A weak formulation of Roe's approximate Riemann Solver applied to 'Barotropic' flows

A weak formulation of Roe's approximate Riemann solver is applied to the equations of ‘barotropic’ flow, including the shallow water equations, and it is shown that this leads to an approximate Riemann solver recently presented for such flows.

Remarks concerning the double cascade as a necessary mechanism for the instability of steady equivalent-barotropic flows

n a recent paper, Petroniet al. claim that a necessary condition for the instability of two-dimensional steady flows is a «double cascade» of energy and enstrophy respectively to larger and to smaller scales of motion. It is shown here that the analytical reasoning employed by Petroniet al. is flawed and that their conclusions are incorrect. What is true is that in any scale interaction (whether an instability or not), neither energy nor enstrophy can be transferred in one spectral direction only, but this result is extremely well known.

Wave transformation and wave-driven flow across a steep coral reef

Observations of waves, setup, and wave-driven mean flows were made on a steep coral forereef and its associated lagoonal system on the north shore of Moorea, French Polynesia. Despite the steep and complex geometry of the forereef, and wave amplitudes that are nearly equal to the mean water depth, linear wave theory showed very good agreement with data. Measurements across the reef illustrate the importance of including both wave transport (owing to Stokes drift), as well as the Eulerian mean transport when computing the fluxes over the reef. Finally, the observed setup closely follows the theoretical relationship derived from classic radiation stress theory, although the two parameters that appear in the model-one reflecting wave breaking, the other the effective depth over the reef crest-must be chosen to match theory to data. © 2013 American Meteorological Society.

Calibration and validation of hydrodynamic, salt and heat transport models for Ria de Aveiro lagoon (Portugal)

Ria deAveiro is a very complex shallow water coastal lagoon located on the northwest of Portugal. Important issues would be left unanswered without a good understanding of hydrodynamic and transport processes occurring in the lagoon. Calibration and validation of hydrodynamic, salt and heat transport models for Ria de Aveiro lagoon are presented. The calibration of the hydrodynamic model was performed adjusting the bottom friction coefficient, through the comparison between measured and predicted time series of sea surface elevation for 22 stations. Harmonic analysis was performed in order to evaluate the model's accuracy. To validate the hydrodynamic model measured and predicted SSE values were compared for 11 stations, as well as main flow direction velocities for 10 stations. The salt and heat transport models were calibrated comparing measured and predicted time series of salinity and water temperature for 7 stations, and the RMS of the difference between the series was determined. These models were validated comparing the model results with an independent field data set. The hydrodynamic and the salt and heat transport models for Ria de Aveiro were successfully calibrated and validated. They reproduce accurately the barotropic flows and can therefore adequately represent the salt and heat transport and the heat transfer processes occurring in Ria deAveiro.

Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Some conservation laws of fluid mechanics

This thesis contains a study of conservation laws of fluid mechanics. These conservation laws though classical, have been put to extensive studies in t:he past many decades

Exact free-surface flows for shallow-water equations .2. the compressible case

Exact free surface flows with shear in a compressible barotropic medium are found, extending the authors' earlier work for the incompressible medium. The barotropic medium is of finite extent in the vertical direction, while it is infinite in the horizontal direction. The ''shallow water'' equations for a compressible barotropic medium, subject to boundary conditions at the free surface and at the bottom, are solved in terms of double psi-series, Simple wave and time-dependent solutions are found; for the former the free surface is of arbitrary shape while for the latter it is a damping traveling wave in the horizontal direction, For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed. In the case of an isothermal medium, when gamma = 1, we again find simple wave and time-dependent solutions.

Rossby Waves With Linear Topography In Barotropic Fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV (Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV (Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.

Simulating water mixing in a barotropic estuary: the effect of vertical discretization

Mixing between estuarine and coastal waters is strongly dependent on the processes that occur in the vertical direction. This applies both for stratified and homogeneous estuaries. In homogeneous estuaries important recirculation flows in the vertical plane can arise, in regions with strong batimetry gradients, produced by the combined action of inertia and friction. On the Platform close to the inlet this structures can trap estuarine water during the ebb period, releasing it to the interior again during the flood.

The three-dimensional vortical nature of atmospheric and oceanic turbulent flows

Using a novel numerical method at unprecedented resolution, we demonstrate that structures of small to intermediate scale in rotating, stratified flows are intrinsically three-dimensional. Such flows are characterized by vortices (spinning volumes of fluid), regions of large vorticity gradients, and filamentary structures at all scales. It is found that such structures have predominantly three-dimensional dynamics below a horizontal scale LLR, where LR is the so-called Rossby radius of deformation, equal to the characteristic vertical scale of the fluid H divided by the ratio of the rotational and buoyancy frequencies f/N. The breakdown of two-dimensional dynamics at these scales is attributed to the so-called "tall-column instability" [D. G. Dritschel and M. de la Torre Juárez, J. Fluid. Mech. 328, 129 (1996)], which is active on columnar vortices that are tall after scaling by f/N, or, equivalently, that are narrow compared with LR. Moreover, this instability eventually leads to a simple relationship between typical vertical and horizontal scales: for each vertical wave number (apart from the vertically averaged, barotropic component of the flow) the average horizontal wave number is equal to f/N times the vertical wave number. The practical implication is that three-dimensional modeling is essential to capture the behavior of rotating, stratified fluids. Two-dimensional models are not valid for scales below LR. ©1999 American Institute of Physics.

Rossby wave propagation tracks in southern hemisphere mean basic flows associated to generalized frosts over southern South America

Based on previous observational studies on cold extreme events over southern South America, some recent studies suggest a possible relationship between Rossby wave propagation remotely triggered and the occurrence of frost. Using the concept of linear theory of Rossby wave propagation, this paper analyzes the propagation of such waves in two different basic states that correspond to austral winters with maximum and minimum generalized frost frequency of occurrence in the Wet Pampa (central-northwest Argentina). In order to determine the wave trajectories, the ray tracing technique is used in this study. Some theoretical discussion about this technique is also presented. The analysis of the basic state, from a theoretical point of view and based on the calculation of ray tracings, corroborates that remotely excited Rossby waves is the mechanism that favors the maximum occurrence of generalized frosts. The basic state in which the waves propagate is what conditions the places where they are excited. The Rossby waves are excited in determined places of the atmosphere, propagating towards South America along the jet streams that act as wave guides, favoring the generation of generalized frosts. In summary, this paper presents an overview of the ray tracing technique and how it can be used to investigate an important synoptic event, such as frost in a specific region, and its relationship with the propagation of large scale planetary waves.