Particle-bearing currents in uniform density and two-layer fluids

Lock-release gravity current experiments are performed to examine the evolution of a particle bearing flow that propagates either in a uniform-density fluid or in a two-layer fluid. In all cases, the current is composed of fresh water plus micrometer-scale particles, the ambient fluid is saline, and the current advances initially either over the surface as a hypopycnal current or at the interface of the two-layer fluid as a mesopycnal current. In most cases the tank is tilted so that the ambient fluid becomes deeper with distance from the lock. For hypopycnal currents advancing in a uniform density fluid, the current typically slows as particles rain out of the current. While the loss of particles alone from the current should increase the current's buoyancy and speed, in practice the current's speed decreases because the particles carry with them interstitial fluid from the current. Meanwhile, rather than settling on the sloping bottom of the tank, the particles form a hyperpycnal (turbidity) current that advances until enough particles rain out that the relatively less dense interstitial fluid returns to the surface, carrying some particles back upward. When a hypopycnal current runs over the surface of a two-layer fluid, the particles that rain out temporarily halt their descent as they reach the interface, eventually passing through it and again forming a hyperpycnal current. Dramatically, a mesopycnal current in a two-layer fluid first advances along the interface and then reverses direction as particles rain out below and fresh interstitial fluid rises above.

Figure 1

Schematic of the setup in general for experiments performed in a rectangular tank tilted at an angle $\theta$ to the horizontal of particle-bearing fresh water currents released from a triangular lock of length $L_{\ell }$ and height $H_{\ell }$ into a uniform-density or two-layer ambient fluid. In the case of a two-layer ambient (pictured), an upper layer with depth $H_1$ of salty fluid having density ${\rho }_1$ overlies still saltier fluid having density ${\rho }_2$. In most experiments the ambient has uniform density such that ${\rho }_{\ell }<{\rho }_1$ (hypopycnal flow). In experiments with a two-layer ambient fluid either ${\rho }_{\ell }<{\rho }_1$ (hypopycnal flow) or ${\rho }_1<{\rho }_{\ell }<{\rho }_2$ (mesopycnal flow).

Figure 2

Snapshots from an experiment of a hypopycnal current of fresh water with suspended glass ballotini advancing into a uniform density saline ambient at (a) $t=0$ s, (b) $t=15$ s, (c) $t=30$ s, (d) $t=45$ s, (e) $t=60$ s, (f) $t=120$ s, and (g) $t=180$ s. The experiment parameters for the tank slope, lock height, and ambient density are $\theta =6^{\circ },H_{\ell }=2.3\mathrm{cm}$, and ${\rho }_1=1.0310\text{g}/{\text{cm}}^3$. The lock fluid has $2.2\mathrm{g}$ of $d_p=11\mu \mathrm{m}$ ballotini added to the fresh water in the lock, giving it a lock density of ${\rho }_{\ell }=1.0051\text{g}/{\text{cm}}^3$. The red arrow in (d) points at the stopping location measured from horizontal time series. The stopping time occurs at $t=37\mathrm{s}$.

Figure 3

(a) Along-surface and (b) along-slope time series taken from an experiment with snapshots shown in Fig. 2. The white lines in both images indicate the position of the front over time where the intensity decreases significantly due to a change in particle concentration with $x$. In (b) this is drawn only after formation of the hyperpycnal current. The closed circles in (a) and (b) indicate the start and end locations between which a best-fit line is found to the front position. The red arrow in (a) indicates where the front is taken to come to a near halt.

Figure 4

Measured initial speed of hypopycnal current compared with theory for hypopycnal currents of fresh water mixed with particles consisting of $5-\mu \mathrm{m}$-diam (closed circles) and $11-\mu \mathrm{m}$-diam (open circles) glass spheres, particles of silicon carbide (crosses), and different clay samples. The diagonal black line is the one-to-one line where observations match theory.

Figure 5

Measured initial stopping distance of hypopycnal current compared with theory. The diagonal black line is the best-fit line through the data that passes through the origin. Its slope is indicated. Typical error bars for the data are indicated in the lower-right corner of the plot.

Figure 6

Measured height of hyperpycnal current plotted against the depth of the ambient fluid at the predicted hypopycnal current stopping position from the gate. Typical error bars are indicated toward the lower right of the plot. The slope of the best-fit line through all the points is indicated.

Figure 7

Measured speed of hyperpycnal current compared with theory. Symbols represent different particle types as indicated in the legend. The diagonal line is the one-to-one line where theory matches observations. Typical error bars are shown to the bottom right of the plot.

Figure 8

Measured stopping distance of hyperpycnal current compared to predicted stopping distance. The different particle types are as indicated in the legend in Fig. 4.

Figure 9

Snapshots from an experiment of a hypopycnal current of fresh water with suspended glass ballotini advancing into a two-layer ambient fluid at (a) $t=0$ s, (b) $t=15$ s, (c) $t=30$ s, (d) $t=60$ s, (e) $t=90$ s, and (f) $t=210$ s. The experiment parameters for the tank slope, lock height, upper-layer depth, and ambient upper- and lower-layer densities, respectively, are $\theta =8^{\circ },H_{\ell }=3.0\mathrm{cm},H_1=3\mathrm{cm},{\rho }_1=1.0300\text{g}/{\text{cm}}^3$, and ${\rho }_2=1.0600\text{g}/{\text{cm}}^3$. The lock fluid has $4.74\mathrm{g}$ of ${\overline{d}}_p=5\mu \mathrm{m}$ ballotini added to the fresh water in the lock, giving it a lock density of ${\rho }_{\ell }=1.0094\text{g}/{\text{cm}}^3$. The top image shows the unprocessed snapshot in which the interface is visualized by the dark dyeline situated at $3\mathrm{cm}$ below the surface. The snapshots below have the background intensity subtracted out in order to enhance visualization of particle settling.

Figure 10

Same as in Fig. 9 but showing snapshots from an experiment of a mesopycnal current of fresh water with suspended glass ballotini advancing into a two-layer ambient fluid at (a) $t=0$ s, (b) $t=15$ s, (c) $t=30$ s, (d) $t=45$ s, (e) $t=60$ s, (f) $t=90$ s, and (g) $t=120$ s. The experiment parameters are $\theta =8^{\circ },H_{\ell }=3.0\mathrm{cm},H_1=3\mathrm{cm},{\rho }_1=1.0300\text{g}/{\text{cm}}^3$, and ${\rho }_2=1.0600\text{g}/{\text{cm}}^3$. The lock fluid has $18.96\mathrm{g}$ of ${\overline{d}}_p=5\mu \mathrm{m}$ ballotini added to the fresh water in the lock, giving it a lock density of ${\rho }_{\ell }=1.0418\text{g}/{\text{cm}}^3$.