Book contents
- Frontmatter
- Contents
- Contributors
- Editors' preface
- Keynote address to the 1977 Symposium SIR JAMES LIGHTHILL
- Part I The large-scale climatology of the tropical atmosphere
- Part II The summer monsoon over the Indian subcontinent and East Africa
- Part III The physics and dynamics of the Indian Ocean during the summer monsoon
- Part IV Some important mathematical modelling techniques
- 39 On the incorporation of orography into numerical prediction models
- 40 Vertical motion in the monsoon circulation
- 41 A one-dimensional model of the planetary boundary layer for monsoon studies
- 42 The use of empirical orthogonal functions for rainfall estimates
- 43 Applications of perturbation theory to problems of simulation of atmospheric processes
- Part V Storm surges and flood forecasting
- Index
40 - Vertical motion in the monsoon circulation
Published online by Cambridge University Press: 05 November 2011
- Frontmatter
- Contents
- Contributors
- Editors' preface
- Keynote address to the 1977 Symposium SIR JAMES LIGHTHILL
- Part I The large-scale climatology of the tropical atmosphere
- Part II The summer monsoon over the Indian subcontinent and East Africa
- Part III The physics and dynamics of the Indian Ocean during the summer monsoon
- Part IV Some important mathematical modelling techniques
- 39 On the incorporation of orography into numerical prediction models
- 40 Vertical motion in the monsoon circulation
- 41 A one-dimensional model of the planetary boundary layer for monsoon studies
- 42 The use of empirical orthogonal functions for rainfall estimates
- 43 Applications of perturbation theory to problems of simulation of atmospheric processes
- Part V Storm surges and flood forecasting
- Index
Summary
A review is presented of methods for solving the omega-equation by (a) finite differences, and (b) finite elements. The different types of forcing terms that arise when the wind vector is resolved into a rotational and a solenoidal part are described. A computational procedure for evaluating omega by successive approximations is outlined. Computations of omega by the method of finite elements, using prismatic elements, is described. Results of omega computations made by finite differences and by finite elements are presented and discussed.
Introduction
A problem of considerable importance in meteorology is the estimation of vertical velocity. As its magnitude is very small, direct measurements are not possible. Consequently, the pattern of vertical velocity is usually inferred from measurements of horizontal velocity, the pressure and temperature distribution in the atmosphere. A commonly used technique is to derive a solution of the diagnostic omega-equation. An excellent review of vertical velociy computations has been provided by Pearce (1974). In this paper we wish to consider solutions of the omega-equation by (a) finite differences, and (b) by the method of finite elements.
Basic equations
The basic equations express the first law of thermodynamics, the conservation of vorticity and conservation of mass. Pressure coordinates are generally used to derive the omega-equation but, as we shall see later, this gives rise to difficulties in the vicinity of steep orographic features.
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- Monsoon Dynamics , pp. 601 - 614Publisher: Cambridge University PressPrint publication year: 1981