Calculating FRAM’s Dead Water
John Grue
Dedicated to Eugene G. Morozov on his 70th Birthday
The internal wave (dead water) resistance on the Polar ship FRAM is obtained by
two methods. The first is empirical, based on the original observations (Nansen,
F.: Farthest North, Westminster: Archibald Constable and Company, 2 Whitehall
Gardens, 1897. Vol. 1). The second is a strongly nonlinear interfacial method in
three dimensions. The intersection between the empirical and theoretical resistances
determines accurately the ship speed which is investigated varying the depth of the
pycnocline, a quantity that was not measured by Nansen. A reduction to a fifth of
the usual speed of the FRAM because of the dead water, as observed by Nansen,
corresponds to a mid-depth of the pycnocline of slightly less than 4 m while FRAM’s
draught was 5 m. The wave wake at Froude number slightly above 0.5 is calculated
by the nonlinear method. The linear ship wake and dead water resistance are found
to be invalid.
Introduction
This paper concerns the dead water problem—the drag force due to the internal wave
wake of a ship moving along the surface of a stratified fluid. The body may also be
submerged. The phenomenon was first described by Nansen [1] during the Polar
Expedition in 1893-96. The observations were later presented with more details by
J. Grue ( ✉ )
Mechanics Section, Department of Mathematics, University of Oslo, Oslo, Norway
e-mail: johng@math.uio.no
© Springer International Publishing AG, part of Springer Nature 2018
M. G. Velarde et al. (eds.), The Ocean in Motion, Springer Oceanography,
https://doi.org/10.1007/978-3-319-71934-4_6
41
John Grue
Dedicated to Eugene G. Morozov on his 70th Birthday
The internal wave (dead water) resistance on the Polar ship FRAM is obtained by
two methods. The first is empirical, based on the original observations (Nansen,
F.: Farthest North, Westminster: Archibald Constable and Company, 2 Whitehall
Gardens, 1897. Vol. 1). The second is a strongly nonlinear interfacial method in
three dimensions. The intersection between the empirical and theoretical resistances
determines accurately the ship speed which is investigated varying the depth of the
pycnocline, a quantity that was not measured by Nansen. A reduction to a fifth of
the usual speed of the FRAM because of the dead water, as observed by Nansen,
corresponds to a mid-depth of the pycnocline of slightly less than 4 m while FRAM’s
draught was 5 m. The wave wake at Froude number slightly above 0.5 is calculated
by the nonlinear method. The linear ship wake and dead water resistance are found
to be invalid.
Introduction
This paper concerns the dead water problem—the drag force due to the internal wave
wake of a ship moving along the surface of a stratified fluid. The body may also be
submerged. The phenomenon was first described by Nansen [1] during the Polar
Expedition in 1893-96. The observations were later presented with more details by
J. Grue ( ✉ )
Mechanics Section, Department of Mathematics, University of Oslo, Oslo, Norway
e-mail: johng@math.uio.no
© Springer International Publishing AG, part of Springer Nature 2018
M. G. Velarde et al. (eds.), The Ocean in Motion, Springer Oceanography,
https://doi.org/10.1007/978-3-319-71934-4_6
41