9.4 Similitude and Dimensional Analysis
319
combined with the 11 and 12 !Jm channels is used to correct for various atmospheric factors (such as water vapour content) which can contaminate the
temperature readings. The correction procedure is known as the 'split-window'
method. According to Bernstein (1982), AVHRR data can be used to study climate variations with an accuracy of 0.5-1.0
D
C. The comparisons of the satellite
SST with precision radiometric measurements made from a ship published by
Schluessel et al. (1987) showed that satellite derived SST, when computed using a multichannel algorithm and corrected by HIRS (High Resolution Infrared
Sounder) provide a reliable estimate of SST in the absence of visible cloud.
The monitoring of exchange or fluxes between the atmosphere and ocean,
and in this regard, surface wind measurements and SST observations, together
with estimates of rainfall, are important parameters as input to a global climate model. Other elements are the surface currents which provide a reference
velocity in situ. Examples of these are westward-moving equatorial long wave
patterns observed in both the Atlantic and Pacific oceans. They have a spatial
scale of about 1000 km, and move westward with an average phase speed of
40 km/day (Barrett and Curtis, 1992). Sea surface temperature observations
in the equatorial Pacific, using the Along Track Scanning Radiometer ( ATSR)
flying on ERS-l satellite reveal the dynamics of these waves. Several eastward
propagating signals have been discovered during January, March and April 1992
(onset of the 1992-1993 EI Nino). The phase speed of these observed Kelvin
waves was about 2.4 m/s (Llewellyn-Jones et al., 1996).
9.4 Similitude and Dimensional Analysis
9.4.1 Introduction
In the previous chapters we demonstrated that numerous problems in marine fluid mechanics can be solved using theoretical and/or numerical models.
However, there are still many problems for which such solutions are not possible. They are studied using experimental data, both from field and laboratory
experiments. In the case of laboratory experiments, the basis of physical modelling is the idea that the model behaves in all aspects in a manner similar to
the prototype it is designed to emulate. Requirements for similarity usually
are expressed in terms of criteria of similitude or conditions of similarity.
Field and laboratory experiments provide a large quantity of various types of
data. If no theoretical formulation of the problem is known, only various combinations of experimental data give us the possibility to establish the relationship
between measured variables. Obviously, the number of such combinations can
sometimes be very large. However, if several variables can be combined in the
form of a single dimensionless variable, then the number of combinations can
be significantly reduced. This approach is known as dimensional analysis. In
next sections we will briefly describe an application of the similitude concept
and dimensional analysis for marine fluid mechanics.
319
combined with the 11 and 12 !Jm channels is used to correct for various atmospheric factors (such as water vapour content) which can contaminate the
temperature readings. The correction procedure is known as the 'split-window'
method. According to Bernstein (1982), AVHRR data can be used to study climate variations with an accuracy of 0.5-1.0
D
C. The comparisons of the satellite
SST with precision radiometric measurements made from a ship published by
Schluessel et al. (1987) showed that satellite derived SST, when computed using a multichannel algorithm and corrected by HIRS (High Resolution Infrared
Sounder) provide a reliable estimate of SST in the absence of visible cloud.
The monitoring of exchange or fluxes between the atmosphere and ocean,
and in this regard, surface wind measurements and SST observations, together
with estimates of rainfall, are important parameters as input to a global climate model. Other elements are the surface currents which provide a reference
velocity in situ. Examples of these are westward-moving equatorial long wave
patterns observed in both the Atlantic and Pacific oceans. They have a spatial
scale of about 1000 km, and move westward with an average phase speed of
40 km/day (Barrett and Curtis, 1992). Sea surface temperature observations
in the equatorial Pacific, using the Along Track Scanning Radiometer ( ATSR)
flying on ERS-l satellite reveal the dynamics of these waves. Several eastward
propagating signals have been discovered during January, March and April 1992
(onset of the 1992-1993 EI Nino). The phase speed of these observed Kelvin
waves was about 2.4 m/s (Llewellyn-Jones et al., 1996).
9.4 Similitude and Dimensional Analysis
9.4.1 Introduction
In the previous chapters we demonstrated that numerous problems in marine fluid mechanics can be solved using theoretical and/or numerical models.
However, there are still many problems for which such solutions are not possible. They are studied using experimental data, both from field and laboratory
experiments. In the case of laboratory experiments, the basis of physical modelling is the idea that the model behaves in all aspects in a manner similar to
the prototype it is designed to emulate. Requirements for similarity usually
are expressed in terms of criteria of similitude or conditions of similarity.
Field and laboratory experiments provide a large quantity of various types of
data. If no theoretical formulation of the problem is known, only various combinations of experimental data give us the possibility to establish the relationship
between measured variables. Obviously, the number of such combinations can
sometimes be very large. However, if several variables can be combined in the
form of a single dimensionless variable, then the number of combinations can
be significantly reduced. This approach is known as dimensional analysis. In
next sections we will briefly describe an application of the similitude concept
and dimensional analysis for marine fluid mechanics.