NUMERICAL MODELLING OF COASTAL UPWELLING ALONG THE EAST COAST OF INDIA
A THESIS SUBMITTED
FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY
By
CHAMARTHI SRINIVAS
Centre for Atmospheric Sciences
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
NEW DELHI-110016 INDIA JULY, 1996
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DEDICATED at the lotus feet of
His Holiness SRILA ROMAPADA SWAMI Initiating Spiritual Master
INTERNATIONAL SOCIETY FOR KRSNA CONSCIOUSNESS
CERTIFICATE
This is to certify that the thesis entitled 'NUMERICAL MODELLING OF COASTAL UPWELLING ALONG THE EAST COAST OF INDIA' being submitted by CHAMARTHI SRINIVAS for the award of the degree of DOCTOR OF PHILOSOPHY, is a record of the original bonafide research work carried out by him. He has worked under our joint guidance and supervision and has fulfilled the requirements for the submission of this thesis. The results presented in this thesis have not been submitted in part or full to any other University or Institute for award of any degree/diploma.
( P.C. SINHA ) Professor & Head
Centre for Atmospheric Sciences Indian Institute of Technology
New Delhi
.
( A.D. RAO )
Principal Scientific officer Centre for Atmospheric Sciences Indian Institute of Technology New Delhi
Date : 13. .95
ACKNOWLEDGEMENTS
It was my happy good fortune as a student to have a series of marvelous teachers.
Out of all, my primary thanks should go to Prof. SINHA, P.C. and Dr. RAO, A.D. for their diligent guidance and helpful suggestions during this work. My sincere thanks especially to Dr. RAO, A.D., who poured over every inch of the manuscript with painstaking attention to detail and made a semi-infinite number of helpful suggestions and attempted to correct my dyslexic spelling.
Also, I would like to thank Prof. DUBE, S.K., CAS-IITD, for his personal enquiries and suggestions at appropriate moments through which I learnt a lot for my life and work.
I owe special gratitude to Dr. KRISHNAN, P. V., Applied Mechanics Department IITD, under whose watchful eyes I could develop the vision of equanimity towards work and life through KRSNA CONSCIOUSNESS.
I am deeply indebted to my father Shri C. GANGADHARAM and brother Mr. C. V. SATYANARAYANA, DGM-MTNL, BOMBAY, for their immense help during the course of this work.
Last - but - not - the - least, my sincere thanks should also go to my friends Mr. RAMACHANDRA RAO, Y. for his encouraging words and affectionate understanding, Mr. SRINIVASAN, K. for his MAY-I-HELP-YOU mood which has seen me through this work.
Finally, thanks to all those, who are not mentioned by name but were with me time and time again.
CHAMARTHI SRINIVAS
SUMMARY
The main objective of this thesis is to develop numerical models for coastal upwelling process along the east coast of India. It consists of six chapters. In the first chapter, a brief review of the literature relevant to the studies made in this thesis has been presented. It also contains review of state of art in development of numerical models till date.
Starting from the basic set of hydro-dynamical equations governing the fluid motion, Chapter II describes the development of a multi-level, breadth-averaged, baroclinic numerical model. This model is applied for simulation of flow and salinity characteristics in the Vasishta Godavari estuary. Numerical experiments are performed with the combined effect of the semi-diurnal tide and the seasonal variation of the freshwater discharge into the estuary. The computed current and salinity values along the estuary are in good agreement with the observations.
In Chapter III, the development of a 2-dimensional continuously stratified, multi-level baroclinic numerical model for coastal upwelling has been described. Conservation equations are applied for mass, momentum, thermal energy, salinity and turbulence energy. Stretched coordinate system is used to obtain increased resolution in the region near the surface and bottom where high velocity shear occurs.
Also it is applied in the horizontal as fine resolution is required near the coast in the upwelling zone. A series of experiments are described to simulate the response of the coastal ocean to the pure wind stress forcing and the bathymetric variations. A diagnostic study is carried out to understand the dynamics of upwelling in terms of balance between various terms of the momentum equations both in the upwelling and the open-ocean regions.
The effect of estuarine discharge on the coastal upwelling process has been discussed in Chapter IV. The 2-dimensional model described in Chapter III has been suitably modified by applying an open boundary instead of a coastal rigid
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boundary. The model is applied in a plane perpendicular to the coast where Godavari estuary joins the Bay of Bengal. The model simulations both with and without estuarine discharge reveal suppressing of the upwelling near the mouth of the estuary.
Based on the 2-dimensional model as explained in Chapter III, the Chapter V describes a 3-dimensional numerical model for coastal upwelling. The model is applied to study the coastal ocean response off east coast of India to pure wind stress forcing. Experiments are performed with mean monthly wind stress forcing of the pre-monsoon months. A detailed analysis of the thermal and dynamical response of the ocean off Visakhapatnam was carried out. The model produced known features of coastal upwelling like coastal under current, upwarping of the isotherms etc. The simulated fields in a vertical cross-shelf section off Visakhapatnam compare fairly well with the available observations.
Effect of small time scale atmospheric disturbances such as a tropical storm on the dynamics of the coastal upwelling is discussed in Chapter VI. The model explained in Chapter V is used for this study. The cyclonic wind stress of a moving storm is superimposed on the dynamical response of the model for pure wind stress forcing and the subsequent simulations are analyzed in terms of thermal and current fields. The efficacy of the model in producing the field structures is qualitatively found to be satisfactory.
CONTENTS
SUMMARY
CHAPTER-I INTRODUCTION
1.1 Introduction 2
1.2 Coastal upwelling regions 4
1.2.1 Observations 4
1.3 Modelling studies 10
1.3.1 Analytical models 10
1.3.2 Numerical models 12
1.4 Purpose of the present study 19
CHAPTER-II 2-DIMENSIONAL NUMERICAL MODEL FOR THE GODAVARI ESTUARY
2.1 Introduction 28
2.2 Formulation 29
2.2.1 Governing equations 29
2.2.2 Boundary conditions 34
2.3 Coordinate transformation 36
2.4 Finite-difference equation 38
2.5 Numerical experiments 44
CHAPTER-III 2-DIMENSIONAL MODEL OF COASTAL UPWELLING
3.1 Introduction 55
3.2 Formulation 55
3.2.1 Governing equations 55
3.2.2 Boundary conditions 60
3.3 Coordinate transformation 62
3.4 Further coordinate transformation 64
3.5 Finite-difference equations 67
3.6 Numerical experiments 76
3.6.1 Introduction 76
3.6.2 Expt. 1 : Flat bottom case 76
3.6.2.1 Circulation and thermal structures 79
3.6.2.2 Balance analysis 87 3.6.3 Expt. 2 : Variable depth case 96 3.6.3.1 Circulation and thermal structures 97
3.6.3.2 Balance analysis 105
CHAPTER-IV EFFECT OF ESTUARIAN DISCHARGE ON UPWELLING
4 1 Introduction 111
4.2 Formulation 111
4.2.1 Governing equations 111
4.2.2 Boundary conditions 112
4.3 Finite-difference equations 112
4.4 Numerical experiments 113
4.4.1 Case 1: U0 = 0.0 114
4.4.2 Case 2: Uo = 1.0 122
CHAPTER-V 3-DIMENSIONAL MODEL OF COASTAL UPWELLING
5.1 Introduction 133
5.2 Formulation 135
5.2.1 Governing equations 135
5.2.2 Boundary conditions 137
5.3 Coordinate transformation 139
5.4 Finite-difference equations 144
5.5 Numerical experiments 149
CHAPTER-VI COASTAL OCEAN'S RESPONSE TO A MOVING STORM
6.1 Introduction 169
6.2 Formulation 170
6.2.1 Governing equations 170
6.2.2 Storm parameters 171
6.3 Numerical experiments 171
CONCLUSIONS 184
REFERENCES 187
