Wave patterns generated by an axisymmetric obstacle in a two-layer flow

Lacaze, Laurent; Paci, Alexandre; Cid, Emmanuel; Cazin, Sébastien; Eiff, Olivier; Esler, J. G.; Johnson, E. R.

doi:10.1007/s00348-013-1618-z

Cited by 18 publications

(26 citation statements)

References 33 publications

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“…10 Recently, internal waves generated by a three-dimensional geometry, towed with a constant speed along a wave tank of finite width, were measured by Lacaze et al 11 We shall compare the present calculations to their observations and analysis. Nonlinear two-dimensional studies of transcritical two-layer flow past topography and upstream influence include, theoretically, hydraulic nonlinear theory 12,13 or weakly dispersive models.…”

Section: Introductionmentioning

confidence: 85%

“…From their interfacial elevation measurements, Lacaze et al 11 obtained the available potential energy trapped in the waves, which they denoted by E L H p , see their Eq. (2) and the subsequent text, and plotted E L H p /M 5/3 as function of Γ = (Fr − 1)M −2/3 , where M = b 0 /h 0 in our notation.…”

Section: A Force Calculationsmentioning

confidence: 99%

“…The accuracy of the method is judged by evaluating the terms accounting for cubic couplings in the successive approximations, see the text prior to (11 Grue 25 for two-dimensional wave tanks. The cubic corrections have not been implemented in the three-dimensional interfacial model.…”

Section: B Wave Wakementioning

confidence: 99%

“…21,22 The work done by the moving ship and thus the energy flux of the generated waves are readily obtained. We also perform a set of computations of the experiments by Lacaze et al 11 and discuss a potential representation of the drag force, inspired by Esler, Rump, and Johnson. 23 Nonlinear and linear calculations are compared.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dead water resistance at subcritical speed

Grue

2015

Physics of Fluids

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The dead water resistance F1=12CdwρSU2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0–0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ∼ 0.875–1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.

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Section: Introductionmentioning

confidence: 85%

Section: A Force Calculationsmentioning

confidence: 99%

Section: B Wave Wakementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear dead water resistance at subcritical speed

Grue

2015

Physics of Fluids

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“…This facility was used in recent years for studies of boundary layers and internal waves [38], in particular those topographically induced and trapped at a density jump, e.g., [39,40]. The flume was used here as a 22-m-long, 1-m-high, 3-m-wide closed glass tank (Figure 1).…”

Section: Experimental Designmentioning

confidence: 99%

Water Tank Experiments on Stratified Flow over Double Mountain-Shaped Obstacles at High-Reynolds Number

et al. 2017

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Abstract:In this article, we present an overview of the HyIV-CNRS-SecORo (Hydralab IV-CNRS-Secondary Orography and Rotors Experiments) laboratory experiments carried out in the CNRM (Centre National de Recherches Météorologiques) large stratified water flume. The experiments were designed to systematically study the influence of double obstacles on stably stratified flow. The experimental set-up consists of a two-layer flow in the water tank, with a lower neutral and an upper stable layer separated by a sharp density discontinuity. This type of layering over terrain is known to be conducive to a variety of possible responses in the atmosphere, from hydraulic jumps to lee waves and highly turbulent rotors. In each experiment, obstacles were towed through the tank at a constant speed. The towing speed and the size of the tank allowed high Reynolds-number flow similar to the atmosphere. Here, we present the experimental design, together with an overview of laboratory experiments conducted and their results. We develop a regime diagram for flow over single and double obstacles and examine the parameter space where the secondary obstacle has the largest influence on the flow. Trapped lee waves, rotors, hydraulic jumps, lee-wave interference and flushing of the valley atmosphere are successfully reproduced in the stratified water tank. Obstacle height and ridge separation distance are shown to control lee-wave interference. Results, however, differ partially from previous findings on the flow over double ridges reported in the literature due to the presence of nonlinearities and possible differences in the boundary layer structure. The secondary obstacle also influences the transition between different flow regimes and makes trapped lee waves possible for higher Froude numbers than expected for an isolated obstacle.

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Drag associated with 3D trapped lee waves over an axisymmetric obstacle in two‐layer atmospheres

Teixeira

Miranda

2017

Quart J Royal Meteoro Soc

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Mountain‐wave drag is evaluated explicitly using linear theory and verified against numerical simulations for the flow of idealized two‐layer atmospheres with piecewise‐constant stratification over an axisymmetric mountain. Static stability is either higher in the bottom layer and lower in the top layer (Scorer's atmosphere) or neutral in the bottom layer and positive in the top layer, separated by a sharp temperature inversion (Vosper's atmosphere). The drag receives contributions from long mountain waves propagating vertically in the upper layer and from short trapped lee waves propagating downstream, either in the lower layer or at the inversion. This trapped lee‐wave drag, which is typically not represented in parametrizations, acts on the atmosphere at low levels. As in flow over a 2D ridge, this drag has several maxima as a function of the height of the interface between the two layers for Scorer's atmosphere and is maximized by a marked Scorer parameter contrast between those layers. In Vosper's atmosphere, there is a single trapped lee‐wave drag maximum for Froude numbers near one, when the wind speed matches the phase speed of the dominant interfacial waves, and this drag is maximized for relatively low interface elevations, for which waves at the inversion have higher amplitude. The 3D flow geometry allows resonant wave modes to have various horizontal orientations and a continuous spectrum, forming a dispersive ‘Kelvin ship wave’ pattern, and expanding the regions in parameter space where the drag is non‐zero relative to 2D flow, but it also decreases the drag magnitude dispersively. Nevertheless, the trapped lee‐wave drag on an axisymmetric obstacle can still equal or exceed the drag associated with vertically propagating waves and the reference hydrostatic drag valid for a uniformly stratified atmosphere.

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Wave patterns generated by an axisymmetric obstacle in a two-layer flow

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Cited by 18 publications

References 33 publications

Nonlinear dead water resistance at subcritical speed

Nonlinear dead water resistance at subcritical speed

Water Tank Experiments on Stratified Flow over Double Mountain-Shaped Obstacles at High-Reynolds Number

Drag associated with 3D trapped lee waves over an axisymmetric obstacle in two‐layer atmospheres

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