On the front conditions for gravity currents in channels of general cross-section

Ungarish, Marius

doi:10.1007/s10652-015-9443-y

Cited by 4 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of their influence in the dynamics of the atmosphere, the ocean and even industrial applications (Fleischmann et al, 1994), gravity currents have been the subject of numerous studies. Many of them have focused on experimental gravity currents propagating over smooth flat bottoms or over smooth slopes using the typical lock-exchange configuration (Mitsudera and Baines, 1992;Simpson, 1980;Reuten et al, 2010;Linden, 2006;Shin et al, 2004;Adduce et al, 2011;Lowe et al, 2002;Ungarish, 2016;Balasubramanian and Zhong, 2018;Mukherjee and Balasubramanian, 2020;Mukherjee and Balasubramanian, 2021.). Nevertheless, in nature, gravity currents propagate over complex topographies.…”

Section: Introductionmentioning

confidence: 99%

Experimental downslope gravity currents over a synthetic topography

Cuevas

Ruiz‐Angulo

Ramos-Musalem

et al. 2023

Atm.

View full text Add to dashboard Cite

Experimental lock-release gravity currents are investigated as they propagate downslope over a synthetic varying topography. We emulate and investigate the dynamics of thermally driven winds that propagate downslope while interacting with the roughness of a topographic surface. The mixing processes between the gravity currents and their surroundings are studied with Particle Image Velocimetry (PIV) and entrainment is quantified. The magnitude of the entrainment coefficient is shown to increase as the roughness of the slope increases. Shadowgraph visualizations qualitatively reproduce this behavior. Finally, pressure fields are estimated from velocity fields and the arrival of gravity currents is shown to be detected in pressure time series. This last result may be useful to detect atmospheric gravity currents using only surface pressure measurements.

show abstract

Section: Introductionmentioning

confidence: 99%

Experimental downslope gravity currents over a synthetic topography

Cuevas

Ruiz‐Angulo

Ramos-Musalem

et al. 2023

Atm.

View full text Add to dashboard Cite

show abstract

Thin-layer models for gravity currents in channels of general cross-section area, a review

Ungarish

2017

Environ Fluid Mech

View full text Add to dashboard Cite

Benjamin’s gravity current into an ambient fluid with an open surface

Ungarish

2017

J. Fluid Mech.

View full text Add to dashboard Cite

We present the solution of the idealized steady-state gravity current of height $h$ and density $\unicode[STIX]{x1D70C}_{1}$ that propagates into an ambient motionless fluid of height $H$ and density $\unicode[STIX]{x1D70C}_{2}$ with an upper surface open to the atmosphere (open channel) at high Reynolds number. The current propagates with speed $U$ and causes a depth decrease $\unicode[STIX]{x1D712}$ of the top surface. This is a significant extension of Benjamin’s (J. Fluid Mech., vol. 31, 1968, pp. 209–248) seminal solution for a fixed-top channel ($\unicode[STIX]{x1D712}=0$). In the present case, the determination of $\unicode[STIX]{x1D712}$ is part of the problem. The dimensionless parameters of the problem are $a=h/H$ and $r=\unicode[STIX]{x1D70C}_{2}/\unicode[STIX]{x1D70C}_{1}$. We show that a control-volume analysis determines $\tilde{\unicode[STIX]{x1D712}}=\unicode[STIX]{x1D712}/H$ and $\mathit{Fr}=U/(g^{\prime }h)^{1/2}$ as functions of $a$ and $r$, where $g^{\prime }=(r^{-1}-1)g$ is the reduced gravity. The system satisfies balance of volume and momentum (explicitly), and vorticity (implicitly). We develop two branches (models) of solution for the control-volume balances. The first assumes that the outflow velocity $u_{2}$ is $z$-independent, accompanied by a similarly homogeneous headloss; this model is exactly the counterpart of Benjamin’s solution ($z$ is the vertical coordinate). The second model assumes that $u_{2}$ increases from $0$ in a layer of finite thickness $\unicode[STIX]{x1D702}$ (say) above the $z=h$ interface, and the headloss occurs in this layer only (a vortex wake). The $\mathit{Fr},\tilde{\unicode[STIX]{x1D712}}$ results of these models are in excellent agreement, and this increases the confidence concerning the physical relevance of the analysis. (The solution is obtained numerically.) The predicted flows are in general dissipative, and thus physically energetically valid only for $a\leqslant a_{max}(r)\approx 0.5r$, where non-negative dissipation appears. In this range of validity, the open-surface $\mathit{Fr}(a,r)$ is smaller than Benjamin’s $\mathit{Fr}_{b}(a)$, but the reduction is not dramatic, typically a few per cent. The current with thickness $h=a_{max}H$ is energy conserving. For given $r$, the energy conserving $a_{max}(r)$ provides the maximum height depression $\tilde{\unicode[STIX]{x1D712}}_{max}(r)\approx 0.45r^{1/4}(1-r)$. The largest possible depression is $\tilde{\unicode[STIX]{x1D712}}_{max}\approx 0.25$ at $r\approx 0.20$, and this corresponds to the minimum of $\mathit{Fr}(a,r)/\mathit{Fr}_{b}(a)$ which is approximately 0.75. For $r<0.68$, the propagation is subcritical; for $r>0.68$, the subcritical flow condition reduces the applicability slightly to $a\leqslant a_{\mathit{crit}}\approx 0.345$. For a Boussinesq system with $r\approx 1$, we obtain $\tilde{\unicode[STIX]{x1D712}}\ll 1$, and the present $\mathit{Fr}$, dissipation and $a_{\mathit{crit}}$ results differ only slightly from Benjamin’s classical predictions, as expected.

show abstract

On the front conditions for gravity currents in channels of general cross-section

Cited by 4 publications

References 29 publications

Experimental downslope gravity currents over a synthetic topography

Experimental downslope gravity currents over a synthetic topography

Thin-layer models for gravity currents in channels of general cross-section area, a review

Benjamin’s gravity current into an ambient fluid with an open surface

Contact Info

Product

Resources

About