Ondas inerciales de gravedad

Priego Wood, Martín. (2015). Ondas inerciales de gravedad Master Thesis, Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias

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Título Ondas inerciales de gravedad
Autor(es) Priego Wood, Martín
Abstract Inertial gravity waves (IGWs) play a fundamental role in many atmospheric and oceanic processes and appear spontaneously during the development of the baroclinic instability, which has a dominant influence on large-scale meteorology. While IGWs have recently been detected in numerical simulations of the baroclinic annulus filled with water or high-Prandtl-number liquids, they have not been found in analogous simulations for low-Prandtl-number fluids, such as air. Hence, it has been suggested that the Prandtl number may affect the occurrence IGWs. In this work, the existence and characteristics of IGWs are studied in a simple model for a thermally stratified rotating fluid that incorporates the effects of viscosity and thermal conductivity. The model is derived in full detail, starting from the basic equations of compressible flow, passing through the Boussinesq approximation and the perturbation equations, and finally arriving at a characteristic cubic dimensionless equation that determines the growth rate of perturbations. The discussion of the solutions to the characteristic equation with respect to the Prandtl P, Rayleigh R, Taylor T, and wave numbers is greatly facilitated by a transformation that reduces the number of parameters from five to two. The analysis of the real part of the growth rate confirms the stability of the equilibrium state and reveals that perturbations are generally more damped the smaller the P. The analysis of the imaginary part corroborates the known results for the inertial limit, where rotation is dominant and oscillations exist for any T, and for the gravitational limit, where stratification prevails and oscillations only appear above a critical R. The main result is however that IGWs only exist in a specific infinite region of the two-dimensional parameter space. This theoretical finding supports the experimental and numerical evidence that, in addition to R and T, P plays a role in the appearance of IGWs. By condensing the dependencies with respect to the P, R, T, and wave numbers in just two parameters, the developed framework also eases the calculation, visualisation, and comparison of the damping and frequency characteristics of IGWs. For example, for two well-documented numerical studies of the baroclinic annulus with P = 0.7 and 16, the model predicts that, far away from the exclusion regions of IGWs, the oscillations for the lower P should be faster and more damped.
Notas adicionales Trabajo de Fin de Máster. Máster Universitario en Física de Sistemas Complejos. UNED
Materia(s) Física
Editor(es) Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias
Director/Tutor Crespo del Arco, Emilia
Fecha 2015-10-13
Formato application/pdf
Identificador bibliuned:master-Ciencias-FSC-Mpriego
Idioma spa
Versión de la publicación acceptedVersion
Nivel de acceso y licencia http://creativecommons.org/licenses/by-nc-nd/4.0
Tipo de recurso master Thesis
Tipo de acceso Acceso abierto

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Creado: Fri, 18 Dec 2015, 01:52:42 CET