Gravity currents propagating into shear

Nasr-Azadani, Mohamad M.; Meiburg, Eckart

doi:10.1017/jfm.2015.398

Cited by 7 publications

(19 citation statements)

References 31 publications

(69 reference statements)

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“…with respect to y i and using boundary condition , we obtain

ξ (y_{normali}) = - y_{normali} + h + \frac{H}{ΔU} \sqrt{2 ĝh} \times 2.45em (1 - {({}, 1 - \frac{{(U_{normalg} + \frac{ΔU}{2})}^{2} - {(U_{normalg} + \frac{ΔU}{2} - \frac{ΔU}{H} y_{normali})}^{2}}{2 ĝh})}^{\frac{1}{2}} 2.45em) .

Imposing the boundary condition at ξ ( H ) = 0 in Eq. provides the gravity‐current velocity in form

U_{normalg} = (1 - \frac{h}{H}) \sqrt{2 ĝh} - \frac{1}{2} {(1 - \frac{h}{H})}^{2} ΔU,

which is identical to the result obtained by Nasr‐Azadani and Meiburg (). We remark that Xu () extended Benjamin ()'s approach to the same configuration and analyzed flows with and without energy dissipation.…”

Section: Validation and Comparisonsupporting

confidence: 82%

“…Rotunno et al , ; Xu and Moncrieff, ). Several idealized models have been introduced for such configurations, among them ambient flows with constant shear or a sharp velocity jump (Xu, ; Xue et al , ; Xue, ; Nasr‐Azadani and Meiburg, ). The present framework allows us to move beyond these highly idealized models and to consider more general nonlinear velocity and density profiles.…”

Section: Model Predictions Versus Simulation Resultsmentioning

confidence: 99%

“…By comparing model predictions with direct numerical simulation (DNS) results, the authors demonstrate that their approach results in improved accuracy compared with earlier ones. Most recently, Nasr‐Azadani and Meiburg () extended this vorticity‐based modelling approach to gravity currents propagating into unstratified ambients with constant or two‐layer shear and demonstrated very good agreement with DNS results.…”

Section: Introductionmentioning

confidence: 89%

“…The above derivation is valid for quasi‐steady, supercritical gravity currents propagating into ambients characterized by continuous density and velocity profiles. presents the extension to flows with discontinuous, multi‐layered velocity and density profiles (Xue et al , ; Xue, ; White and Helfrich, ; Nasr‐Azadani and Meiburg, ). To determine whether or not the gravity‐current velocity U g is supercritical, we define the Froude number

Fr = \frac{U_{normalg}}{α scriptNH} .

Here,

scriptN

denotes the buoyancy frequency in the ambient, and α = 1/ π for linearly stratified ambients.…”

Section: Problem Definition and Theoretical Modelmentioning

confidence: 99%

“…Gravity currents propagating into constant density ambients with uniform shear have been investigated by several authors (see Xu, ; Xue et al , ; Xue, ; Bryan and Rotunno, , ; Nasr‐Azadani and Meiburg, ). In the steady reference frame, we define the velocity far upstream as

u_{normali} (y_{normali}) = U_{normalg} + \underset{U_{normali} (y_{normali})}{\underset{\frac{ΔU}{2} (1 - \frac{2 y_{normali}}{H})}{false}},

where ΔU denotes the velocity difference between the bottom and top walls at the inlet.…”

Section: Validation and Comparisonmentioning

confidence: 99%

See 4 more Smart Citations

Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity‐based modelling

Nasr-Azadani

Meiburg

2016

Quart J Royal Meteoro Soc

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We develop a vorticity-based approach for modelling quasi-steady, supercritical gravity currents propagating into a finite-height channel with arbitrary density and velocity stratification. The model enforces the conservation of mass, horizontal and vertical momentum. In contrast to previous approaches, it does not rely on empirical, energybased closure assumptions. Instead, the effective energy loss of the flow can be calculated a posteriori. The present model results in the formulation of a second-order, nonlinear ordinary differential equation (ODE) that can be solved in a straightforward fashion to determine the gravity-current velocity, along with the downstream ambient velocity and density profiles. Comparisons between model predictions and direct numerical simulations (DNS) show excellent agreement. Furthermore, they indicate that, for high Reynolds numbers, the gravity-current height adjusts itself so as to maximize the loss of energy.

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“…with respect to y i and using boundary condition , we obtain

ξ (y_{normali}) = - y_{normali} + h + \frac{H}{ΔU} \sqrt{2 ĝh} \times 2.45em (1 - {({}, 1 - \frac{{(U_{normalg} + \frac{ΔU}{2})}^{2} - {(U_{normalg} + \frac{ΔU}{2} - \frac{ΔU}{H} y_{normali})}^{2}}{2 ĝh})}^{\frac{1}{2}} 2.45em) .

Imposing the boundary condition at ξ ( H ) = 0 in Eq. provides the gravity‐current velocity in form

U_{normalg} = (1 - \frac{h}{H}) \sqrt{2 ĝh} - \frac{1}{2} {(1 - \frac{h}{H})}^{2} ΔU,

Section: Validation and Comparisonsupporting

confidence: 82%

Section: Model Predictions Versus Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 89%

Fr = \frac{U_{normalg}}{α scriptNH} .

Here,

scriptN

denotes the buoyancy frequency in the ambient, and α = 1/ π for linearly stratified ambients.…”

Section: Problem Definition and Theoretical Modelmentioning

confidence: 99%

u_{normali} (y_{normali}) = U_{normalg} + \underset{U_{normali} (y_{normali})}{\underset{\frac{ΔU}{2} (1 - \frac{2 y_{normali}}{H})}{false}},

where ΔU denotes the velocity difference between the bottom and top walls at the inlet.…”

Section: Validation and Comparisonmentioning

confidence: 99%

See 3 more Smart Citations

Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity‐based modelling

Nasr-Azadani

Meiburg

2016

Quart J Royal Meteoro Soc

Self Cite

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Gravity and Turbidity Currents: Numerical Simulations and Theoretical Models

Meiburg

Nasr-Azadani

2017

Mixing and Dispersion in Flows Dominated by Rotation and Buoyancy

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Kinematics of an Ebb Plume Front in a Tidal Crossflow

Honegger,

Ralston,

Jurisa

et al. 2024

JGR Oceans

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X‐band marine radar observations and a hindcast simulation from a 3D hydrostatic model are used to provide an overview of Connecticut River (USA) ebb plume front expansion into the strong tidal crossflow of eastern Long Island Sound. The model performance is evaluated against in situ and remote sensing observations and demonstrates dominant control of the front by semidiurnal tides. The recurring frontal evolution is classified into three dynamical stages of arrest, propagation, and advection. A conceptual model that follows this progressing balance between outflow buoyancy and crossflow momentum qualitatively reproduces frontal evolution in both the radar observations and the hindcast. The majority of the residual, intertidal variability of front timing and geometry is explained by co‐varying tidal amplitude, freshwater discharge, and wind stress using a multi‐linear regression analysis of the radar observation record. Intrinsic front speeds in the modeled frontal propagation are compared with the analytical model of Benjamin (1968, https://doi.org/10.1017/s0022112068000133), with better agreement achieved after accounting for ambient near‐surface shear associated with wind forcing.

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Gravity currents propagating into shear

Cited by 7 publications

References 31 publications

Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity‐based modelling

Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity‐based modelling

Gravity and Turbidity Currents: Numerical Simulations and Theoretical Models

Kinematics of an Ebb Plume Front in a Tidal Crossflow

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