Lock-exchange test

Figure 5.24 a side-by-side comparison is presented of the FVCOM salinity current and the laboratory salinity density current. Figure 5.23 compares the measured speeds in the primary and secondary salinity density currents with the FVCOM prediction for two coefficients of friction (Full-slip and 0.05). The speed of the primary density current is accurately represented by FVCOM; however, the speed of the secondary current is overestimated. This may be due to internal losses (internal hydraulic jump) that are not represented in the hydrostatic version of FVCOM that was used here (Zhu and Lawrence, 2000).

Table 5.6 shows a reasonable match for the constant-speed phase of the process, not only for the full-slip condition but also for condition with a high friction coefficient.

Table 5.6: Root Mean Square speed of propagation for the primary saltwater density current

Case RMS Speed of propagation for the saltwater

current, cm/s Standard deviation cm/s ,

Observed 5.23 0.36

Modeled full-slip 5.44 0.37

Modeled Cf=0.05 5.41 0.30

Figure 5.23: Speed of propagation versus time of the lock-exchange test with 21 sigma levels. Time, seconds U ve lo ci ty, cm /s 0 50 100 150 200 250 300 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Modeled full-slip Modeled Cf=0.05 Observed

Figure 5.24: Advancement of the saltwater plume in the lock exchange test for both the experiment and numerical cases [side view]. Note: the FVCOM Images have greater vertical distortion.

5.2.3.2 25% Constriction

In a similar way to the lock exchange test, the 25% constricted case shows an accelerating phase for the first seconds of the run, and a constant-speed phase before the gravity current reaches the end wall. Simpson (1987) described similar results in his experiments. For this case, during the constant-speed phase, the speed of the density current is smaller than that of the lock exchange test because the constriction restricts the advancement of the plume. Figure 5.25 compares the salinity density current speed predicted by FVCOM with the observed speed. The acceleration phase and the primary density currents are very well modeled. The secondary current speed is overestimated as it was in the lock exchange scenario. Table 5.6 compares the primary salinity density current speed predicted by FVCOM with the observed value. The agreement for the primary density current is acceptable; however, the model overestimated the propagation speeds for the secondary and subsequent density currents. As in Scenario 1, it is suspected that the internal losses and mixing due to the internal jump may have not been fully captured by the hydrostatic version of FVCOM.

Table 5.6: Root Mean Square velocities for the saltwater density current for the observed data

Case RMS Speed of

propagation for the saltwater current cm/s FVCOM Primary Speed cm/s

Lock Exchange Test 5.23 5.4-5.44*

25% Constriction 4.43 3.9-4.4

50% Constriction 4.15 4.2-4.25

86% Constriction 4.21 4.3-4.4

The Brunt-Vaisala frequency of approximately 1/6 Hz (~1 rad/s) is captured by the FVCOM model in the primary density current; however the frequency for the secondary current is slightly underestimated relative to the physical model observations.

Time, seconds U v e lo c it y, cm /s 0 50 100 150 200 250 300 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Modeled full-slip Modeled Cf=0.05 Observed

Figure 5.25: Speed of propagation versus time of 25% constriction case with 21 sigma levels

5.2.3.3 50% Constriction

In this experiment, Figure 5.26 shows that the speed of propagation of the saltwater plume is even smaller than that of the 25% constriction. Table 5.6 shows the RMS speed of propagation for the constant-speed for all the cases. The RMS velocity for

the 50% case was 4.15 cm/s, which is the smallest of all the experiments. Table 5.6 shows that the full-slip and the 0.05 friction coefficient FVCOM predicted the speed of propagation of this primary density current very well. As in Scenarios 1 and 2 the secondary density current speed is overestimated. The primary Brunt-Vaisala frequency is captured but the secondary frequency is underestimated.

Time, seconds U ve lo city, cm /s 0 50 100 150 200 250 300 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Modeled full-slip Modeled Cf=0.05 Observed

Figure 5.26: Speed of propagation versus time of the 50% constriction case with 21 sigma levels.

5.2.3.4 86% Constriction

Figure 5.27 presents the observed and modeled salinity density currents for Scenario 4.

As shown in Table 5.6, the RMS speed of propagation of the saltwater plume is smaller than that of the 25% constriction, but slightly larger than the speed of the 50% constriction. The mean speed of the primary density current is modeled adequately for the first 100 s. The FVCOM model predicts larger secondary current (return flow) from the end wall than the physical model; it is likely that the hydrostatic model has

underestimated the mixing processes in the enclosed basin. The primary Brunt-Vaisala frequency is captured but the amplitude is underestimated by FVCOM.

Overshooting is predicted by the numerical model, the case with a high shear stress coefficient approaches more to the observed results; however, the model does not account for all the internal losses probably due to non-hydrostatic effects (Zhu and Lawrence, 2000).

Time, seconds Uv e lo c it y , c m /s 0 50 100 150 200 250 300 -7 -6 -5 -4 -3 -2 -1 0 1 2 Modeled full-slip Modeled Cf=0.005 Observed

Figure 5.27: Speed of propagation versus time of the 86% constriction case with 21 sigma levels for Scenario 4.

Table 5.6 shows the speed of propagation decreased with increasing constriction until at the 86% constriction, the speed of propagation increased. Since the density current is passing through a very narrow opening, it undergoes an internal transcritical condition forcing the flow to accelerate on leaving the dense-fluid reservoir upstream from the opening as illustrated in Figure 5.29. The reservoir behaves as a potential energy source, which is converted into kinetic energy by motion of the fluid that not only

experiences an internal critical condition but also a hydraulic jump downstream from the contraction. Army (1986) confirms that these conditions can occur in flows through a contraction.

Figure 5.28: Advancement of the saltwater plume through the 86% constriction for both the experiment and FVCOM (Plan view). Note: longitudinal scale is compressed relative to the Physical Model

For the time interval between the 110 and 180 seconds; despite the high friction coefficient, the model did not match the observed results. Overprediction of the speed could be influenced by non-hydrostatic and friction effects because the model does not completely account for: all internal energy losses, shear stresses at the sidewalls, interface shear between the two layers, and non-hydrostatic effects (Zhu and Lawrence, 2000 and 1998). Fringer et al., (2006) indicates in their results that non-hydrostatic simulation captures the correct front speed for both the overflow and underflow cases, whereas the hydrostatic simulation underpredicts both speeds. The hydrostatic simulation does not properly capture neither the generation of the Kelvin-Helmholtz billows nor the Holmboe instabilities. Zhu and Lawrence (1998 and 2000) found that CFD models based only on the hydrostatic assumption limit the prediction of the hydrodynamic variables. Figures 5.30 and 5.31 show the Kelvin-Helmholtz and Holmboe instabilities observed in the cases of 86% constriction and Lock Exchange test, respectively. FVCOM is a hydrostatic model, and it captures the Brunt-Vaisala frequency of 1 rad/s or 6 seconds shown in Figure 5.23. According to Linden and Kleissl (2007), the strength of the stratification is proportional to this frequency. If a parcel of fluid in a stable equilibrium experiences a vertical displacement, it will move towards the equilibrium position but it will over-shoot and then oscillate about the equilibrium position until the system is damped. The

Figure 5.30: Kelvin-Helmholtz instabilities developed in the case with a constricted width of 86% [Side view]

Figure 5.31: Holmboe instabilities developed in the lock exchange test case [Side view] According to Smyth and Peltier (1989), Holmboe instabilities are predominant when the degree of stratification is strong, as in the case of the lock exchange test case, where half-depth of the water column is filled with saltwater an the other half with freshwater. On the contrary, weak stratification tends to develop Kelvin-Helmholtz billows, as in the case with 86% constriction. For this case, the constricted passage restricts the advancement of the denser fluid; hence, the thin layer of saltwater that has passed through the constriction, in combination with a majority of freshwater in the rest of the water column brings the condition to a weak stratification.