Chapter 3
Basics of Geophysical Fluid Dynamics
Abstract This chapter introduces the reader to scalars and vectors, Newton’s laws
of motion, waves and steady-state f ows, the buoyancy force, the Coriolis force, a
number of conservation principles, turbulence, and, finall , to the Navier–Stokes
equations of flui motion. Practical exercises focus on the interference of waves,
movement of a buoyant object in a stratifie water column, and movement of objects
under the sole influenc of the Coriolis force.
3.1 Units
The International System of Units will be used in most instances. Distances are
expressed in metres (m), time lapse in seconds (s), and mass in kilograms (kg).
For convenience, temperatures are expressed in degrees Celsius (
◦
C), which is the
thermodynamic temperature in Kelvin (K) plus a constant of 273.16. Time lapse is
translated into more convenient units such as minutes, hours, days, weeks, months,
years, etc. Other units can be derived from the above base units. For example, volume is expressed in cubic metres (m
3
). Often, we also use symbols for multipliers
such as:
micro (μ) = 10
−6
= 0.00001
milli (m) = 10
−3
= 0.001
centi (c) = 10
−2
= 0.01
kilo (k) = 10
3
= 1000
3.2 Scalars and Vectors
3.2.1 Difference Between Scalars and Vectors
A scalar is a physical quantity without directional information. Temperature and
pressure are examples of this. A vector, on the other hand, carries information of
both magnitude and direction. Velocity is an example of this. A car moves at a
certain speed into a certain direction.
J. K¨ ampf, Ocean Modelling for Beginners,
DOI 10.1007/978-3-642-00820-7 3, C
Springer-Verlag Berlin Heidelberg 2009
17
Basics of Geophysical Fluid Dynamics
Abstract This chapter introduces the reader to scalars and vectors, Newton’s laws
of motion, waves and steady-state f ows, the buoyancy force, the Coriolis force, a
number of conservation principles, turbulence, and, finall , to the Navier–Stokes
equations of flui motion. Practical exercises focus on the interference of waves,
movement of a buoyant object in a stratifie water column, and movement of objects
under the sole influenc of the Coriolis force.
3.1 Units
The International System of Units will be used in most instances. Distances are
expressed in metres (m), time lapse in seconds (s), and mass in kilograms (kg).
For convenience, temperatures are expressed in degrees Celsius (
◦
C), which is the
thermodynamic temperature in Kelvin (K) plus a constant of 273.16. Time lapse is
translated into more convenient units such as minutes, hours, days, weeks, months,
years, etc. Other units can be derived from the above base units. For example, volume is expressed in cubic metres (m
3
). Often, we also use symbols for multipliers
such as:
micro (μ) = 10
−6
= 0.00001
milli (m) = 10
−3
= 0.001
centi (c) = 10
−2
= 0.01
kilo (k) = 10
3
= 1000
3.2 Scalars and Vectors
3.2.1 Difference Between Scalars and Vectors
A scalar is a physical quantity without directional information. Temperature and
pressure are examples of this. A vector, on the other hand, carries information of
both magnitude and direction. Velocity is an example of this. A car moves at a
certain speed into a certain direction.
J. K¨ ampf, Ocean Modelling for Beginners,
DOI 10.1007/978-3-642-00820-7 3, C
Springer-Verlag Berlin Heidelberg 2009
17