Calculating FRAM’s Dead Water
43
provides a rather accurate estimate of the ship speed in the observations. The wave
wake at the small actual range of ship speeds is evaluated. Section “Conclusion”
provides a conclusion.
Nansen’s Observations of the Dead Water
The nonlinear calculations in section “Nonlinear Interfacial Model” and section
“Dead Water Resistance” are directly fitted to the original observations made during the FRAM expedition while passing north of Sibiria. The observations of the
dead water were described in Nansen [1, pp. 172–177]. Regarding the wave wake as
observed by the view of the ocean surface, Nansen noted:
Dead water manifests itself in the form of larger or smaller ripples or waves stretching across
the wake, the one behind the other, arising sometimes as far forward as almost amidships.
The dead water wave wake corresponding to the observations is computed and visualised in Fig. 5 below. Regarding the speed of the FRAM, Nansen noted:
Our speed was reduced to about a fifth part of what it would otherwise have been.
The descriptions in Ekman [2, pp. 9–11] provide more details and corrections of
the original observations. The observations given in the two publications are summarised in Table 1.
The most important among the observations include:
1. The engine was working at full pressure without and with dead water;
2. The speed reduction to a fifth part;
3. The speed of the FRAM without dead water, of 4.5 or 5 knots;
4. Salt water at the level of the bottom cock, at 4 m depth.
The informations 1., 2., 3. are used to calculate, from the observational data, the
dead water resistance on Fram, see section “Calculating the Dead Water Resistance
from the Observations”. These calculations are cross-compared to the nonlinear
interfacial calculations of the deadwater resistance on a model of FRAM, see section
“Calculations”. The actual speed the FRAM had in the observations is subsequently
calculated for comparison to the observational data.
The information 4. is used as an estimate of the mid-depth of the pycnocline in
the observations. This depth is also used for the interface at rest in the interfacial
model, where the upper layer depth is put to h 0 = 4 m. This enables an estimate of
the internal wave reference speed (layer depths and densities, see Fig. 2):
c 0 =
(
g ′ h 0
í µí¼ 0 ∕í µí¼ 1 + h 0 ∕h 1
) 1∕2 ≃ 1.02ms
−1
,
(1)
where the densities corresponding to the field observations are í µí¼ 0 = 1.0 kg dm −3 and
í µí¼ 1 = 1.028 kg dm
−3 , g
′
= gí µí»¥í µí¼∕í µí¼ 1 , and g the acceleration of gravity. For comparison,
43
provides a rather accurate estimate of the ship speed in the observations. The wave
wake at the small actual range of ship speeds is evaluated. Section “Conclusion”
provides a conclusion.
Nansen’s Observations of the Dead Water
The nonlinear calculations in section “Nonlinear Interfacial Model” and section
“Dead Water Resistance” are directly fitted to the original observations made during the FRAM expedition while passing north of Sibiria. The observations of the
dead water were described in Nansen [1, pp. 172–177]. Regarding the wave wake as
observed by the view of the ocean surface, Nansen noted:
Dead water manifests itself in the form of larger or smaller ripples or waves stretching across
the wake, the one behind the other, arising sometimes as far forward as almost amidships.
The dead water wave wake corresponding to the observations is computed and visualised in Fig. 5 below. Regarding the speed of the FRAM, Nansen noted:
Our speed was reduced to about a fifth part of what it would otherwise have been.
The descriptions in Ekman [2, pp. 9–11] provide more details and corrections of
the original observations. The observations given in the two publications are summarised in Table 1.
The most important among the observations include:
1. The engine was working at full pressure without and with dead water;
2. The speed reduction to a fifth part;
3. The speed of the FRAM without dead water, of 4.5 or 5 knots;
4. Salt water at the level of the bottom cock, at 4 m depth.
The informations 1., 2., 3. are used to calculate, from the observational data, the
dead water resistance on Fram, see section “Calculating the Dead Water Resistance
from the Observations”. These calculations are cross-compared to the nonlinear
interfacial calculations of the deadwater resistance on a model of FRAM, see section
“Calculations”. The actual speed the FRAM had in the observations is subsequently
calculated for comparison to the observational data.
The information 4. is used as an estimate of the mid-depth of the pycnocline in
the observations. This depth is also used for the interface at rest in the interfacial
model, where the upper layer depth is put to h 0 = 4 m. This enables an estimate of
the internal wave reference speed (layer depths and densities, see Fig. 2):
c 0 =
(
g ′ h 0
í µí¼ 0 ∕í µí¼ 1 + h 0 ∕h 1
) 1∕2 ≃ 1.02ms
−1
,
(1)
where the densities corresponding to the field observations are í µí¼ 0 = 1.0 kg dm −3 and
í µí¼ 1 = 1.028 kg dm
−3 , g
′
= gí µí»¥í µí¼∕í µí¼ 1 , and g the acceleration of gravity. For comparison,