In an earlier paper (Smith, 1977) it is shown that when viscous effects are important only on a time scale much longer than that for incipient wave growth, the amplitude evolution of a marginally unstable baroclinic wave in a two-layer, quasi-geostrophic zonal flow is governed by an infinite system of ordinary differential equations. These equations have a steady solution which under certain conditions is unstable with respect to small perturbations in wave amplitude. In the case where viscous effects are nonzero but are exceedingly small, the asymptotic analysis in Smith (1977) shows that a stable limit cycle solution is also possible and when the steady solution is unstable, an initially incipient wave evolves toward the limit cycle, which represents an amplitude vacillation of the wave. In this paper, some numerical integrations of the amplitude equations are presented for the case of moderate viscosity. These are compared with solutions obtained from the amplitude equations derived by Pedlosky (1971) in a theory which omits a certain boundary condition an the mean zonal flow (Smith, 1974). Although the two sets of amplitude equations differ considerably, our results confirm the important prediction of Pedlosky that for sufficiently small viscosity and/or if the steady solution is unstable, an incipient wave evolves to a state in which its amplitude undergoes regular pulsations, or vacillations, described by a stable limit cycle solution. However, the parameter range for which the steady solution is unstable is widely different in the two analyses, except for vanishingly small viscosity.
An improved version of a minimal model for a tropical cyclone is described. The model is used to revisit some fundamental aspects of vortex behaviour in the prototype problem for tropical cyclone intensification. After rapidly intensifying to a mature phase in which the maximum tangential wind speed remains quasi‐steady for a few days, the vortex ultimately decays. In a 20‐day simulation, the vortex never becomes globally steady. In particular, the upper anticyclone continues to expand for the duration of the integration. These results are consistent with those of recent studies using more sophisticated numerical models. As in the latter models, an important feature of the dynamics of spin‐up is the development of supergradient winds in the boundary layer and the vertical advection of the associated high tangential‐momentum air from the boundary layer to spin up the eyewall region. This mechanism, while consistent with some recently reported results, is not part of the classical theory of spin‐up.
The development of regenerative medicine has opened up many new therapeutic avenues in veterinary medicine. The focus of regenerative medicine in the horse lies primarily in the musculoskeletal system, where the consequences of injury make tendons, ligaments and joints particularly desirable targets for such interventions. This article focuses on what has been learned from the use of regenerative medicine in naturally-occurring tendon, ligament and joint disease in the horse.
Abstract Two methods for solving the Eliassen equation for the corresponding balanced secondary circulation of a numerically simulated, high‐resolution tropical cyclone vortex are compared. In idealized calculations for a symmetrically stable vortex, both methods (successive overrelaxation [SOR] and multigrid) converge and the solutions are broadly similar. In more typical cases, where the vortex has regions of inertial or symmetric instability, it is necessary to coarsen the data from the numerical simulation to determine the balanced secondary circulation. A convergent solution can be obtained with the multigrid method for a finer grid spacing than with the SOR method. However, the multigrid method fails to converge when the vertical grid spacing is similar to that of the numerical simulation. Results using both methods confirm the inability of the balance formulation to capture the strong inflow and resulting tangential wind spin‐up in the frictional boundary layer during a period of rapid intensification. Typical tropical cyclone simulations show an inflow layer just beneath the upper‐level outflow layer, and the corresponding balanced secondary circulation may show such an inflow layer also. However, caution is called for in attributing this inflow layer to a balanced flow response driven by the distribution of diabatic heating and tangential momentum forcing. Our study suggests that this inflow layer is likely an artifact of the ad hoc regularization procedure that is necessary to keep the Eliassen equation globally elliptic in regions of inertial and/or symmetric instability.
Abstract Observational data are presented on southerly nocturnal wind surges, which sometimes give rise to spectacular “morning glory”-type roll clouds in the southern part of the Gulf of Carpentaria region of northern Australia. Like their more frequent northeasterly counterparts in the region, southerly surges are shown to have the character of an undular bore propagating on the nocturnal low-level stable layer. Synoptic mean sea level pressure patterns conducive to the formation of southerly surges are identified and possible mechanisms for the genesis of surges are discussed. The possibility that some southerly surges are generated by the movement of a front across central Australia, as suggested by Smith et al., does not appear to be the most usual generation mechanism. In fact, an analysis of time-height cross sections of velocity components derived from six hourly rawinsoundings from Mount Isa point to a strong association between the occurrence of southerly surges and the formation of the nocturna...
Abstract Solutions of the partial differential equation ψ zzzz + ψ x + 0 of the type ψ = x ¼n w(y), where y = zx −¼ and n is an integer, are investigated. The equation occurs as a boundary-layer approximation in certain rotating and stratified fluid flows in which the production of vorticity (due, for example, to changes in the Coriolis parameter with latitude in two-dimensional flows on a beta plane, or by the buoyant generation of vorticity in a Boussinesq fluid) is opposed by a diffusive process. The similarity functions w(y) satisfy the fourth order differential equation . These functions have many properties analogous to those of error functions and parabolic cylinder functions. When n is a non-negative integer, there exist polynomial solutions of the latter equation. These have analogies with Hermite polynomials, although they do not form an orthogonal set in any useful sense. The main properties of the similarity functions are listed, including their series expansions, integral representations, asymptotic expansions and recurrence relations. In particular, a pair of independent solutions, Jo n (y) and Ko n (y), are denned such that Jo n (y) and Ko n (y) are real for real y and vanish at an exponential rate as y → + ∞. The function Jo n (y) also decays exponentially as y → − ∞ if n is negative, and grows algebraically as y → − ∞ if n is positive. Curves of the functions Jo n (y) and Ko n (y) are given for |n| ≤ 3 and 0 < y < 6, and their more useful properties are listed.
Optimal management of tendon overuse injuries in equine and human athletes should avoid the formation of excessive scar tissue, regenerate normal tendon matrix, and reduce re-injury rates. We hypothesized that the implantation of marrow-derived stromal stem cells (BM-MSCs), in far greater numbers than are present normally within tendon tissue, would synthesize a matrix more closely resembling tendon matrix than scar tissue, and hence increase the capacity to return to performance successfully. This article reviews the technique used clinically in the horse and the current outcome data for horses treated by the autologous implantation of BM-MSCs into moderate to severe acute superficial digital flexor tendon (SDFT) injuries. Bone marrow was aspirated from the sternum under standing sedation. The nucleated adherent cell population (containing the BM-MSCs) were isolated and expanded so that, after approximately three weeks, the cells were re-suspended in the supernatant from the bone marrow and implanted into injured SDFT under ultrasonographic guidance. The horses then entered a 48-week rehabilitation period consisting of an ascending exercise regime. By September 2006, 168 racehorses had undergone this regimen. For horses which had returned to full work, 18% had re-injured, which compared favourably to previous studies on conventional management (56% re-injury rate). No adverse effects were noted other than needle tracts visible ultrasonographically. Autologous implantation of mesenchymal stem cells into tendon injuries may therefore improve clinical outcome although definitive proof of efficacy, which is still lacking, will require randomized controlled trials.
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