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

Author(s):  
Karim Medjdoub ◽  
Imre M. Jánosi ◽  
Miklós Vincze

<p> ‘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.</p>

2019 ◽  
Vol 61 (1) ◽  
Author(s):  
Karim Medjdoub ◽  
Imre M. Jánosi ◽  
Miklós Vincze

Abstract Interfacial internal wave excitation in the wake of towed ships is studied experimentally in a quasi-two-layer fluid. At a critical ‘resonant’ towing velocity, whose value depends on the structure of the vertical density profile, the amplitude of the internal wave train following the ship reaches a maximum, in unison with the development of a drag force acting on the vessel, known in the maritime literature as ‘dead water’. The amplitudes and wavelengths of the emerging internal waves are evaluated for various ship speeds, ship lengths and stratification profiles. The results are compared to linear two- and three-layer theories of freely propagating waves and lee waves. We find that despite the fact that the observed internal waves can have considerable amplitudes, linear theories can still provide a surprisingly adequate description of subcritical-to-supercritical transition and the associated amplification of internal waves. We argue that the latter can be interpreted as a coalescence of frequencies of two fundamental stable wave motions, namely lee waves and propagating interfacial wave modes. Graphic abstract


Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.


1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.


Author(s):  
Callum J. Shakespeare ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg

AbstractInternal waves generated at the seafloor propagate through the interior of the ocean, driving mixing where they break and dissipate. However, existing theories only describe these waves in two limiting cases. In one limit, the presence of an upper boundary permits bottom-generated waves to reflect from the ocean surface back to the seafloor, and all the energy flux is at discrete wavenumbers corresponding to resonant modes. In the other limit, waves are strongly dissipated such that they do not interact with the upper boundary and the energy flux is continuous over wavenumber. Here, a novel linear theory is developed for internal tides and lee waves that spans the parameter space in between these two limits. The linear theory is compared with a set of numerical simulations of internal tide and lee wave generation at realistic abyssal hill topography. The linear theory is able to replicate the spatially-averaged kinetic energy and dissipation of even highly non-linear wave fields in the numerical simulations via an appropriate choice of the linear dissipation operator, which represents turbulent wave breaking processes.


2012 ◽  
Vol 708 ◽  
pp. 250-278 ◽  
Author(s):  
Nicolas Grisouard ◽  
Oliver Bühler

AbstractWe present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave–mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.


2021 ◽  
pp. 109314
Author(s):  
Cheng-An Wang ◽  
Duo Xu ◽  
Ji-Peng Gao ◽  
Jian-Yu Tan ◽  
Zhi-Quan Zhou

2020 ◽  
Vol 117 (29) ◽  
pp. 16770-16775
Author(s):  
Johan Fourdrinoy ◽  
Julien Dambrine ◽  
Madalina Petcu ◽  
Morgan Pierre ◽  
Germain Rousseaux

A ship encounters a higher drag in a stratified fluid compared to a homogeneous one. Grouped under the same “dead-water” vocabulary, two wave-making resistance phenomena have been historically reported. The first, the Nansen wave-making drag, generates a stationary internal wake which produces a kinematic drag with a noticeable hysteresis. The second, the Ekman wave-making drag, is characterized by velocity oscillations caused by a dynamical resistance whose origin is still unclear. The latter has been justified previously by a periodic emission of nonlinear internal waves. Here we show that these speed variations are due to the generation of an internal dispersive undulating depression produced during the initial acceleration of the ship within a linear regime. The dispersive undulating depression front and its subsequent whelps act as a bumpy treadmill on which the ship would move back and forth. We provide an analytical description of the coupled dynamics of the ship and the wave, which demonstrates the unsteady motion of the ship. Thanks to dynamic calculations substantiated by laboratory experiments, we prove that this oscillating regime is only temporary: the ship will escape the transient Ekman regime while maintaining its propulsion force, reaching the asymptotic Nansen limit. In addition, we show that the lateral confinement, often imposed by experimental setups or in harbors and locks, exacerbates oscillations and modifies the asymptotic speed.


2019 ◽  
Vol 124 (12) ◽  
pp. 8949-8968 ◽  
Author(s):  
Zhigang Lai ◽  
Guangzhen Jin ◽  
Yongmao Huang ◽  
Haiyun Chen ◽  
Xiaodong Shang ◽  
...  

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