Calculating FRAM’s Dead Water
53
of its usual speed, is perhaps one of the most accurate measures of the observations.
This speed reduction is found to occur for a mid-depth of the pycnocline of slightly
less than 4 m. Calculations illustrate the internal wave wake of a model of FRAM
moving at Fr = 0.525 and 0.55. Linear theory is incapable of obtaining the internal
wave wake and resistance force at the very small Froude numbers.
References
1. Nansen, F. (1897). Farthest North, Westminster: Archibald Constable and Company, 2 Whitehall Gardens (Vol. 1).
2. Ekman, V. W. (1904). XV. On dead-water. In Nansen. F. (Ed.) The Norwegian north polar
expedition 1893–1896. Scientific results, Brögger, Christiania
3. Hudimac, A. A. (1961). Ship waves in a stratified ocean. Journal of Fluid Mechanics, 11, 229–
243.
4. Crapper, G. D. (1967). Ship waves in a stratified ocean. Journal of Fluid Mechanics, 29, 667–
672.
5. Keller, J. B., & Munk, W. H. (1970). Internal wave wakes of a body moving in a stratified fluid.
Physics of Fluids, 13, 1425–1431.
6. Yeung, R. W., & Ngyuen, T. C. (1999). Waves generated by a moving source in a two-layer
ocean of finite depth. Journal of Engineering Mathematics, 35, 85–107.
7. Miloh, T., Tulin, M. P., & Zilman, G. (1993). Dead-water effects of a ship moving in stratified
seas. Journal of Offshore Mechanics and Arctic Engineering, 115, 105–110.
8. Tulin, M. P., Yao, Y., & Wang, P. (2000). The generation and propagation of ship internal waves
in a generally stratified ocean at high densimetric Froude numbers, including nonlinear effects.
Journal of Ship Research, 44(3), 197–227.
9. Watson, G., Chapman, R. D., & Apel, J. R. (1992). Measurements of the internal wave wake
of a ship in a highly stratified sea loch. Journal of Geophysical Research, 97(C6), 9689–9703.
10. Mercier, J. M., Vasseur, R., & Dauxious, T. (2011). Resurrecting dead-water phenomenon.
Nonlinear Processes in Geophysics, 18, 193–208.
11. Grue, J. (2015). Nonlinear dead water resistance at subcritical speed. Physics of Fluids, 27,
082103. https://doi.org/10.1063/1.4928411.
12. Grue, J., Bourgault, D., & Galbraith, P.S. (2016). Supercritical dead water: Effect of nonlinearity and comparison with observations. Journal of Fluid Mechanics, 803, 436–465. https://
doi.org/10.1017/jfm.2016.518.
13. Gou, Y., Xu, W. B., Zhang, X. W., Teng, B. Experiment study on the towing resistance of a
barge in a two-layer fluid. In Proceedings of the 32nd International Workshop on Water Waves
and Floating Bodies, Dalian, China. Retrieved April 23–26, 2017, from http://www.iwwwfb.
org.
14. Newman, J. N. (1977). Marine hydrodynamics. MIT Press
15. Grue, J., Jensen, A., Rusås, P.-O., & Sveen, J. K. (1999). Properties of large-amplitude internal
waves. Journal of Fluid Mechanics, 447, 257–278.
53
of its usual speed, is perhaps one of the most accurate measures of the observations.
This speed reduction is found to occur for a mid-depth of the pycnocline of slightly
less than 4 m. Calculations illustrate the internal wave wake of a model of FRAM
moving at Fr = 0.525 and 0.55. Linear theory is incapable of obtaining the internal
wave wake and resistance force at the very small Froude numbers.
References
1. Nansen, F. (1897). Farthest North, Westminster: Archibald Constable and Company, 2 Whitehall Gardens (Vol. 1).
2. Ekman, V. W. (1904). XV. On dead-water. In Nansen. F. (Ed.) The Norwegian north polar
expedition 1893–1896. Scientific results, Brögger, Christiania
3. Hudimac, A. A. (1961). Ship waves in a stratified ocean. Journal of Fluid Mechanics, 11, 229–
243.
4. Crapper, G. D. (1967). Ship waves in a stratified ocean. Journal of Fluid Mechanics, 29, 667–
672.
5. Keller, J. B., & Munk, W. H. (1970). Internal wave wakes of a body moving in a stratified fluid.
Physics of Fluids, 13, 1425–1431.
6. Yeung, R. W., & Ngyuen, T. C. (1999). Waves generated by a moving source in a two-layer
ocean of finite depth. Journal of Engineering Mathematics, 35, 85–107.
7. Miloh, T., Tulin, M. P., & Zilman, G. (1993). Dead-water effects of a ship moving in stratified
seas. Journal of Offshore Mechanics and Arctic Engineering, 115, 105–110.
8. Tulin, M. P., Yao, Y., & Wang, P. (2000). The generation and propagation of ship internal waves
in a generally stratified ocean at high densimetric Froude numbers, including nonlinear effects.
Journal of Ship Research, 44(3), 197–227.
9. Watson, G., Chapman, R. D., & Apel, J. R. (1992). Measurements of the internal wave wake
of a ship in a highly stratified sea loch. Journal of Geophysical Research, 97(C6), 9689–9703.
10. Mercier, J. M., Vasseur, R., & Dauxious, T. (2011). Resurrecting dead-water phenomenon.
Nonlinear Processes in Geophysics, 18, 193–208.
11. Grue, J. (2015). Nonlinear dead water resistance at subcritical speed. Physics of Fluids, 27,
082103. https://doi.org/10.1063/1.4928411.
12. Grue, J., Bourgault, D., & Galbraith, P.S. (2016). Supercritical dead water: Effect of nonlinearity and comparison with observations. Journal of Fluid Mechanics, 803, 436–465. https://
doi.org/10.1017/jfm.2016.518.
13. Gou, Y., Xu, W. B., Zhang, X. W., Teng, B. Experiment study on the towing resistance of a
barge in a two-layer fluid. In Proceedings of the 32nd International Workshop on Water Waves
and Floating Bodies, Dalian, China. Retrieved April 23–26, 2017, from http://www.iwwwfb.
org.
14. Newman, J. N. (1977). Marine hydrodynamics. MIT Press
15. Grue, J., Jensen, A., Rusås, P.-O., & Sveen, J. K. (1999). Properties of large-amplitude internal
waves. Journal of Fluid Mechanics, 447, 257–278.