I= MATHEMATICAL MODEL OF OCEANOGRAPHY
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Title of Thesis
MATHEMATICAL MODEL OF OCEANOGRAPHY

Author(s)
Mushtaq Hussain
Institute/University/Department Details
Department of Mathematics/ University of Karachi
Session
2006
Subject
Mathematics
Number of Pages
141
Keywords (Extracted from title, table of contents and abstract of thesis)
oceanography, marine inhabitants, sediments, discharge pattern, geological environment, indus delta, sea water, hydrodynamic

Abstract
Oceanography is defined as the science of the ocean that integrates, synthesizes and blends many types of knowledge. It began when man first pushed off from the shore and realize that the winds and currents influenced his movements. As he ventured further, the stars become important in finding his way at sea. A large exploitation of ocean started in 1872 when HMS Challenger with scientists onboard remained at sea for about four years. During their stay at sea the scientists collected a number of valuable data and information that leads them for optimum utilization of the oceans.

The present study includes an overview of Oceanography however main emphasis should be given to Indus Delta which is the lifeline of Pakistan. In the recent years a high proportion of fresh water from the river Indus has been diverted for irrigation and production of hydroelectricity. Thus considerably reducing the effective discharge, subsequently affecting the marine inhabitants, sediments discharge pattern and the geological environment of the Indus Delta.

In view of the alarming situation and to avoid further damage to the Indus Delta an effort is being made to develop a mathematical model of the oceanography to explore/find ways and means with the help of mathematical methods to suggest remedial actions to control/improve the existing condition.

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3523.63 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
217.04 KB
2 1 Oceanography 1
579.14 KB
  1.1 Introduction 1
  1.2 Topography 1
  1.3 The Parameters Of State Of Sea Water 5
  1.4 The Equation Of State Of Water 11
  1.5 The Representation Of The Process Of Maxing On The Temperature Salinity (Ts) Diagram 13
  1.6 T-S Curve Of The Waters Of The Oceans 20
  1.7 The Line Integral In The T-S Plan 21
3 2 Hydrodynamic Equation Of The Sea 21
573.89 KB
  2.1 Gravitational Forces 29
  2.2 The Continuity Equation 30
  2.3 Effects Of Spin 32
  2.4 Effects Of Spin 36
  2.5 The Coriolis Force 36
  2.6 Tidal Force 38
  2.7 Total Potential Caused By The Gravity & Rotations 39
  2.8 Internal Force In A Viscous Fluid 40
  2.9 The Salinity Equation 41
  2.10 Waves Dynamics 42
4 3 Indus Delta 51
774.39 KB
  3.1 Indus River Discharge 51
  3.2 Growth Of Indus Delta 54
  3.3 Tectonic Activities In Indus Deltaic Region 53
  3.4 Geology Of Indus Delta 54
  3.5 Sediments 60
  3.6 Manā€™s Influence On Sediment Discharge 70
  3.8 Future Of Indus River System And Estuary 72
5 4 Reduction In Indus River Discharge And Its Implication 74
193.32 KB
  4.1 Introduction 74
  4.2 Indus River Discharge Pattern 74
  4.3 Changes In River Discharge Due To Dams Channel Etc 75
  4.4 Mathematical Model, Itā€™s Formulation And Application 76
  4.5 Ecological Change 78
  4.6 Conclusion 81
6 5 Numerical Simulation Of A Large-Scale Atmospheric And Oceanic Circulation 83
366.64 KB
  5.1 Introduction 83
  5.2 A Large-Scale Dynamics Of The Atmosphere And Ocean 83
  5.3 Integral Laws Of Conservation 86
  5.4 The Symmetrized Form Of The Equations Of The Atmosphere Dynamics And The Evolutionary Formulation Of The Problem In The Ocean Dynamics 92
7 6 Materials In Sea Water 102
341.36 KB
  6.1 Dissolved Materials 102
  6.2 The Major Constituents 103
  6.3 The Dissolved Gases 104
  6.4 The Nutrients 107
  6.5 The Trace Elements 109
  6.6 Salinity Variations 111
8 7 Mathematical Model For Evaluating The Mass Of Mangroves Forest Along Coast Line Of Karachi / Indus Delta 115
203.51 KB
  7.1 Introduction 115
  7.2 Mathematical Modeling 117
  7.3 Results And Discussions 120
  7.4 Conclusions 120
9 8 An Empirical Model To Predict The Tidal Level At The Coast Areas Of Karachi 121
124.56 KB
  8.1 Introduction 121
  8.2 Mathematical Modeling 123
  8.3 Results And Discussion 124
  8.4 Conclusion 125
10 9 Results 126
349.66 KB
  9.1 Discussion 128
  9.2 Conclusions 133
  9.3 Recommendations 137