01) and denitrification potentials (r = 840, P < 0.01), respectively. The N concentration of stems and leaves of C. indica were significantly higher in the constructed wetland with earthworms (P < 0.05). Earthworms had greater impact on nitrification potentials than denitrification potentials. The removal efficiency of N was improved via stimulated nitrification potentials by earthworms and higher N uptake by wetland plants.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.