Propagating and evanescent internal waves in a deep ocean model

Paoletti, Matthew S.; Swinney, Harry L.

doi:10.1017/jfm.2012.284

Cited by 23 publications

(32 citation statements)

References 18 publications

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“…Amplitude attenuations in reflected and leakage through critical level 2D internal waves beams calculated in [31] were tested in special experiments, where velocity field was measured by particle image velocimeter (PIV) instrument. The vertical velocity fields of the incoming and reflected waves agree within few percent with theory of beams in an arbitrary smooth stratification [32].…”

Section: Theory Of Periodic Internal Wave Propagationsupporting

confidence: 60%

“…Unfortunately PIV instruments are characterized by low spatial resolutions, in experiments [32] δx = 3.9 mm and Δz = 2.9 mm. These values exceed the U so the instrument [32] cannot resolve fine scale flow components accompanying the periodic internal wave beam and forming on critical level, as it was calculated in [31], too.…”

Section: Theory Of Periodic Internal Wave Propagationmentioning

confidence: 99%

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Differential Fluid Mechanics—Harmonization of Analytical, Numerical and Laboratory Models of Flows

Chashechkin

2015

Computational Methods in Applied Sciences

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Concepts of a "solid body motion" and "fluid flow" are compared taking into account the condition of inobservability of a "fluid particle". General properties of the fundamental set of fluid mechanics equations, accepted for describing fluid flows, are analyzed taking into account the compatibility condition. Hierarchy of periodic flows is classified basing on the order of linearized set of governing equations. Results of theoretical analysis of infinitesimal periodic flows in a stably stratified fluid including periodic internal waves and accompanied family of small scale components are given. Calculations of periodic internal waves propagation and generation in a fluid with arbitrary stable profile of buoyancy are compared with data of schlieren observations in laboratory. Fine flow structure observed behind uniformly towing strip is discussed in context of a given model. Some conclusions and recommendations on improvement techniques of a fluid dynamics experiment are presented.

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Section: Theory Of Periodic Internal Wave Propagationsupporting

confidence: 60%

Section: Theory Of Periodic Internal Wave Propagationmentioning

confidence: 99%

Differential Fluid Mechanics—Harmonization of Analytical, Numerical and Laboratory Models of Flows

Chashechkin

2015

Computational Methods in Applied Sciences

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“…The beam slope becomes large in the deep ocean, as observed in the Bay of Biscay by Pingree and New, 47 and even diverges if there is a turning depth. 42,43 The nonhydrostatic effects that arise from weak stratifications reduce the radiated power below hydrostatic estimates; this should be considered in making global estimates of the internal wave power radiated by deep ocean topography.…”

Section: Discussionmentioning

confidence: 99%

“…Internal waves reflect from turning depths where N(z) = ω M2 , and become evanescent (exponentially damped) below. 42,43 The internal wave slope S IW diverges at a turning depth, where the direction of propagation becomes vertical (θ ≡ arcsin (ω/N ) reaches 90; see the red curve in Fig. 1).…”

Section: Nonhydrostatic Effects and Turning Depthsmentioning

confidence: 99%

Internal wave and boundary current generation by tidal flow over topography

2013

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The relationship between boundary currents generated by tidal flow over topography and the radiated internal wave power is examined in two-dimensional numerical simulations of a uniformly stratified fluid. The radiated power PIW and kinetic energy density of the boundary currents are computed as a function of the internal wave slope SIW and the criticality parameter ε (ratio of the maximum topographic slope to SIW). Both SIW and ε are varied two orders of magnitude about unity by changing the tidal frequency, stratification, or topographic shape and slope. We consider cases where the hydrostatic approximation is valid (SIW ≪ 1), as well as test theoretical predictions for models of the deep ocean where the beam slope diverges and the hydrostatic approximation fails. We confirm that resonant boundary currents characterized by large kinetic energy densities form over critical topography (ε = 1). However, we find that this resonance phenomenon does not extend to the power radiated by internal waves that propagate away from the topography. Further, by directly comparing the kinetic energy density to the energy flux of the generated internal waves, we find that the more easily measured kinetic energy density cannot be used as a proxy to characterize the conversion of tidal energy to radiated internal wave power. Whether the hydrostatic approximation is valid or fails, our measurements of the radiated power can be described as PIW = Ptidef (ε, shape)/SIW, where Ptide is the effective tidal power that interacts with the topography, and π/8 < f (ε, shape) < π/4 is bounded below by the theoretical prediction of Bell [“Topographically generated internal waves in the open ocean,” J. Geophys. Res. 80, 320–327 (1975)] for ε → 0 and above by Llewellyn Smith and Young [“Tidal conversion at a very steep ridge,” J. Fluid Mech. 495, 175–191 (2003)] for ε → ∞.

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“…Particle image velocimetry 35 has been used in laboratory studies of internal waves to characterize the velocity fields, 27,28,[36][37][38][39][40][41] and synthetic schlieren has been used in a few studies to measure density perturbations averaged along the line of sight; [42][43][44] however, measurements of the accompanying pressure fields have not been made owing to technical challenges in doing so. To circumvent the difficulty in measuring the pressure field to obtain the energy flux of two-dimensional internal waves, Echeverri et al 39 decomposed their experimental velocity fields into the three lowest vertical modes, 45 which could be used to estimate the internal wave energy flux using Eq.…”

Section: Introductionmentioning

confidence: 99%

Experimental determination of radiated internal wave power without pressure field data

et al. 2014

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We present a method to determine, using only velocity field data, the time-averaged energy flux J and total radiated power P for two-dimensional internal gravity waves. Both J and P are determined from expressions involving only a scalar function, the stream function ψ. We test the method using data from a direct numerical simulation for tidal flow of a stratified fluid past a knife edge. The results for the radiated internal wave power given by the stream function method agree to within 0.5% with results obtained using pressure and velocity data from the numerical simulation. The results for the radiated power computed from the stream function agree well with power computed from the velocity and pressure if the starting point for the stream function computation is on a solid boundary, but if a boundary point is not available, care must be taken to choose an appropriate starting point. We also test the stream function method by applying it to laboratory data for tidal flow past a knife edge, and the results are found to agree with the direct numerical simulation.Supplementary Material includes a Matlab code with a graphical user interface (GUI) that can be used to compute the energy flux and power from any two-dimensional velocity field data.

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Propagating and evanescent internal waves in a deep ocean model

Cited by 23 publications

References 18 publications

Differential Fluid Mechanics—Harmonization of Analytical, Numerical and Laboratory Models of Flows

Differential Fluid Mechanics—Harmonization of Analytical, Numerical and Laboratory Models of Flows

Internal wave and boundary current generation by tidal flow over topography

Experimental determination of radiated internal wave power without pressure field data

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