A version of This Work has been submitted to _J. Physical Oceanography_ This Work has not yet been peer-reviewed and is provided by the contributing Author(s) as a means to ensure timely dissemination of scholarly and technical Work on a noncommercial basis. Copyright and all rights therein are maintained by the Author(s) or by other copyright owners. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each Author’s copyright. This Work may not be reposted without explicit permission of the copyright owner. Copyright in this Work may be transferred without further notice. ABSTRACT Deep estuaries are often separated from the open ocean by sills and constrictions. These constrictions are areas of intense mixing often dominating the total estuarine mixing. The amount and depth of the estuarine exchange depends sensitively on the mixing and the densities of the waters on the two sides of the mixing region. Thus, the density, nutrient concentration, oxygen saturation, and dissolved inorganic carbon content of the incoming estuarine flow depend on local tidal mixing processes and large scale buoyancy dynamics. We have investigated this process using a numerical model (SalishSeaCast) of the Salish Sea on the West Coast of North America, straddling the Canada/USA border. The region receives considerable freshwater dominated by the outflow of the Fraser River. The Fraser River first flows into the deep Strait of Georgia but the freshwater must traverse the strongly tidally mixed shallower passages through the Gulf/San Juan Islands before it reaches the Pacific Ocean. The model correctly reproduces the deep water flow into the Strait of Georgia as evaluated against Ocean Networks Canada (ONC) four bottom-mounted, continuously recording, conductivity-temperature instruments which capture this incoming flow. Using a four-year hindcast from the model we determine the amount, depth and position of the outflow and inflow. We show that 95% of the variance of the 4-day average baroclinic flux through the tidal mixing region can be explained by the density difference across the region and a Richardson Number based on the tidal velocities. The outgoing flux includes both surface and intermediate waters and the incoming flux includes both intermediate and deep waters. Laterally, fluxes into and out of the Strait of Georgia and across Victoria Sill show the impact of the Coriolis force and local bathymetry. INTRODUCTION A classic lock exchange experiment in a laboratory separates two different densities by a lock that is removed (_e.g._ ). As the lock is removed, the lighter water flows over the heavier and the heavier water flows under the lighter. These two gravity current flows travel quickly, on the order of the internal wave speed, quickly redistributing the density. Performing the experiment on a rotating table reduces the lateral width of the gravity currents but does not significantly change their speed . On the other hand, introducing turbulence, say in the form of a bubble region, breaks up the gravity currents and significantly increases the time for density exchange . These basic dynamics, a contrast in densities driving exchange, and turbulence reducing the rate of exchange, are expected to explain real oceanographic situations. Here we look at their application to an estuarine system with a highly constricted, very turbulent tidal mixing “hotspot”. Using the results from a well-resolved three-dimensional ocean model, we ask if the laboratory dynamics apply and what they tell us about the exchange flow for this estuary. In the oceanographic literature, the estuarine exchange problem has a long, and mostly separate history from these laboratory studies. In a real estuary, the problem is greatly complicated by the presence of tides. We cannot remove them (even from our model) as they are determining the mixing in the system. However, at any given time, the instantaneous velocity is largely determined by the tides, advecting water in and out. A traditional way to determine the net estuarine transport from observations is to assume two layers and to use Knudsen’s Relations, that is, conservation of water and salt. However, adding symmetrical mixing, as opposed to just entrainment into the upper layer, makes the system under-determined. One can use temperature and heating versus salinity to remove this ambiguity and then invert temperature and salinity profiles to determine the transport assuming a layer structure . The water advected in and the water advected out by the tides may be largely the same, and what we want to extract is the difference. From model results, one can analyze time averages, giving the tidally averaged velocities and tidally averaged salinity. However, this process neglects the strong correlations in the fluctuations. A more complete way to do this is to bin the water and salt fluxes by salinity bin and calculate TEF or total exchange flow . This method captures both the estuarine exchange flow and the transport due to the tides, and thus is a total or maximal exchange . The estuary we will consider is the large, semi-enclosed Strait of Georgia (SoG), which is connected to the Pacific Ocean through a western and a northern entrance (Figure [fig:map]). The primary flow is through the western entrance; the northern entrance is small and flux and exchange there are significantly smaller than at the west. The major source of fresh water is the Fraser River, about 60% of the total to the SoG which enters the SoG near its south end. At the south end of the SoG are the Gulf/San Juan Islands that form lateral constrictions. The water through this region is also shallower (Figure [fig:transects]). Thus, tidal flows are high, up to 4.5 m s−1, and turbulent mixing is strong (Figure [fig:transects]). Water exiting the SoG flows through this region and then into the relatively straight Juan de Fuca Strait (Figure [fig:map]), although there is a significant sill, Victoria Sill, at the eastern end of Juan de Fuca Strait (Figure [fig:transects]). Exchange through this region has been studied through observations and models . Exchange is seasonally variable with pulses of freshwater exiting Juan de Fuca Strait during the Fraser River Freshet, weak neap tides, and winds to the south in SoG . Deep water renewals similarly occur during neap tides during spring through fall . The observed dense water cascading from Boundary Pass Sill into the deep SoG has been successfully explained as a gravity current . Net fluxes have been estimated at 46 mSv out from Boundary Pass or 114 mSv in from Victoria Sill . These estimates are based on mass, salt and heat balances and are necessarily coarse in their vertical resolution and do not include lateral resolution. Using the TEF method the flux into the SoG is estimated as 83 mSv , updated to 70 mSv . These two estimates include both the estuarine component and the net tidal impact. Estimates not including the tidal impact are lower (28 mSv, ). However, all these estimates include both the flux that transitions the turbulent region and flux that is recycled within it. In particular, the flux into and out of Haro Strait is different in because much of the deep flow into Haro Strait is entrained into the surface flow and exits back out in the surface outflow to Juan de Fuca Strait. Indeed, although the exchange is maximum during neap tides, the maximum residual flow actually occurs at spring tides due to this entrained flux . This short-circuited flow is referred to as the reflux ( _e.g.,_ , ). Here we will use a Lagrangian tracking method that allows us to separate the reflux and focus on the flux that travels through the mixing region. This method does include the effect of the tides. Typically the SoG is divided into three layers: a surface layer above 50 m, an intermediate layer, and a deep layer below 200 m (e.g. , ; , ). Looking at the monthly climatology in the central SoG these depths would correspond to salinities of 30 g kg−1 (range 29.9 g kg−1 (July) to 30.4 g kg−1 (November)), for 50 m and 31.2 g kg−1 (range 31.0 g kg−1 (May) to 31.4 g kg−1 (October)) for 200 m.
