Laboratory Experiments of Dense Water Descending on Continental Slope

Nagata, Yutaka; Kimura, Ryuji; Honji, Hiroyuki; Yamazaki, Y. H.; Kawaguchi, Kazuhiro; Hosoyamada, Tokuzo

doi:10.1016/s0422-9894(08)71335-7

Cited by 10 publications

(18 citation statements)

References 10 publications

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“…This was also observed by Condie (1995) for low viscosity and intermediate rotation rates, as well as Etling & Chabert d'Hieres (1997) for high rotation rates, low slope, low density excess and a weak source rate. Similar laboratory observations of eddy production by a constant source of dense fluid have been made by Nagata et al (1993) and Zatsepin, Didkovski & Semenov (1998). (For laboratory studies of the propagation characteristics of the eddies themselves, see Mory, Stern &Griffiths 1987 andWhitehead et al 1990.)…”

Section: Introductionsupporting

confidence: 76%

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On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

Choboter

Swaters

2000

J. Fluid Mech.

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The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections of that layer are not small with respect to its scale height. The upper-layer dynamics are quasi-geostrophic, with the Eulerian velocity field principally driven by baroclinic stretching and a background topographic vorticity gradient.Necessary conditions for instability, a semicircle-like theorem for unstable modes, bounds on the growth rate and phase velocity, and a sufficient condition for the existence of a high-wavenumber cutoff are presented. The linear stability equations are solved exactly for the case where the gravity current initially corresponds to an annulus flow with parabolic height profile with two incroppings, i.e. a coupled front. The dispersion relation for such a current is solved numerically, and the character istics of the unstable modes are described. A distinguishing feature of the spatial structure of the perturbations is that the perturbations to the downslope incropping are preferentially amplified compared to the upslope incropping. Predictions of the model are compared with recent laboratory data, and good agreement is seen in the parameter regime for which the model is valid. Direct numerical simulations of the full model are employed to investigate the nonlinear regime. In the initial stage, the numerical simulations agree closely with the linear stability characteristics. As the in stability develops into the finite-amplitude regime, the perturbations to the downslope incropping continue to preferentially amplify and eventually evolve into downslope propagating plumes. These finally reach the deepest part of the topography, at which point no more potential energy can be released.

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Section: Introductionsupporting

confidence: 76%

“…Smith 1977;Nagata et al 1993;Zatsepin et al 1996Zatsepin et al , 1998 the dispersion relation when h � B = −1. The growth rate and phase speed appear qualitatively similar to those shown in figure 2.…”

Section: Solution For a Parabolic Height Profilementioning

confidence: 98%

On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

Choboter

Swaters

2000

J. Fluid Mech.

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“…To examine dense water formation and the transient behavior of descending dense water plumes on continental slopes, we propose a time‐dependent, two‐layer, reduced‐gravity model with a rotation and vertical viscosity [this model includes that of Nagata et al [1993] as a special case as follows: where V 1 = u 1 + iv 1 , V 2 = u 2 + iv 2 , with i = . Boundary and conjunction boundary conditions are and the initial conditions (t = 0) are where the subscripts 1 and 2 denote the upper and lower layers, respectively (Figure 1), v is vertical viscosity (units are m 2 s −1 ), f is the Coriolis parameter (units are s −1 ), g ′ = g Δρ/ρ is the reduced gravity (where Δρ = ρ 2 − ρ 1 ).…”

Section: A Two‐layer Reduced‐gravity Modelmentioning

confidence: 99%

“…If it is further assumed that the system is irrotational and steady state ( f = 0 and ∂/∂ t = 0), then we can only obtain a downslope transport of the dense water with no alongshore component. This case has been thoroughly investigated by laboratory experiment [ Nagata et al , 1993] and numerical modeling [ Jungclaus and Backhaus , 1994; Jiang and Garwood , 1996; Wang et al , 1999]. Therefore, no further discussion is necessary.…”

Section: A Two‐layer Reduced‐gravity Modelmentioning

confidence: 99%

“…The density difference between the ambient water and the dense water plume was also examined. Nagata et al [1993] developed an analytical, steady state, two‐layer model to explain these experimental results. The classic, steady state bottom Ekman layer solution was obtained; however, no detailed explanation of the bottom Ekman layer contribution to dense water offshore transport was given, because their steady state model cannot explain transient (time‐dependent) behavior of the formation of the dense water.…”

Section: Introductionmentioning

confidence: 99%

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A theoretical, two‐layer, reduced‐gravity model for descending dense water flow on continental shelves/slopes

2003

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A theoretical, two‐layer, reduced‐gravity model for descending dense water flow on continental shelves/slopes has been developed to investigate the dynamics of bottom dense water plumes. The model is nonsteady state and includes vertical viscosity, the Coriolis force, and bottom friction. An integral solution rather than a perfect analytical expression is derived and, thus, the Simpson's 1/3 rule to approximate the integral is applied. At the very bottom, the dense water plume moves about 45° to the right (left) in the Northern (Southern) Hemisphere, looking downslope. From the bottom, the velocity vector rotates anticyclonically upward, indicating a bottom Ekman spiral that mimics the atmospheric Ekman boundary layer. The dense water within the bottom Ekman layer obeys a three‐force balance, while the dense water above the bottom Ekman layer is governed by a two‐force balance, which is a geostrophic flow with superimposed cycloidal inertial oscillations oriented from about 25° to 140° to the right (left) of the downslope direction in the Northern (Southern) Hemisphere. The transport within the bottom Ekman layer is directed about 60–70° to the right (left) of the downslope direction in the Northern (Southern) Hemisphere, forming an offshore (cross‐isobath) transport in the absence of eddy flux and wind‐forcing. The ratio of offshore transport to alongshore transport within the bottom Ekman layer is about 0.19 (19%), while the ratio above the bottom Ekman layer (i.e., geostrophic layer of the dense water) is only 3% (negligible compared to its alongshore transport), which, however, is equivalent in magnitude to its counterpart in the bottom Ekman layer if O(DE/h) ∼ 0.1 (where DE is the bottom Ekman layer thickness and h is the dense water layer thickness). In other words, the bottom Ekman layer and the geostrophic (dense) layer contribute equivalent dense water offshore (each contributes 50%). The magnitude of the descending dense water velocity depends linearly on reduced gravity and sin(θ) (slope angle).

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Experiments on turbulent convection over a rotating continental shelf–slope

2008

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A series of Southern Hemisphere experiments have been performed to study turbulent convection on a continental shelf–slope placed in a large rotating tank filled with fresh water. Dense salt water was uniformly released at the fluid surface above the shelf. The resulting negatively buoyant bottom flow travelled over the shelf and then downslope. The non-dimensional reduced gravity of the dense downslope flow was found to scale as$G'\,{=}\,g'h^{4/3}/(B_{0}^{2/3}W)$for a fixed slope angle, whereB0the buoyancy flux at the surface,g′ the reduced gravity of the bottom flow,hthe water depth above the shelf andWthe width of the dense water source. Under rotation, a bottom Ekman layer, with superimposed roll waves, propagated down the slope and towards the left sidewall when looking down the slope. As the modified natural Rossby numberPdecreased, whereP= (B0/f3h2)1/2W/handfis the Coriolis parameter, the appearance of the bottom layer had four different forms: laminar flow, the continuous formation of waves, the periodic release of wave groups, and the periodic generation of eddies. Vortices generated on the surface were cyclonic, suggesting, but not proving, that eddies in the dense bottom layer as originally formed were anticyclonic.With a canyon cut from the middle of the shelf to the bottom of the slope,G′ values measured in dense flows to the left of the canyon, were significantly reduced. The canyon channelled a large amount of dense fluid with a buoyancy considerably larger than that of dense flows on the slope. However, the flow regime criteria remained basically unchanged with eddies and downslope Ekman layer being able to partially cross the canyon.

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Laboratory Experiments of Dense Water Descending on Continental Slope

Cited by 10 publications

References 10 publications

On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

A theoretical, two‐layer, reduced‐gravity model for descending dense water flow on continental shelves/slopes

Experiments on turbulent convection over a rotating continental shelf–slope

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