EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Experimental and numerical study of the resonant feature of internal gravity waves in the case of ‘dead water’ phenomenon

Karim Medjdoub1, Imre M. Jánosi2, and Miklós Vincze3
Karim Medjdoub et al.
  • 1Doctoral school of environmental sciences, ELTE Eötvös Loránd University, Budapest, Hungary (
  • 2Department of Physics of Complex Systems, ELTE Eötvös Loránd University, Budapest, Hungary (
  • 3MTA-ELTE Theoretical Physics Research Group, ELTE Eötvös Loránd University, Budapest, Hungary (

 ‘Dead water’ phenomenon, which is essentially a ship-wave in a stratified fluid is studied experimentally in a laboratory tank. Interfacial waves are excited by a moving ship model in a quasi-two-layer fluid, which leads to the development of a drag force that reaches the maximum at the largest wave amplitude in a critical ‘resonant’ towing speed, whose value depends on the structure of the vertical density profile. We utilize five ships of different lengths but of the same width and wet depth. The experimental analysis focuses on the variability of the interfacial wave amplitudes and wavelengths as a function of towing speed in different stratifications. Data evaluation is based on linear two- and three-layer theories of freely propagating interfacial waves and lee waves. We observe that although the internal waves have considerable amplitude, linear theory still gives a surprisingly adequate description of subcritical to supercritical transition and the associated amplification of internal waves.

How to cite: Medjdoub, K., Jánosi, I. M., and Vincze, M.: Experimental and numerical study of the resonant feature of internal gravity waves in the case of ‘dead water’ phenomenon , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8302,, 2020

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Presentation version 2 – uploaded on 06 May 2020
I've corrected the co-author's name in the title page.
  • AC1: Comment on EGU2020-8302, Miklos Vincze, 08 May 2020

    Nice presentation, Karim! :) It's just a test to check if you get notifications about comments. :)

  • CC1: Comment on EGU2020-8302, Wolf-Gerrit Fruh, 08 May 2020

    Very nice presentation indeed :)

    Do the numbers #5, 8, 9, 10 on slide 6 refer to the stratification cases shown in slide 5 counting from left to right?, e.g. #5 with zi ~ 5cm and rho_2 ~ 1.030 kg/l,  and # 10 with zi ~ 7 cm and rho2 ~ 1.005 kg/l?

    • AC2: Reply to CC1, Karim Medjdoub, 08 May 2020

      Thank you for the comment.

      yes, it's counting from left to right, in which #5, 8, 9, 10 refers to the stratification cases where h2 (the thickness of the bottom layer) is 5, 9, 9, 7cm, respectively. and rho2 is 1.047, 1.02, 1.048, 1.004kg/l, respectively.

  • CC2: Comment on EGU2020-8302, Miguel Teixeira, 08 May 2020

    Hi. Very interesting presentation.

    One aspect that is striking in slide 9 is that you are able to get resonant waves for value sof U/c substantially larger than 1, which is not predicted either by the 2-layer or 3-layer models, although not to such an extent by the second. I assume these are linear models. Since the flow is 2D, I think linear 2D theory is intrinsically limited to U/c<1. To what physical process do you attribute the resonant waves for U/c>1: nonlinearity of the waves, a smoothed interface between the two layers, both aspects, or some other aspect (e.g. frictional effects)?

    Thanks in advance.

    Miguel Teixeira (University of Reading)

  • AC3: Comment on EGU2020-8302, Miklos Vincze, 08 May 2020

    Many thanks for the comment! I think tha wave in the U/c >1 domain are not "resonant" in our terminology. The maximum amplification (largest amplitude) typically occurs typically around 0.8*c. Surely there are nonlinear wave theories to describe this, but what we proposed instead is a combination of two linear wave modes. One is a (linear) three-layer theory c(k), and the other is the most simple case of lee-wave excitation in the middle (gradient) layer, that goes simply by the c_lee(k) ~ N/k dispersion relation (with N being the buoyancy frequency of the middle layer). The idea is that the maximum amplitude (that's what we call "resonance", but maybe "coalescence of waves" would be a better term) can be observed where the c(k) and c_lee(k) dispersion relation curves intersect, as sketched in slide 13. So there are two types of waves present in the system, but obviously the one that can be observed is the one with the larger wavenumber k at a given towing speed U in all cases. (For more, please check our paper: Medjdoub, Karim, Imre M. Jánosi, and Miklós Vincze. "Laboratory investigations on the resonant feature of ‘dead water’phenomenon." Experiments in Fluids 61.1 (2020): 6. ) Unfortunately this system here does not allow posting links, but the paper is OA. :) Best, MV   

  • CC3: Comment on EGU2020-8302, Miguel Teixeira, 08 May 2020

    Hi again.

    Thanks for your response and for the reference to your paper. I will check it out soon.


Presentation version 1 – uploaded on 05 May 2020 , no comments