Internal waves in a shear background current: Transition from solitary-wave regime to dispersive-wave regime

Xu, Chengzhu; Stastna, Marek

doi:10.1103/physrevfluids.4.094801

Cited by 9 publications

(7 citation statements)

References 32 publications

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“…is held fixed (Dunphy et al, 2011;Xu & Stastna, 2019). In contrast with weakly nonlinear theories, which are approximate, solutions found by using the variational technique are exact solutions of Euler's equations.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…In the algorithm neither the wave amplitude, nor the wave propagation speed is specified. Instead, the kinetic energy of the disturbance is minimized under the constraint that the available potential energy (scaled by ρ 0 gH )

normalAPE (η) = \frac{1}{H} {true \int}_{0}^{H} {true \int}_{- \infty}^{+ \infty} {true \int}_{0}^{η} ([], \overset{ρ}{true} (z - η) - \bar{ρ} (z - s)) normald s normald x normald z,

is held fixed (Dunphy et al., 2011; Xu & Stastna, 2019). In contrast with weakly nonlinear theories, which are approximate, solutions found by using the variational technique are exact solutions of Euler's equations.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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Breaking Location of Internal Solitary Waves Over a Sloping Seabed

et al. 2021

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Internal solitary waves (ISWs) consist of hump-shaped large undulations of the pycnocline with a permanent form, resulting from a balance between nonlinearity, which tends to steepen it, and dispersion, which tends to flatten it (Grimshaw et al., 2010; Helfrich & Melville, 2006; Sutherland et al., 2013). ISWs are mostly generated by the interaction between tidal flows and bottom topographic features, such as underwater sills and the continental shelf-slope region (Helfrich & Melville, 2006; Osborne & Burch, 1980). Packets of shoreward-propagating ISWs, separated by tidal periods, are a ubiquitous feature of the coastal oceans (Dwi

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Section: Theoretical Backgroundmentioning

confidence: 99%

normalAPE (η) = \frac{1}{H} {true \int}_{0}^{H} {true \int}_{- \infty}^{+ \infty} {true \int}_{0}^{η} ([], \overset{ρ}{true} (z - η) - \bar{ρ} (z - s)) normald s normald x normald z,

Section: Theoretical Backgroundmentioning

confidence: 99%

Breaking Location of Internal Solitary Waves Over a Sloping Seabed

et al. 2021

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“…In this algorithm neither the wave amplitude, nor the wave propagation speed are specified. Whereas, the kinetic energy of the disturbance is minimized under the constraint that the available potential energy (scaled by ρ 0 gH )

APE (η) = \frac{1}{H} \int_{0}^{H} \int_{- \infty}^{+ \infty} \int_{0}^{η} ([], \bar{ρ} (z - η) - \bar{ρ} (z - s)) normald s normald x normald z,

is held fixed (Dunphy et al., 2011; Xu & Stastna, 2019), with

\bar{ρ}

density profile scaled by the reference density ρ 0 .…”

Section: Model Validation and Prediction Of The Mixing Efficiencymentioning

confidence: 99%

“…is held fixed (Dunphy et al, 2011;Xu & Stastna, 2019), with 𝐴𝐴 𝐴 𝐴𝐴 density profile scaled by the reference density ρ 0 .…”

Section: Experimental and Numerical Assessmentmentioning

confidence: 99%

Mixing Efficiency for Breaking Internal Solitary Waves

et al. 2021

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“…Thus, unlike a solitonic-type wave, the front wave is asymmetrical, the front wave and the whelps spread out (their amplitudes decrease, and their wavelengths increase). From the front wave skewness or the ratio between its amplitude and wavelength, Xu et al [18] give several criteria to decide if an internal wave has a solitonic behavior or a dispersive undulating depression one. According to them, if after 100 seconds of propagation the wave has an amplitude greater than 3% of its half-length, then the structure is not linear.…”

Section: Scott Russell-like Experiment: Proof Of a Linear Dispersive mentioning

confidence: 99%

The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags

Fourdrinoy

Dambrine

Petcu

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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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.

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Internal waves in a shear background current: Transition from solitary-wave regime to dispersive-wave regime

Cited by 9 publications

References 32 publications

Breaking Location of Internal Solitary Waves Over a Sloping Seabed

Breaking Location of Internal Solitary Waves Over a Sloping Seabed

Mixing Efficiency for Breaking Internal Solitary Waves

The dual nature of the dead-water phenomenology: Nansen versus Ekman wave-making drags

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