Degeneration of internal Kelvin waves in a continuous two-layer stratification

Ulloa, Hugo N.; Winters, Kraig B.; Fuente, Alberto de la; Niño, Yarko

doi:10.1017/jfm.2015.311

Cited by 18 publications

(13 citation statements)

References 51 publications

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“…[24,11,14,12,20,18,25,31] and references therein). As is well-know, wave propagation in big lakes can be also affected by the Earth's rotation [5,7,28,32,29]. In particular, the dynamics of solitary waves has been investigated within the framework of the Ostrovsky equation and it has been established that they cannot propagate steadily due to the permanent radiation of small-amplitude long waves [23,9] (they can steadily propagate, however, being supported by a long background wave [10,27]).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Stepanyants

2019

Fluids

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We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate of modulation instability is maximal. An envelope solitary wave of this frequency can be described by the conventional nonlinear Schrödinger equation. A soliton solution to this equation is presented for the time-like version of the nonlinear Schrödinger equation. When such envelope soliton enters a coastal zone where the bottom gradually linearly increases, then it experiences an adiabatical transfor-arXiv:1903.07817v2 [physics.flu-dyn] 22 Mar 2019mation. This leads to an increase of soliton amplitude, velocity, and period of a carrier wave, whereas its duration decreases. It is shown that the soliton becomes taller and narrower. At some distance it looks like a breather, a narrow nonstationary solitary wave. The dependences of soliton parameters on the distance when it moves towards the shoaling are found from the conservation laws and analysed graphically. Estimates for the real ocean are presented.

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Section: Introductionmentioning

confidence: 99%

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Stepanyants

2019

Fluids

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“…The potential energy is smaller for stratified conditions than for well-mixed conditions [44][45][46]. Consequently, with Equation (4) we computed the difference between PE of the well-mixed reservoir and PE of the stratified reservoir for each time step, where for the former we used the spatial average of the water density.…”

Section: Vertical Mixingmentioning

confidence: 99%

Modeling the Multi-Seasonal Link between the Hydrodynamics of a Reservoir and Its Hydropower Plant Operation

Carpentier

Haas

Olivares

et al. 2017

Water

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Abstract:The hydrodynamics of many hydropower reservoirs are controlled by the operation of their power plant, but the associated water quality impact is often poorly understood. In particular, significant hydropeaking operations by hydropower plants affect not only the downstream ecosystem but also the reservoir water temperature. This paper contributes to understanding that link. For this, we coupled a hydrodynamic model (Estuary, Lake and Coastal Ocean Model, ELCOM) to a grid-wide power system scheduling model. In a case study (Rapel, Chile), we observe the behavior of variables related to the flow regime and water quality (including sub-daily hydrologic alteration, seasonal and sub-daily thermal pollution of the downstream river, and vertical mixing in the reservoir). Additionally, we evaluate how environmental constraints (ECs) can improve the conditions for a wet, normal and dry water-type year. We found that the unconstrained operation produces a strong sub-daily hydrologic alteration as well as an intense thermal pollution of the outflow. We show that these effects can clearly be avoided when implementing ECs. The current (unconstrained) vertical mixing makes the reservoir susceptible to algae blooms. Implementing ECs may intensify the stratification in the reservoir near the dam in some scenarios. The grid-wide economic cost of Rapel's ECs is a modest 0.3%.

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“…The dynamics of Kelvin and Poincaré waves has been widely studied in systems where rotation plays a first-order role,  ∼ (10 −2 -10 −1 ) , via field observations in large-to mid-size lakes [2,10,11,44,46]. Additionally, numerical simulations, both in real and ideal basins [4,13,17,47,54], and laboratory experiments [33,45,53,57] have provided a robust understanding of the basin-scale wave dynamics in systems with rotational regimes characterised by 0.1 ≤  < 1 . In particular, laboratory-scale results show that rotational regimes with  ≤ 0.5 are associated with strong degeneration and decay of the basin-scale internal gravity waves via the boundary friction and nonlinear processes associated with the gravest sub-inertial Kelvin wave [45,48,53,57].…”

Section: Introductionmentioning

confidence: 99%

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

2018

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Gravity waves are prominent physical features that play a fundamental role in transport processes of stratified aquatic ecosystems. In a two-layer stratified basin, the equations of motion for the first vertical mode are equivalent to the linearised shallow water equations for a homogeneous fluid. We adopted this framework to examine the spatiotemporal structure of gravity wavefields weakly affected by the background rotation of a single-layer system of equivalent thickness h , via laboratory experiments performed in a cylindrical basin mounted on a turntable. The wavefield was generated by the release of a diametral linear tilt of the air-water interface, , inducing a basin-scale perturbation that evolved in response to the horizontal pressure gradient and the rotation-induced acceleration. The basin-scale wave response was controlled by an initial perturbation parameter,  * = 0 ∕h , where 0 was the initial displacement of the air-water interface, and by the strength of the background rotation controlled by the Burger number, . We set the experiments to explore a transitional regime from moderate-to weak-rotational environments, 0.65 ≤  ≤ 2 , for a wide range of initial perturbations, 0.05 ≤  * ≤ 1.0. The evolution of was registered over a diametral plane by recording a laser-induced optical fluorescence sheet and using a capacitive sensor located near the lateral boundary. The evolution of the gravity wavefields showed substantial variability as a function of the rotational regimes and the radial position. The results demonstrate that the strength of rotation and nonlinearities control the bulk decay rate of the basin-scale gravity waves. The ratio between the experimentally estimated damping timescale, T d , and the seiche period of the basin, T g , has a median value of T d ∕T g ≈ 11 , a maximum value of T d ∕T g ≈ 10 3 and a minimum value of T d ∕T g ≈ 5. The results of this study are significant for the understanding the dynamics of gravity waves in waterbodies weakly affected by Coriolis acceleration, such as mid-to small-size lakes.

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Degeneration of internal Kelvin waves in a continuous two-layer stratification

Cited by 18 publications

References 51 publications

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

Modeling the Multi-Seasonal Link between the Hydrodynamics of a Reservoir and Its Hydropower Plant Operation

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

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