Geophysical Fluid Dynamics Models Research Articles

On grid generation for numerical models of geophysical fluid dynamics

A simple geometric condition that defines the class of classical (stereographic, conic and cylindrical) conformal mappings from a sphere onto a plane is derived. The problem of optimization of computational grid for spherical domains is solved in an entire class of conformal mappings on spherical (geodesic) disk. The characteristics of computational grids of classical mappings are compared for different spherical radii of geodesic disk. For a rectangular computational domain, the optimization problem is solved in the class of classical mappings and respective area of the spherical domain is evaluated.

Numerical solution of the reaction–advection–diffusion equation on the sphere

A finite volume algorithm for the solution of the reaction–advection–diffusion equation on the sphere is derived and evaluated using analytical solutions. The proposed approach is based on the principle of semidiscretization. The convective and diffusive fluxes are approximated first, and then the resulting set of the ordinary differential equations (ODEs) is solved using the appropriate time stepping algorithm. In the first part of the paper, solutions to both the linear advection and the advection–diffusion problems for a single conservative scalar are discussed. The monotonicity of the scheme is achieved with the explicit adaptive dissipation. The development as well as the selected applications of the method are illustrated using a finite volume mesh constructed on the basis of geodesic icosahedral grid, which, in the past 40 years, has been frequently applied in different models of geophysical fluid dynamics. The performance of the solver is assessed using a suite of standard tests based on solid body rotation for different initial conditions. After analysis of the advection–diffusion problem, the extension of the method for the equations with reactive terms is presented. The performance of the solver is assessed by comparing the results to the analytical solution of the linearized reaction–diffusion system. In the final part of the paper, the application of the solver for studies of nonlinear reactions on the sphere is illustrated. The main intended application of the proposed method includes the simulation of transport of chemical constituents in the Earth’s atmosphere as well as the forecasting of moisture and cloud water fields in numerical weather prediction and climate models.

Nonlinear phase of the compressional m=1 diocotron instability: Saturation and analogy with geophysical fluid dynamics

The nonlinear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column, is studied. A new cylindrical particle-in-cell code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a number of tests. The code is then used to compare the dynamics of three different models: the standard Euler or drift-Poisson model, the modified drift-Poisson model [J. Finn et al. Phys. Plasmas 6, 3744 (1999); Phys. Rev. Lett. 84, 2401 (2000)] with compressional effects, and the quasigeostrophic model of geophysical fluid dynamics in the limit of the γ-plane approximation. The results of this investigation show that Penning traps can be used to simulate geophysical fluids. Moreover, the results for the m=1 diocotron instability reproduce qualitatively the experiments [C. F. Driscoll, Phy. Rev. Lett. 64, 645 (1990); C. F. Driscoll et al. Phys. Fluids B 2, 1359 (1990)]: The instability turns the plasma “inside-out” resulting at the end in a stable, monotonic profile.

Water vapor as an active scalar in tropical atmospheric dynamics.

Water vapor is a constituent of the tropical atmosphere which, though to a significant extent locally controlled by vertical advection, precipitation, and surface evaporation, is also affected by horizontal advection. Water vapor affects the flow in turn, because a humid atmosphere supports deep, precipitating convection more readily than a dry atmosphere. Precipitation heats the atmosphere, and this heating drives the flow. Water vapor is thus a dynamically active constituent. Simplifications to the primitive equations of dynamical meteorology, based on the so-called weak temperature gradient approximation, are presented which highlight this behavior. The weak temperature gradient approximation is valid on large scales near the equator. It eliminates gravity waves, leaving only balanced dynamics, though the fundamental balance occurs in the temperature rather than the momentum equation (as is customary in most balance models of geophysical fluid dynamics). The dynamical role of water vapor is examined in a couple of idealized contexts, where either the vertical or horizontal structure of the flow is severely simplified. (c) 2002 American Institute of Physics.

Dissipation in Lie–Poisson systems and the Lorenz-84 model

The relation between dissipation and the symplectic structure of the momentum-space is studied in so(3) Lie algebra and in 2D fluid dynamics. Three kinds of dissipative mechanisms are discussed and a general bracket formalism is introduced. A chaotic dynamical system due to Lorenz, and largely studied in low-dimensional models of geophysical fluid dynamics, is analysed in its geometric and dynamical features, by means of the formalism previously introduced. A mechanism of energy transfer for this low-order model is discussed.

Multipetal vortex structures in two-dimensional models of geophysical fluid dynamics and plasma

A new class of strongly nonlinear steadily rotating vortices is found. The Hamiltonian contour dynamics is proposed as a new approach for their study in some models of geophysical fluid dynamics and plasma. Using the Euler description as a starting point, we present a systematic procedure to reduce the two-dimensional dynamics of constant-vorticity and constant-density patches to the Hamiltonian dynamics of their contours for various parametrizations of the contour. The special Dirac procedure is used to eliminate the constraints arising in the Hamiltonian formulations with the Lagrangian parametrization of the contour. Numerical estimations illustrating the physical significance of the results and the range of model parameters where these results can be applicable are presented. Possible generalizations of the approach based on the application of the Hamiltonian contour dynamics to nonplanar and 3D flows are discussed.

A unified view of Kolmogorov and Lorenz systems

The discussion on the relation between the Kolmogorov system, considered as low-order approximation of Navier–Stokes equations, and the well-known Lorenz equations is still not completely understood. In this Letter, referring to the mathematical theory of motion on Lie groups, a particular class of Kolmogorov systems, largely studied in low-dimensional models of geophysical fluid dynamics, is extended and analysed in its geometric and dynamical features. The dynamical behaviour of this extended and unifying system generally shows chaos, contrarily to the original Kolmogorov one, and actually two well known Lorenz models, useful as toy-models in geophysical fluid dynamics, are included in it.

Jetlet Formation from Diabatic Forcing with Applications to the 1994 Palm Sunday Tornado Outbreak

Abstract The three-dimensional responses of simple stably stratified barotropic and baroclinic flows to prescribed diabatic forcing are investigated using a dry, hydrostatic, primitive equation numerical model (the North Carolina State University Geophysical Fluid Dynamics Model). A time-dependent diabatic forcing is utilized to isolate the effects of latent heat release in a midlatitude convective system. Examination of the mass-momentum adjustments to the diabatic forcing is performed with a focus on the development of an isolated midlevel wind maximum. The results of both cases suggest the formation of a midlevel wind maximum in the form of a perturbation meso-β-scale cyclone, which later propagates downstream as the heating is decreased. The scale of the perturbation cyclone remains at a sub-Rossby radius of deformation length scale. Therefore, the mass perturbations adjust to the wind perturbations as the mesocyclone propagates downstream. Transverse vertical circulations, which favor ascent on the r...

The Cauchy Problem and the Continuous Limit for the Multilayer Model in Geophysical Fluid Dynamics

We study a multilayer model in geophysical fluid dynamics that approximately governs the large-scale motions of the atmosphere or the ocean. The model consists of n two-dimensional Euler equations which represent the evolution of n layers of liquid. These equations are written using the potential vorticity. The potential vorticity in each layer is obtained from the velocity potential of the adjacent layers. We show that the Cauchy problem for this model is globally well-posed in time for smooth initial data. In the second part of the paper, we let the number of layers tend to infinity while their thickness tends to zero. We write the system as a suitable finite-element approximation of a continuous model and show the convergence of this approximation to the classical quasi-geostrophic model.

Formulations of Lateral Diffusion in Geophysical Fluid Dynamics Models

ABSTRACT We discuss several approaches to the problem of lateral diffusion in geophysical fluid dynamics models. It is shown that the diffusion model should include, in addition to the usual linear or nonlinear formulation involving deformations or iterated Laplacians, a gradient-of-divergence term representing sub-grid scale dynamic pressure effects related to interactions between vortical modes and inertia-gravity modes. General forms of the former terms, valid in particular for stretched-coordinate models, are also presented, as well as primitive equation formulations of the Anticipated Potential Vorticity Method, in entropy or other vertical coordinates.

On discontinuous periodic solution and discontinuous solitary wave of two-dimension shallow water equation

In this paper we discuss discontinuous periodic solution and discontinuous solitary wave of the shallow water model of geophysical fluid dynamics. When we consider the properties of trajectory near non-equilibrium point, i.e. singular point, we find that if we introduce the concept of generalized solution (piecewise smoothing continuous solution), then the system will produce discontinues periodic solution and the condition of discontinuous periodic solution can he obtained. When the system is degenerated, we find that the discontinuous solitary wave is existent in the system. In this paper we consider a series of problems and obtain analytic expression of discontinuous solution. This result is compared with squall line in the atmosphere, and both of them have many things in common.

The domain of validity of the KdV-type solitary rossby waves in the shallow water β-plane model

Abstract The Domain, where the necessary and sufficient conditions for the existence of the KdV-type solitary Rossby waves are satisfied is defined in the shallow water β-plane model. The KdV-type solitary Rossby waves are the Rossby waves whose time-longitude dependence is determined by the KdV equation. As far as an appropriate amplitude and an appropriate ratio of the scales of the east-west and north-south directions are given, the KdV-type solitary Rossby waves can exist for every basic zonal flow. This result suggests the large validity of the soliton model in geophysical fluid dynamics. The KdV-type solitary Rossby waves are classified into four categories: (1) shear solitons studied by Long, Larsen, Benny, Redekop, and Hukuda, (2) β-divergent solitons studied by Clarke, Yamagata, and Nogami, (3) β-solitons found in the case of the strong stratification, and (4) divergent solitons which exist in the planetary-geostrophic-scale zonal flow. A remarkable result is that, in addition to the conventional east-west elongated solitons, the north-south elongated solitons can also exist for the case of the divergent solitons.