Dynamics of Oil Slicks

Fanneløp, T. K.; Waldman, G. D.

doi:10.2514/3.50127

Cited by 117 publications

(43 citation statements)

References 1 publication

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“…The Boussinesq approximation is achieved by setting δ = 0 wherever it is not multiplied by g. In this case eqs. (21) and (22) coincide and gives that Figure 4 compares our results from the 2LSWE, eq. (23), to the model by Benjamin, 18 eq.…”

Section: Derivation Of Froude Numbers From the 2lswesupporting

confidence: 54%

“…The non-Boussinesq case has more recently received attention in the literature, 60,61 and eqs. (21) and (22) could be of interest in this regard.…”

Section: Derivation Of Froude Numbers From the 2lswementioning

confidence: 99%

“…The value of β has been discussed in the literature and is commonly set to β = 1.31 in the one-dimensional case and β = 1.41 in the axisymmetric case. 2,3,5,21 A more general approach than the Fay model is the two-layer shallow-water equations (2LSWE), which are derived from the Euler equations by assuming a negligible vertical velocity. 22,23 These equations model the flow of two layers of shallow liquids and may be used to simulate for instance gravity currents.…”

Section: Introductionmentioning

confidence: 99%

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A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

Fyhn¹,

Lervåg

Ervik

et al. 2019

Physics of Fluids

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The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. These phenomena are commonly described by the two-layer shallow-water equations (SWE). When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer SWE. It has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions to correct the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly captures the behaviour of shocks and contact discontinuities without additional closure relations. The result shows that simplification to an effective one-layer model is justified mathematically and can be made without additional knowledge of the shock behaviour. The shock speed in the proposed model is consistent with empirical models and identical to front conditions that have been found theoretically by e.g. von Kármán and by Benjamin. This suggests that the breakdown of the SWE in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the SW framework to shocks by studying one-dimensional lock-exchange/-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. The equations are solved numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer SWE. We also compare numerical results from the model with results from experiments, and find good agreement. arXiv:1902.04648v3 [physics.flu-dyn]

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Section: Derivation Of Froude Numbers From the 2lswesupporting

confidence: 54%

“…The non-Boussinesq case has more recently received attention in the literature, 60,61 and eqs. (21) and (22) could be of interest in this regard.…”

Section: Derivation Of Froude Numbers From the 2lswementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

Fyhn¹,

Lervåg

Ervik

et al. 2019

Physics of Fluids

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“…By investigating the leakage regularity of underwater crude oil pipes, the diffusion area of spilled oil can be predicted before it reaches the water’s surface, thereby reducing emergency response time (Wang 2006). Although crack leakages of submarine pipelines generally attract considerable attention, leakages of river-bottom pipelines garner little research concern (Gao et al 2007; Fannelop 1972; Hoult and Fay 1970). Hence, it is necessary to put importance on the study of diffusion predictability of river-bottom crude oil pipelines.…”

Section: Introductionmentioning

confidence: 99%

Leakage diffusion of underwater crude oil in wind fields

Chen

Liu

Li³

et al. 2016

SpringerPlus

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Leakage of underwater crude oil pipes causes severe pollution to soil and water, and results in great economic loss. To predict the diffusion area of spilled oil before it reaches the water’s surface and to reduce the time required for emergency response, numerical simulations were conducted on underwater spilled oil diffusion of bare crude oil pipes using FLUENT software. The influences of water-surface wind speed, leakage hole diameter, water velocity, and initial leakage velocity on oil diffusion were analyzed. The results revealed the following: (1) with wind blowing on the surface of the water, the vertical displacement of spilled oil jet-flow was affected by the combined action of water flow and wind, making it difficult for a high-speed jet-flow to form. A horizontal oil flow mostly moved in the direction of the bottom water, and frontier oil droplets dispersed quickly; (2) during the diffusion of spilled oil in water, the maximum horizontal displacement mostly increased linearly, while the maximum vertical displacement initially increased quickly and then slowed; (3) the greater the initial velocity and leakage hole diameter, the higher the oil jet-flow and the wider the diffusion area; the higher the water flow rate and water-surface wind speed, the smaller the vertical displacement of spilled oil. The existence of water-surface wind had no obvious influence on the horizontal displacement of underwater spilled oil.

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“…These currents are primarily horizontal, occurring as either top or bottom boundary currents or as intrusions at some buoyantly stable intermediate level. The density differences driving such flows may be due to temperature differences as is the case in the formation of the so‐called thermal bar in dimictic lakes [2], salinity contrasts in oceanic settings [3], the presence of suspended material, as in the case of turbidity currents [4], as well as combinations of these mechanisms and others [5, 6].…”

Section: Introductionmentioning

confidence: 99%

Thermally Enhanced Motions of Variable‐Inflow Surface Gravity‐Driven Flows

2005

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In this paper, we report on theoretical and numerical studies of models for suddenly initiated variable-inflow surface gravity currents having temperature-dependent density functions when these currents are subjected to incoming radiation. This radiation leads to a heat source term that, owing to the spatial and temporal variation in surface layer thickness, is itself a function of space and time. This heat source term, in turn, produces a temperature field in the surface layer having nonzero horizontal spatial gradients. These gradients induce shear in the surface layer so that a depth-independent velocity field can no longer be assumed and the standard shallow-water theory must be extended to describe these flow scenarios. These variable-inflow currents are assumed to enter the flow regime from behind a partially opened lock gate with the lock containing a large volume of fluid whose surface is subjected to a variable pressure. Flow filament theory is used to arrive at expressions for the variable inflow velocity under the assumptions of an inviscid and incompressible fluid moving through a small opening under a lock gate at one end of a large rectangular tank containing the deep slightly more dense ambient fluid. Finding this time-dependent inflow velocity, which will then serve as a boundary condition for the solution of our two-layer system, involves solving a forced Riccati equation with time-dependent forcing arising from the surface pressure applied to the fluid in the lock.The results presented here are, to the best of our knowledge, the first to involve variable-inflow surface gravity currents with or without thermal

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Dynamics of Oil Slicks

Cited by 117 publications

References 1 publication

A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

Leakage diffusion of underwater crude oil in wind fields

Thermally Enhanced Motions of Variable‐Inflow Surface Gravity‐Driven Flows

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