# The characterization of the dynamics of a continuous gravity current

Mohamad Harrouk, Rabah Mehaddi, Boris Arcen, Yvan Dossmann

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## To cite this version:

Mohamad Harrouk, Rabah Mehaddi, Boris Arcen, Yvan Dossmann. The characterization of the dynamics of a continuous gravity current. EGU General Assembly 2024, Apr 2024, Vienna (AUSTRIA), Austria. 10.5194/egusphere-egu24-10029. http://hal-04847310

HAL Id: hal-04847310

https://hal.science/hal-04847310v1

Submitted on 19 Dec 2024

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# The characterization of the dynamics of a continuous gravity current

Mohamad Harrouk, Rabah Mehaddi, Boris Arcen, and Yvan Dossmann

CNRS/UL, LEMTA, Vandoeuvre-les-Nancy, France (mohamad.harrouk@univ-lorraine.fr)

The present work investigates the dynamical characteristics of a gravity current produced by a continuous and steady release of a dense fluid, with a source density $ρ_0$, into a lighter ambient fluid, with density $ρ_0 < ρ_0$. A planar geometry is considered in which the ambient fluid is initially at rest inside a rectangular tank and the dense current is continuously released from a source located at the bottom-left corner of the tank. The released current propagates along the horizontal bottom boundary of the domain displacing the ambient fluid. This configuration has been considered experimentally by Sher & Woods (2017). A numerical study has been carried out using the Direct Numerical Simulations (DNS) of the governing equations via the NEK5000 solver. Instantaneous three-dimensional velocity, pressure and density fields were extracted and two-dimensionalized by width-averaging. The state of the release is characterized by the source Froude number $Fr_0 = u_0 / \sqrt{g'_0 h_0}$ with $u_0$ being the velocity of the release, $h_0$ being the height at the inlet, and $g'_0 = g (ρ_0 - ρ_∞)/ρ_∞$ being the source buoyancy. Throughout the series of simulations, we control the state of the current at the source by only varying the source density $ρ_0$, resulting in a range of source Froude number between 0.6 < $Fr_0$ < 2.7, and we seek to record the effects of this variation on the dynamics. The source discharge $Q_0 = u_0 h_0$ and buoyancy flux $B_0 = Q_0 g'_0$ are kept constant over time. The front speed, $u_f$, was shown to remain steady; a well-known feature of continuous gravity currents. A dimensionless parameter, $\lambda = u_f/B_0^{1/3}$, that characterizes the front speed was computed as a function of $Fr_0$ and the result shows a good agreement with the range recorded by Sher & Woods (2017). The entrainment of ambient fluid into the current is parametrized with two methods. First, we estimate the rate of change of the volume of the current, $dV/dt$, and we recorded the range $1.8Q_0 < dV/dt < 2.1Q_0$ for the selected $Fr_0$ range. Secondly, the theory of inclined plumes introduced by Ellison & Turner (1959) was considered to estimate a local entrainment parameter, $E$, as a function of the local stratification represented by the local Richardson number $Ri$. The well-known relation, $E$ proportional to $Ri^{-1}$, was held when $Ri < 0.8$; otherwise, the entrainment parameter tends to near-zero values.