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Fig. (e–h) Vertical x‐z slices of the density field (after subtracting 1000 kg m−3) at 4 different times (phases) in a tidal cycle. (a–d) Spanwise‐averaged streamwise velocities, u (z, t) m/s and density profiles, ρ(z, t, x = 0) at corresponding phases. Background linear density (dashed blue line) profile is also shown. Note that u, x are horizontal while z is vertical. Figure 3a and 3e correspond to maximum downward boundary flow, Figures b and 3f correspond to flow reversal from down to up, Fig. c and 3g correspond to peak up‐slope velocity and, finally, Figure d and 3h correspond to flow reversal from up to down. Here, arrows indicate the flow structures.
The simulation starts with the phase of peak downslope velocity. There is transition to turbulence within approximately 3 hrs in the upper flank of the beam and in approximately 6 hrs at the bottom wall, followed by distinct turbulent mixing events that repeat periodically at different phases of the internal tide cycle as explained below. Figure illustrates the phase variability of density and velocity by showing snapshots at four different times. Figure a at t = 12.8 hrs corresponds to a phase when the downslope flow is near its peak. The corresponding density deviation, ρ*, is small and spans a short region, 0 < z < 20 m. Inspection of Figures (a–d) shows that ρ* lags u by 90°; it is maximum when u is minimum and vice‐versa. At t = 12.8 hrs, the near‐wall shear is large and, in the sheared zone of 0 < z < 20 m, the corresponding density field in Figure e is indicative of both shear instability and fine scale turbulence. From t = 12.8 hrs until t = 16 hr when the velocity becomes approximately zero, the downward flow continues to bring water from above. Consequently, the region between 5 m and 30 m which, at t = 12.8 hrs was occupied by water with density shown by green in Figure e, is replaced by lighter, warmer water at t = 16 hrs, shown by red and yellow in Figure f. Furthermore, this body of relatively lighter, warmer water passes underneath the colder water above it that, being at the edge of the beam, has low velocity. The density profile that results at t = 16 hrs indicates a density inversion as shown in Figure b. The corresponding density field in Figure f shows a mushroom shaped plume suggesting convective instability. The shear at this time is near zero. Note that the density inversion is even more prominent a little earlier at t = 14.5 hrs. Later in time, the large‐scale overturns collapse and break into smaller structures. The shear starts increasing and at t = 18.7 hrs, the velocity profile in Figure c shows maximum upslope velocity and, correspondingly, the near wall flow is again susceptible to shear instability as shown in Figure 3g. The velocity in the next snapshot, Figure d, is almost zero and corresponds to t = 21.4 hrs when the flow reverses from up to down. Between t = 18.7 and 21.4 hrs, the flow decelerates but continues to move upslope and heavy, cold fluid associated with the central portion of the internal tide beam surges up beneath the lighter, low‐velocity fluid above. The cumulative effect of this upsurge is to strengthen the stratification in the upper flank of the beam as shown by the region, 20 < z < 60 m, in the density profile of Figure d. A the same time, the upsurge overtakes low‐velocity, lighter fluid near the wall leading to a density inversion with light fluid beneath dense fluid. Therefore, during flow reversal from up to down, a convective instability with the formation of a mushroom shaped structure occurs in the lower part of the flow as shown in Figure h. The height of the density overturn (<15 m) is significantly smaller than that observed earlier at t = 16 hr during flow reversal from down to up.