Turbulent Mixing During an Admiralty Inlet Bottom Water Intrusion. Coastal and Estuarine Fluid Dynamics class project, August 2006

Transcription

1 Turbulent Mixing During an Admiralty Inlet Bottom Water Intrusion Coastal and Estuarine Fluid Dynamics class project, August 2006 by Philip Orton Summary Vertical turbulent mixing is a primary determinant of transport in all but the most stratified estuaries, with vigorous turbulence promoting retention, and stratification promoting along-channel dispersion. A fundamental problem with numerical hydrodynamic modeling, however, is the incomplete representation of the nonlinear physics of turbulence. Numerical models require turbulence parameterizations because of computer processing constraints, but studies have shown that the many available schemes do not reflect turbulence variability over a wide range of freshwater forcing (e.g. Stacey et al., 1999). Studies have clarified the important role of bottom boundary layer turbulence in estuarine dynamics (e.g. Geyer et al., 2000; Chant et al., 2006), a process that is well-predicted by numerical models. Strong stratification or bathymetric forcing can cause more heterogeneous mixing processes to dominate upper water column transports (Sharples et al. 2003; Stenstrom, 2004), and it has been acknowledged that internally driven turbulence (e.g. shear instability) is a more difficult modeling task (Simpson et al., 1996). The purpose of this paper is to examine the degree of localization of mixing during an Admiralty Inlet bottom water intrusion event. The null hypothesis is that mixing during 1

2 the period was spatially uniform. The paper includes: (1) a summary of methods for estimating mixing and dissipation, (2) a consistency check, where the estimated total tidal energy dissipation was compared with an existing estimate of the mean based on tidal records, (3) an analysis of spatial variability with cross-channel and along-channel transects of buoyancy flux, (4) a dynamical explanation that may explain the low mixing during the study, and (5) conclusions relating to the bottom water intrusion into Admiralty Inlet observed during the study. Data Collection From August 4, 2006, 10:28h to August 5, 14:11h, we sampled from the R/V Centennial in three along-thalweg transects and a repeated cross-channel pattern in Admiralty Inlet (Figure 1). The Centennial's SeaBird Electronics SBE19 CTD was used for profiling, with a sampling rate of 2 Hz. The vertical resolution was 0.3 m, based on a 0.6 m s -1 vertical instrument velocity and the assumption that samples are independent. A 300 khz Acoustic Doppler Current Profiler (ADCP), mounted on a vertical pole alongside the vessel, continuously measured current velocity. A narrow bandwidth mode was used for maximum sampling range. The vertical resolution is 4 m, and velocity data are averages of 20 samples over 30 seconds, resulting in velocity standard error of m s -1. A Simrad ES60 38/120 khz split-beam echo sounder provides acoustic backscatter "imagery" below the vessel, with a 5 Hz sampling rate. The tidal range during sampling was 3m (NOAA, unpublished data for Bush Point), and encompassed a strong flood, weak ebb, weak flood, strong ebb, and strong flood. A 2

3 continuous wavelet transform tidal analysis (following methods of Jay and Flinchem, 1999) of predicted tidal data reveals that this was near the annual minimum for semidiurnal band amplitude and a moderate and increasing diurnal band amplitude. Winds were light, and vessel motion minimal during the CTD casts. Turbulence methods, quality control, and uncertainty A CTD instability length scale analysis was conducted using the 138 CTD profiles, with strict quality control and a bootstrap uncertainty analysis. Using a procedure known as the Thorpe sort, a vertical density profile is sorted so that it is monotonically increasing, and the distances over which water parcels were displaced are used to estimate various turbulence parameters. Recent studies show that CTD "fine structure" (i.e. order of 10 cm vertical resolution measurements) can give comparable results to turbulent kinetic energy dissipation () and eddy diffusivity (K ) estimates from microstructure instrumentation for regions with measurable vertical density gradients and energetic mixing (e.g. Klymak and Gregg, 2004). The process of sorting density yields a profile of L, the vertical distance over which each gravitationally unstable density data point has been moved. We compute the Thorpe scale L T as the rms value of L in each "overturn patch", defined as an unstable region where the values of L sum to zero (Seim and Gregg, 1994). Strict quality control methods of Galbraith and Kelley (1996) are used to avoid spurious overturns from measurement noise. Overturn patches with rms density inversions less than the accuracy of the sensor are also eliminated. 3

4 Assumptions of these methods include: (a) the Ozmidov scale (L O ) may be approximated using L T, (b) an overturn has TKE proportional to the available PE, (c) L O is the turbulent energy containing scale, and (d) N is the time-scale for dissipation. Dissipation of turbulent kinetic energy is estimated as (Thorpe, 1977): a Lt N (1) Here, angle brackets denote an average over an overturning patch and the overbar an average over several turbulence patches. There is significant debate over the value of the coefficient a, the ratio of Thorpe to Ozmidov turbulence scales, but for cases with nonnegligible stratification, a 1 is a reasonable approximation (Peters and Johns, 2004; Klymak and Gregg, 2004). The buoyancy frequency, N = [(g/d/dz)] 0.5, is computed over overturn patch heights (Ferron et al., 1998), with a minimum height of 0.25 m. Eddy diffusivity can be computed as (Peters and Johns, 2004): K 2 2 a N L T (2) Here, the mixing efficiency is approximated as 0.22 for coastal stratified flows (Kay and Jay, 2003; Macdonald and Geyer, 2004). The buoyancy flux is then: B = K N 2 = (3) Estimates of B are presented in some cases with bootstrapped 95% confidence intervals, for which a minimum of 10 turbulence patches was required to consider the average representative. In total, 499 patches were found in the 138 CTD profiles. Typically, the CTD observed overturns in about 0-59% of the water column, and estimates of K and are first computed only within these overturning patches (rectangles in Figure 2). 4

5 Where CTD measurements show no overturn, this only demonstrates that there were no overturns with a larger vertical scale or density difference than the resolution of the measurements. Regions with high diffusivity generally coincide with subcritical Richardson number values (Ri<0.25), as expected. The relationship between Ri and K for all profiles combined has substantial scatter, but generally Ri is inversely proportional to K. Results and Discussion Total tidal dissipation An examination of total tidal energy dissipation provides a useful consistency check on our turbulence estimates, yet also roughly distinguishes bottom boundary layer turbulence from internally driven turbulence. The dissipation mean over the entire study was 6.4 x 10-4 W m -3, which is small in comparison to the Hudson River estuary (neap, 10-3, spring, 10-2 W m -3 ; Peters, 1999). Scaled up by the volume of the estuary, this gives a total tidal energy dissipation of 12 MW. This is very small compared with the mean total tidal energy dissipation for the entire Inlet of 514 MW (Lavelle et al., 1988). However, the tidal range was about 3/4 of normal, so we would only expect ~(3/4) 3 or ~40% of this value (using a scaling of U~tidal range, then ~U 3 ). Also, depth-integrated dissipation rates are dominated by the BBL (Peters and Bokhorst, 2000). The total dissipation was estimated as the sum of the "observed" overturn dissipation (12 MW) and the near-bed log-layer dissipation, which is not observed due to negligible vertical density gradients: 5

6 3 h1 * 1 dz ln z0 z0 U Here, the bed roughness length was estimated as 1 mm, and shear velocity (U * ) was computed using a quadratic drag law and drag coefficient of and velocity bin at 5-10 m above the bed. The bottom layer height (h 1 ) was the minimum of: (a) 0.2 times water depth, (b) the first height above the bed where overturns were detected, or (c) the first height above bed where the vertical density gradient was non-negligible (for the CTD resolution). The log layer dissipation, scaled up for the entire estuary, equals 112 MW, so the total during our study was 124 MW, close to that which should be expected based the prior study. h (4) Spatial variability Mixing estimates for the along- and across-channel surveys are presented in Figure 5. There is along-channel spatial variability, with Station 16 having a 95% confidence interval outside the confidence intervals for all the other sites in the southern half of the Inlet. The across-channel survey averages are inconclusive, as the 95% confidence intervals overlap. Moreover, it appears as though cross-channel mixing variability at Bush Point during this period was small. In conclusion, along-channel variability is observed, disproving the null hypothesis. Dynamical explanation for low mixing over most the estuary Computations of the horizontal Richardson number suggest that low levels of mixing in most regions of the estuary are a result of tidal straining of the density field. Assuming 6

7 vertical advection and horizontal diffusion are negligible, the simplified stratification conservation equation is (Stacey et al., 2001): S t z U z S x z 2 2 K S S z (5) The horizontal Richardson number scales the competition between tidal straining and vertical mixing (Stacey et al., 2001): Ri x 2 g h (6) u 2 * The horizontal Richardson number was estimated using a cruise-average ds/dx of 4 x 10-5, the aforementioned U * estimates, a cruise-average value of = 7.58 x 10-4, and depth measured by the ADCP. These show that, apart from the shallow water end of the crosschannel survey, values of Ri x were typically above unity (Figure 6). This provides strong evidence that tidal straining was dominating over vertical mixing in the stratification balance of the estuary during our study. The value for ds/dx was about double the norm in prior studies of the region (Geyer and Cannon, 1982; Lavelle et al., 1991), likely due to relatively strong estuarine circulation and low mixing during the weak tides in the days prior to this study. Conclusions Addressing our null-hypothesis -- was mixing during our study spatially uniform? In terms of cross-channel variability, results were inconclusive. In terms of along-channel variability, our results disprove the hypothesis -- mixing was elevated by O(10) in at least one hotspot. Tidal dissipation estimates were consistent with a prior study, downscaled for small tidal range. Finally, a simplified balance of terms from the stratification 7

8 equation shows that tidal straining can explain the low mixing that occurred in most of the estuary. These conditions were likely highly conducive for a bottom water intrusion event, which was in fact observed during our study. Weak turbulent mixing likely built stratification to above-normal levels during the days prior to our study that had below normal tidal range. During our study, tidal currents were becoming stronger, yet stratification was still strong enough to cap vertical mixing. References Chant, R.J., W.R. Geyer, R. Houghton, E. Hunter, and J. Lerczak, Estuarine boundary layer mixing processes: Insights from dye experiments. Submitted to the Journal of Physical Oceanography. Ferron, B., H. Mercier, K. Speer, A. Gargett, and K. Polzin, Calculated mixing in the Romanche Fracture Zone. J. Phys. Oceanogr., 28, Galbraith, P.S., and Kelley, D.E., Identifying overturns in CTD profiles. Journal of Atmospheric and Oceanic Technology 13: Geyer, W. R., and G. A. Cannon, 1982: Sill processes related to deep water renewal in a fjord. J. Geophys. Res., 87, Geyer, W. R., J. H. Trowbridge, and M. M. Bowen, 2000: The dynamics of a partially mixed estuary. Journal of Physical Oceanography, 30,

9 Jay, D. A. & Flinchem, E. P Interaction of fluctuating river flow with a barotropic tide: a test of wavelet tidal analysis methods. Journal of Geophysical Research 102, Kay, D.J., and D.A. Jay (2003), Interfacial mixing in a highly stratified estuary 1: Characteristics of mixing, J. Geophys. Res., 108(C3), 3072, doi: /2000jc Klymak, J.M., and M.C. Gregg (2004), Tidally generated turbulence over the Knight Inlet sill, J. Phys. Oceanogr., 34, Lavelle, J.W., H.O. Mofjeld, E. Lempriere-Doggett, G.A. Cannon, D.J. Pashinski, E.D. Cokelet, L. Lytle, and S. Gill A multiply-connected channel model of tides and tidal currents in Puget Sound, Washington and a comparison with updated observations. NOAA Tech. Memo. ERL PMEL pp. Lavelle, J. W.; Cokelet, E. D.; Cannon, G. A., A model study of density intrusions into and circulation within a deep, silled estuary: Puget sound. Journal of Geophysical Research, Volume 96, Issue C9, p Macdonald, D.G. and Geyer, W.R., Turbulent Energy Production and Entrainment at a Highly Stratified Estuarine Front. Journal of Geophysical Research 109, C05004, doi: /2003jc Peters, H., Spatial and temporal variability of turbulent mixing in an estuary, J. Marine Res., 57, Peters, H. and R. Bokhorst, Microstructure observations of turbulent mixing in a partially mixed estuary. I: Dissipation rates, J. Phys. Oceanogr., 30, 1232{1244,

10 Peters, H., and Johns, W.E., Mixing and entrainment in the Red Sea outflow plume. II. Turbulence characteristics. Journal of Physical Oceanography, in press. Seim, H.E. and Gregg, M.C., Detailed observations of a naturally occurring shear instability. J. Geophys. Res. 99 (C5): Sharples, J., Coates, M.J., and Sherwood, J.E., Quantifying turbulent mixing and oxygen fluxes in a Mediterranean-type, microtidal estuary. Ocean Dynamics, 53:126:136. Simpson, J. H., Crawford, W.R., Rippeth, T.P., Campbell, A.R. and Cheok, J. V. S The vertical structure of turbulent dissipation in shelf seas. J. Phys. Oceanogr. 26: Stacey MT, Monismith SG, Burau JR (1999) Observations of turbulence in a partially stratified estuary. J. Phys. Oceanogr. 29: Stacey, M.T., Burau, J.R., and Monismith, S.G., Creation of residual flows in a partially stratified estuary. J. Geophys. Res., 106(C8): Stenstrom, P. (2004), Hydraulics and mixing in the Hudson River estuary: A numerical model study of tidal variations during neap tide conditions, J. Geophys. Res., 109, C04019, doi: /2003jc Stansfield, K., Garrett, C., and Dewey, R., The probability distribution of the Thorpe displacement within overturns in Juan de Fuca Strait. Journal of Physical Oceanography 31:3421:3434. Thorpe, S.A Turbulence and mixing in a Scottish loch. Philos. Trans. R. Soc. London A, 286:

11 Figure 1: Map of study site, with thalweg, kilometer distances from the first station, and station numbers. The cross-channel (triangle) survey location is at center, with stations 7, 8E, 8, and 8W. 11

12 Figure 2: Summary of a Thorpe overturn analysis for one CTD profile, with (left) the unstable density profile; (center) a line showing the sorted minus raw density, scaled up by 100, and boxes scaling the patch height with their height and the Thorpe scale with their width; (right) estimates of and K for each patch. 12

13 Figure 3: Turbulent kinetic energy dissipation per unit volume on the three transects, with extrapolation to the bed using a log layer assumption. 13

14 Figure 4: Computed variables relating to mixing, for the three transects: (top) Gradient Richardson number (Ri) shading, with a black line showing the height at which Ri first increases above (bottom) Buoyancy flux, from the overturn analysis. 14

15 Figure 5: Along (top) and across-channel (bottom) survey depth and time average buoyancy fluxes, with 95% bootstrapped confidence intervals. The total number of turbulence patches observed at each station is displayed at the top of each plot. 15

16 Figure 6: Horizontal Richardson number for the cross-channel (triangle) survey are plotted against tidal phase. "F" is greater flood, "e" lesser ebb, "f" lesser flood, and "E" the greater ebb phase of the diurnal cycle. The threshold between straining and mixing dominant conditions (unity) is shown in red. 16