On the Nature of Turbulence in a Stratified Fluid. Part I: The Energetics of Mixing

Ivey, Gregory; Imberger, Jörg

doi:10.1175/1520-0485(1991)021<0650:otnoti>2.0.co;2

Cited by 333 publications

(480 citation statements)

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“…[30] In Figure 14, values of Ri f for the three passes are plotted against the overturn Froude number, and compared with the DNS results of Ivey et al [1998]. The present results are generally consistent with the DNS simulations, as well as similar results shown by Ivey and Imberger [1991] which suggest that Ri f should reach a maximum at a value of Fr T equal to 1. However, in both of these previous data sets, values of e nN 2 on the order of those observed in the Fraser lift-off were only associated with much higher values of Fr T , and consequently lower values of Ri f .…”

Section: Turbulence Entrainment and Closuresupporting

confidence: 81%

“…An understanding of these turbulent processes at scales relevant to geophysical flows is an important goal both for engineering applications in the natural environment and for a fundamental understanding of regional dynamics. Most investigations concerning the nature of shear-stratified turbulence, however, are based on laboratory experiments [e.g., Ivey and Imberger, 1991] or observations from relatively low-energy geophysical regimes [e.g., Gregg, 1989], due in large part to the difficulty involved in obtaining reliable measurements from more energetic oceanic environments [Gargett and Moum, 1995].…”

Section: Introductionmentioning

confidence: 99%

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Turbulent energy production and entrainment at a highly stratified estuarine front

2004

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[1] Rates of turbulent kinetic energy (TKE) production and buoyancy flux in the region immediately seaward ($1 km) of a highly stratified estuarine front at the mouth of the Fraser River (British Columbia, Canada) are calculated using a control volume approach. The calculations are based on field data obtained from shipboard instrumentation, specifically velocity data from a ship mounted acoustic Doppler current profiler (ADCP), and salinity data from a towed conductivity-temperature-depth (CTD) unit. The results allow for the calculation of vertical velocities in the water column, and the total vertical transport of salt and momentum. The vertical turbulent transport quantities (u 0 w 0 , S 0 w 0 ) can then be estimated as the difference between the total transport and the advective transport. Estimated production is on the order of 10 À3 m 2 s À3 , yielding a value of e(nN 2 ) À1 on the order of 10 4 . This rate of TKE production is at the upper limit of reported values for ocean and coastal environments. Flux Richardson numbers in this highly energetic system generally range from 0.15 to 0.2, with most mixing occurring at gradient Richardson numbers slightly less than 1 = 4 . These values compare favorably with other values in the literature that are associated with turbulence observations from regimes characterized by scales several orders of magnitude smaller than are present in the Fraser River.

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Section: Turbulence Entrainment and Closuresupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Turbulent energy production and entrainment at a highly stratified estuarine front

2004

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“…This mechanism requires F to be small both for well-mixed and highly stratified conditions, with a maximum at some critical stratification value. The physical justification is that for low stratification p' decreases while for high stratification w' is inhibited; additionally, under high stratification the correlation p'w' is reduced as the nature of the flow changes, with internal wave motions becoming more dominant [Ivey and Imberger, 1991]. Linden [1979,1980] reviewed and did many laboratory experiments on grid-generated mixing across density interfaces and found that in all of them, independent of the stirring rate, the dependence was similar to that required by Phillips' mechanism.…”

Section: The Phillips Mechanismmentioning

confidence: 99%

A mechanism for layer formation in stratified geophysical flows

Pelegrí¹,

Sangrà²

1998

J. Geophys. Res.

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Abstract.We discuss the possibility that steplike structures are formed in subcritical regions of vertically stratified shear flow. The mechanism we propose essentially consists of localized intense mixing in highly stratified and sheared flows, probably following frontogenesis. Its main assumption is that the vertical density flux increases monotonically with decreasing gradient Richardson numbers, which corresponds to enhanced stratification and/or diapycnal shear. This differs from Phillips' [1972] mechanism, which we argue may not apply to vertically stratified shear flow. An essential condition for the formation of constant density steps is the incorporation of a Langevin type equation which takes into account that turbulence must last for some finite characteristic time. We present numerical computations for the case of approximately constant diapycnal shear which lead to the formation of a staircase depth-density structure. The Phillips MechanismPhillips [1972] suggested that small perturbations in an initially well stratified density profile will grow with time if a local increase in the vertical density gradient is accompanied by an even larger decrease of the (turbulent) vertical density diffusivity K. In this case, the vertical density flux will become smaller (larger) with increasing (decreasing) stratification, leading to vertical density divergence (convergence) where the density perturbation is negative (positive). The density perturbations will turn into progressively better defined steps, until the turbulent density flux becomes equal in the well-stratified and well-mixed portions of the staircase. He further parameterized K in terms of some local Richardson number, to show that the density layers will form when the turbulent density diffusivity is a large enough inverse function of this local Richardson tions the numerical solution of the density, momentum, and eddy diffusivity equations leads to the formation of evolving staircase type structures. The key assumption for Phillips' mechanism is the dependence of F on density stratification. This mechanism requires F to be small both for well-mixed and highly stratified conditions, with a maximum at some critical stratification value. The physical justification is that for low stratification p' decreases while for high stratification w' is inhibited; additionally, under high stratification the correlation p'w' is reduced as the nature of the flow changes, with internal wave motions becoming more dominant [Ivey and Imberger, 1991]. Linden [1979, 1980] reviewed and did many laboratory experiments on grid-generated mixing across density interfaces and found that in all of them, independent of the stirring rate, the dependence was similar to that required by Phillips' mechanism. Linden [1980] 10, beyond which it became uniform, but they could not accurately confirm that the density flux decreased for values below 1. They further observed that the steps reached an equilibrium state which corresponded to a uniform density flux in the layered regi...

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“…Rose [1966] and Champagne et al [1970], as well as cases L, M, N, O, and P of Tavoularis and Karnik [1989], are excluded as TKE did not show exponential growth in these experiments. For unsheared stratified experiments by Itsweire et al [1986] and Lienhard and van Atta [1990], v′ 2 ¼ u′ 2 is assumed to estimate q, as done by Ivey and Imberger [1991]. Water channel data by Stillinger et al [1983] are not used due to the lack of reported c and availability of similar experiments by Itsweire et al [1986].…”

Section: Discussionmentioning

confidence: 99%

“…Note that there is another common definition Ri f = G/(G + 1) [e.g., Rohr et al, 1984;Ivey and Imberger, 1991], but (12) is used in this study because it is more convenient in developing the parameterizations. Note also that Ri f → ∞ as Sh d → 0 with this definition, because Sh d = 0 and G = 0 in unsheared stratified flows.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Parameterizing individual effects of shear and stratification on mixing in stably stratified shear flows

Shimizu

2012

J. Geophys. Res.

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[1] This study proposes new parameterizations of diapycnal mixing by reanalyzing the results of previous laboratory and numerical experiments on homogeneous stably stratified shear flows. Unlike previous studies that use either the turbulent Froude number Fr or gradient Richardson number Ri g , this study parameterizes nondimensional momentum and buoyancy fluxes as functions of Fr and a turbulent shear number Sh, in order to quantify individual effects of shear and stratification. Turbulent momentum flux is found to depend linearly on Sh and to decrease monotonically with decreasing Fr. Turbulent buoyancy flux has a peak at moderate Fr. With increasing Sh, it decreases and increases at high and low Fr, respectively. The increase of Sh also cause relatively small but significant decreases of nondimensional turbulent properties, such as the nondimensional conversion rate of turbulent potential energy to background potential energy. The proposed parameterizations lie within the scatter of limited available field data. The parameterizations may be reduced to Ri g -based ones by incorporating the relationship between Ri g and turbulence intensity observed in the field. Existing stability functions for two-equation turbulent closure schemes are found to over-predict mixing efficiency at low Fr.

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On the Nature of Turbulence in a Stratified Fluid. Part I: The Energetics of Mixing

Cited by 333 publications

References 0 publications

Turbulent energy production and entrainment at a highly stratified estuarine front

Turbulent energy production and entrainment at a highly stratified estuarine front

A mechanism for layer formation in stratified geophysical flows

Parameterizing individual effects of shear and stratification on mixing in stably stratified shear flows

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