Search Results (4)

In this paper, the propagation of Rossby waves under barotropic-baroclinic interaction in polar co-ordinates is studied. By starting from the two-layer quasi-geotropic potential vorticity equation (of equal depth) with the $\beta$ effect, the coupled KdV equations describing barotropic-baroclinic waves are derived using multi-scale analysis and the perturbation expansion method. Furthermore, in order to more accurately describe the propagation characteristics of barotropic-baroclinic waves, fifth-order coupled KdV-mKdV equations were obtained for the first time. On this basis, the Lie symmetry and conservation laws of the fifth-order coupled KdV-mKdV equations are analyzed in terms of their properties. Then, the elliptic function expansion method is applied to find the soliton solutions of the fifth-order coupled KdV-mKdV equations. Based on the solutions, we further simulate the evolution of Rossby wave amplitudes and investigate the influence of the high-order terms—time and wave number—on the propagation of barotropic waves and baroclinic waves. The results show that the appearance of the higher-order effect makes the amplitude of the wave lower, the width of the wave larger, and the whole wave flatter, which is obviously closer to actual Rossby wave propagation. The time and wave number will also influence wave amplitude and wave width. Full article

Turbulence is a dominant feature of atmospheric motions. Despite its chaotic nature, it is observed to create and maintain coherent structures such as zonal jets and large-scale waves in the atmosphere. Previous studies on the self-organization of turbulence in a baroclinic two-layered fluid have shown that large-scale coherent structures emerge out of a homogeneous turbulent field through a collective type of instability with a preference for barotropic flows. That is, the barotropic coherent structures reorganize the turbulence in such a way as to reinforce themselves through a positive feedback and emerge in the flow. In this work, a statistical framework (S3T) is utilized in order to study the vorticity and thermal flux feedbacks underlying this instability. It is found that the feedbacks produced by the organization of incoherent barotropic and baroclinic eddies by the coherent emergent structures differ. For large stratification, the feedback that results from the organization of barotropic eddies by baroclinic coherent structures is negative and completely cancels out the positive feedback produced by the organization of the baroclinic eddies. On the contrary, the feedback resulting from the organization of the barotropic and the baroclinic turbulent eddies by the barotropic coherent structures do not cancel each other for most scales and lead to the emergence of these structures in the flow. The spatial features of the emerging coherent structures depend on the value of the non-dimensional planetary vorticity gradient. For small values of the gradient, the maximum value of the feedback is found for zonal jets, while for large values of the gradient, the maximum value of the feedback is found for Rossby waves. Full article

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler equations, as well as the quasi-geostrophic equations for either single-layer or two-layer flows. Optimal closure refers to a general method of reduction for Hamiltonian systems, in which macroscopic states are required to belong to a parametric family of distributions on phase space. In the case of point vortex ensembles, the macroscopic variables describe the spatially coarse-grained vorticity. Dynamical closure in terms of those macrostates is obtained by optimizing over paths in the parameter space of the reduced model subject to the constraints imposed by conserved quantities. This optimization minimizes a cost functional that quantifies the rate of information loss due to model reduction, meaning that an optimal path represents a macroscopic evolution that is most compatible with the microscopic dynamics in an information-theoretic sense. A near-equilibrium linearization of this method is used to derive dissipative equations for the low-order spatial moments of ensembles of point vortices in the plane. These severely reduced models describe the late-stage evolution of isolated coherent structures in two-dimensional and geostrophic turbulence. For single-layer dynamics, they approximate the relaxation of initially distorted structures toward axisymmetric equilibrium states. For two-layer dynamics, they predict the rate of energy transfer in baroclinically perturbed structures returning to stable barotropic states. Comparisons against direct numerical simulations of the fully-resolved many-vortex dynamics validate the predictive capacity of these reduced models. Full article

Estuarine navigation channels have long been recognized as conduits for saltwater intrusion into coastal wetlands. Salt flux decomposition and time series measurements of velocity and salinity were used to examine salt flux components and drivers of baroclinic and barotropic exchange in the Houma Navigation Channel, an estuarine channel located in the Mississippi River delta plain that receives substantial freshwater inputs from the Mississippi-Atchafalaya River system at its inland extent. Two modes of vertical current structure were identified from the time series data. The first mode, accounting for 90% of the total flow field variability, strongly resembled a barotropic current structure and was coherent with alongshelf wind stress over the coastal Gulf of Mexico. The second mode was indicative of gravitational circulation and was linked to variability in tidal stirring and the horizontal salinity gradient along the channel’s length. Tidal oscillatory salt flux was more important than gravitational circulation in transporting salt upestuary, except over equatorial phases of the fortnightly tidal cycle during times when river inflows were minimal. During all tidal cycles sampled, the advective flux, driven by a combination of freshwater discharge and wind-driven changes in storage, was the dominant transport term, and net flux of salt was always out of the estuary. These findings indicate that although human-made channels can effectively facilitate inland intrusion of saline water, this intrusion can be minimized or even reversed when they are subject to significant freshwater inputs. Full article