This book on Ocean Dynamics is a comprehensive collection of materials utilized in my personal teaching at Berhampur University, University of Hyderabad, and Arbaminch University. It is primarily intended for graduate and postgraduate students studying Oceanography, physical oceanography, meteorology, atmospheric sciences, Aeronautical, Agricultural, and space meteorology, as well as various related fields in civil and ocean engineering.
A distinct characteristic of this book is the inclusion of numerous exercises and their solutions under each chapter to enhance comprehension and practical application. The content of the book encompasses virtually all significant topics in physical oceanography, such as currents with and without friction, upwelling and downwelling, water masses and TS-analysis, waves and tides, Estuaries, internal waves, seiches and storm surges, and Rossby and Kelvin waves, among others. Particular emphasis is placed on recent advancements in North Indian Ocean circulation.
This book on Ocean Dynamics: Theory and Exercises with Solutions, though is a compilation from many sources, it mainly forms part of my personal teaching material at Berhampur University, University of Hyderabad and Arbaminch University. This book will be highly useful for graduate and post graduate students of Oceanography, physical oceanography, meteorology, atmospheric sciences, Aeronautical, Agricultural and space meteorlogy and many other related fields in civil and ocean engineering. Special interest in this book is the provision of many exercises and their solutions under each chapter for better understanding and applications.
The two limbs of Arabian Sea and Bay of Bengal form parts of North Indian Ocean (NIO) on the left and right respectively. Though the Arabian Sea and the Bay of Bengal are located in the same latitudinal belt and receive the same amount of solar radiation, oceanographically these two basins exhibit remarkable differences. The reason for it is Bay of Bengal is shallow and less saline due to heavy river water discharge and Arabian Sea is deep and cold and more saline.
To understand the movement of a ocean particle, We have to consider different forces. The forces that are working are pressure gradient force, coriolis force, acceleration due to gravity and friction. The summation of all these forces is balanced by total force. As we consider unit mass, the force is equal to acceleration. The total equation is called equation of motion.
Inertial motion is typically excited when the surface currents are impulsively excited by wind forcing. If the wind were to remain steady—then the currents would eventually reach equilibrium and the time-dependent term would go to zero. But if the winds blew for a few hours and then turned off then the current would be still in motion for some time even if there would be no forcing due to turning off winds.
It is a non-accelerated frictionless horizontal motion where pressure gradient balances coriolis acceleration as shown in Fig.4.1 in both the hemispheres.
The general distribution of density in the oceans is like a two layer ocean as shown in Fig.5.1 below. A layer of more or less uniform density (nearly vertical) near the surface called as isopycnal layer and a deeper layer of higher density below with sharp increase of density is called as pycnocline.
The following scientists greatly contributed to the wind driven circulation. Out of all Ekman, Sverdrup, Stommel and Munk are most important and ever remembered for their work. So in the following pages discussion is mostly concentrated on these four scientists theories.
Wind stress at the sea surface not only causes horizontal movement of water (Ekman Net transport), but also leads to vertical motion (Ekman Pumping). This horizontal movement of water leads to the occurrence of upwelling and down welling throughout the oceans both at coastal boundaries as well as in the open ocean. As divergence of surface water causes rising, convergence of the surface water causes sinking. This rising and sinking of water are called upwelling and down welling.
Harald Ulrik Sverdrup (1888-1957), a Norwegian who began his career studying meteorology with Vilhelm Bjerknes in Oslo, was appointed director of Scripps Oceanographic Institution in 1936. His 1947 paper “Wind-driven currents in a baroclinic ocean”, which showed the link between meridional currents and the curl of the wind stress, began the modern era of dynamical oceanography and initiated large-scale modeling of ocean circulation.
While circulation is a measure of tendency of fluid rotation, vorticity is the same property of fluid for an infinitely small area.
Sverdrup’s contribution could not take into account of the western boundary and so could not explain about the circulation what happened along the west coast of the ocean. Thus his circulation, as shown in Fig.8.1c in the chapter 8, is incomplete. This problem was solved by an American Oceanographer, Henry Stommel, in 1948.
Munk (1950) built upon Sverdrup’s theory, using both the vertical and lateral eddy viscosity. Munk combined the basic features contributed by Ekman, Sverdrup and Stommel to provide the first comprehensive solution of the wind driven circulation, using the real wind field Munk included the effect of eddy viscosity in both the horizontal and the vertical dimensions (both Ah and Az).
As water consists of two positively charged hydrogen ions and a single negatively charged oxygen ion, water is arranged as a polar molecule having positive and negative sides. This molecular polarity leads to water’s high dielectric constant (ability to withstand or balance an electric field). Water is able to dissolve many substances because the polar water molecules align to shield each ion, resisting the recombination of the ions.
The wind blows over the water, changing its surface into ripples and then to waves. Thus most of the normal waves are wind-driven. As waves grow in height, the wind pushes them along faster and higher. Sometimes waves can become unexpectedly strong and destructive. As waves enter shallow water, they become taller and slow down, eventually break on the shore.
Small amplitude wave theory was based on the premise that motions are sufficiently small to allow the free surface boundary condition to be linearized. Finite amplitude wave theories or Stokes’ higher order theories are similar as per the concept in which additional higher order terms that were neglected in the Airy’s theory are included. In general, the higher the order of the wave theory, higher will be the limiting wave height for which it would be valid.
In order to understand the generation of tides first we should understand the motions of earth with respect to sun and moon. Tides are affected by the orbit of the moon around the earth and, less so, by the earth around the sun. The orbital motion of earth with respect to sun and the orbital motion of moon with respect to earth are as shown in Fig.15.1.
The word estuary is derived from the latin word ‘aestus’ meaning tide and the adjective ‘aestuarium’ means tidal. This means low ground covered by the sea at high water.
Important constants required to do the Exercises in all the chapters of this book.
