Parker MacCready

Slippery Bottom Boundary Layers on a Slope

Abstract The turbulent bottom boundary layer for rotating, stratified flow along a slope is explored through theory and numerical simulation. The model flow begins with a uniform current along constant-depth contours and with flat isopycnals intersecting the slope. The boundary layer is then allowed to evolve in time and in distance from the boundary. Ekman transport up or down the slope advects the initial density gradient, eventually giving rise to substantial buoyancy forces. The rearranged density structure opposes the cross-slope flow, causing the transport to decay exponentially from its initial value (given by Ekman theory) to near zero, over a time scale proportional to f/(Nα)2, where f is the Coriolis frequency, N is the buoyancy frequency, and α is the slope angle. The boundary stress slowing the along-slope flow decreases simultaneously, leading to a very “slippery” bottom boundary compared with that predicted by Ekman theory.

River Influences on Shelf Ecosystems: Introduction and synthesis

[1] River Influences on Shelf Ecosystems (RISE) is the first comprehensive interdisciplinary study of the rates and dynamics governing the mixing of river and coastal waters in an eastern boundary current system, as well as the effects of the resultant plume on phytoplankton standing stocks, growth and grazing rates, and community structure. The RISE Special Volume presents results deduced from four field studies and two different numerical model applications, including an ecosystem model, on the buoyant plume originating from the Columbia River. This introductory paper provides background information on variability during RISE field efforts as well as a synthesis of results, with particular attention to the questions and hypotheses that motivated this research. RISE studies have shown that the maximum mixing of Columbia River and ocean water occurs primarily near plume liftoff inside the estuary and in the near field of the plume. Most plume nitrate originates from upwelled shelf water, and plume phytoplankton species are typically the same as those found in the adjacent coastal ocean. River-supplied nitrate can help maintain the ecosystem during periods of delayed upwelling. The plume inhibits iron limitation, but nitrate limitation is observed in aging plumes. The plume also has significant effects on rates of primary productivity and growth (higher in new plume water) and microzooplankton grazing (lower in the plume near field and north of the river mouth); macrozooplankton concentration (enhanced at plume fronts); offshelf chlorophyll export; as well as the development of a chlorophyll ‘‘shadow zone’’ off northern Oregon.

Estuarine Adjustment to Changes in River Flow and Tidal Mixing

Abstract The adjustment of estuarine circulation and density to changes in river flow and tidal mixing is investigated using analytical and numerical models. Tidally averaged momentum and salinity equations in a rectangular estuary are vertically averaged over two levels, resulting in equations that are analytically tractable while retaining a broad range of time-dependent behavior. It is found that both strongly stratified and well-mixed estuaries respond rapidly to either type of forcing change, while those of intermediate stratification respond more slowly. Intermediate estuaries also have the greatest sensitivity to change. Exchange flow dominates the up-estuary salt flux in strongly stratified cases. Changing the river flow in such cases leads to an internal wave propagating the length of the estuary, which accomplishes much of the adjustment. The internal wave speed thus controls the adjustment time. Increased tidal mixing in strongly stratified cases initially decreases the exchange flow contributi...

Dynamics of Willapa Bay, Washington: A Highly Unsteady, Partially Mixed Estuary

Results from 3 yr of hydrographic time series are shown for Willapa Bay, Washington, a macrotidal, partially mixed estuary whose river and ocean end members are both highly variable. Fluctuating ocean conditions— alternations between wind-driven upwelling and downwelling, and intrusions of the buoyant Columbia River plume—are shown to force order-of-magnitude changes in salinity gradients on the event (2‐10 day) scale. An effective horizontal diffusivity parameterizing all up-estuary salt flux is calculated as a function of riverflow: results show that Willapa’s volume-integrated salt balance is almost always far from equilibrium. At very high riverflows (the top 15% of observations) the estuary loses salt, on average, while at all other riverflow levels it gains salt. Under summer, low-riverflow conditions, in fact, the effective diffusivity K is large enough to drive a net increase in salinity that is 3‐6 times the seaward, river-driven salt flux. This diffusion process is amplified, not damped, by increased tidal forcing, contrary to the expectation for baroclinic exchange. Furthermore, K varies along the length of the estuary as ;5% of the rms tidal velocity times channel width, a scaling consistent with density-independent stirring by tidal residuals. To summarize Willapa’s event- and seasonal-scale variability, a simple diagnostic parameter space for unsteady estuarine salt balances is presented, a generalization from the Hansen and Rattray steady-state scheme.

Toward a Unified Theory of Tidally-Averaged Estuarine Salinity Structure

Equations are developed for the tidally-averaged, width-averaged estuarine salinity and circulation in a rectangular estuary. Width and depth may vary along the length of the channel, as may coefficients of vertical turbulent mixing and along channel diffusion. The system is reduced to a single first-order, nonlinear, ordinary differential equation governing the section-averaged salinity. A technique for specifying the ocean boundary condition is given, and solutions are found by numerical integration. Under different assumptions for the diffusion it is possible to reproduce the few existing analytical solutions, in particular the Hansen and Rattray (1965) Central Regime solution, and Chatwins (1976) solution.The mathematical framework allows easy comparison of the results of different channel geometries and mixing coefficients. Of particular interest is the along-channel distribution of the diffusive fraction of up-estuary salt flux. It is shown that the Hansen and Rattray solution is always diffusion-dominated near the mouth. A theory is presented for estimating the diffusion coefficient within a tidal excursion of the mouth. It is shown that the resulting rapid along-channel increase of diffusion may explain some observed patterns of salinity structure: a decrease in both stratification and along-channel salinity gradient near the mouth. The theory is applied to the Delaware Estuary and Northern San Francisco Bay, and shows reasonable agreement with observed sensitivities of salt intrusion distance to river flow.

A Model Study of the Salish Sea Estuarine Circulation

ArealistichindcastsimulationoftheSalishSea,whichencompasses theestuarinesystemsofPugetSound, the Strait ofJuan de Fuca, and the Strait of Georgia, is described for the year 2006. The model shows moderate skill when compared against hydrographic, velocity, and sea surface height observations over tidal and subtidal time scales. Analysis of the velocity and salinity fields allows the structure and variability of the exchange flow to be estimated for the first time from the shelf into the farthest reaches of Puget Sound. This study utilizes the total exchange flow formalism that calculates volume transports and salt fluxes in an isohaline framework, which is then compared to previous estimates of exchange flow in the region. From this analysis, residence time distributions are estimated for Puget Sound and its major basins and are found to be markedly shorter than previous estimates. The difference arises from the ability of the model and the isohaline method for flux calculations to more accurately estimate the exchange flow. In addition, evidence is found to support the previously observed spring‐neap modulation of stratification at the Admiralty Inlet sill. However, the exchange flow calculated increases at spring tides, exactly opposite to the conclusion reached from an Eulerian average of observations.

Seasonal and interannual variability in the circulation of Puget Sound, Washington: A box model study

Abstract A prognostic, time‐dependent box model of circulation in Puget Sound, Washington is used to study seasonal and interannual variations in residence times and interbasin transports. The model is capable of reproducing salinity variability in the Sound at seasonal timescales, and is shown to have hindcast skill at interannual timescales. Modelled transports vary as much between years as between seasons. The largest seasonal feature is a sharp transport drop in late autumn into the deep Main Basin of the Sound, which is shown to be caused by increased river flow into Whidbey Basin. The high degree of transport variability leads to large interannual differences in residence times; for instance, for Whidbey Basin the residence time varies from 33 to 44 days in the period between 1992 and 2001 and for southern Hood Canal it varies from 64 to 121 days. This indicates that residence time estimates based on a year or less of data may not yield representative values. A forcing sensitivity study shows that in all basins except the South Sound, salinity variability in the Strait of Juan de Fuca accounts for more of the seasonal variability than river variability does. However, year‐to‐year variability in river discharge affects interannual variability in transports as much as the Strait of Juan de Fuca salinity does. The model demonstrates poorest skill in the basins most affected by the Strait of Juan de Fuca salinity, indicating that the sparse data available for the Strait may not provide adequate boundary conditions for the model.

Form Drag and Mixing Due to Tidal Flow past a Sharp Point

Barotropic tidal currents flowing over rough topography may be slowed by two bottom boundary‐related processes: tangential stress of the bottom boundary layer, which is generally well represented by a quadratic drag law, and normal stress from bottom pressure, known as form drag. Form drag is rarely estimated from oceanic observations because it is difficult to measure the bottom pressure over a large spatial domain. The ‘‘external’’ and ‘‘internal’’ components of the form drag are associated, respectively, with sea surface and isopycnals deformations. This study presents model and observational estimates of the components of drag for Three Tree Point, a sloping ridge projecting 1 km into Puget Sound, Washington. Internal form drag was integrated from repeat microstructure sections and exceeded the net drag due to bottom friction by a factor of 10‐50 during maximum flood. In observations and numerical simulations, form drag was produced by a lee wave, as well as by horizontal flow separation in the model. The external form drag was not measured, but in numerical simulations was found to be comparable to the internal form drag. Form drag appears to be the primary mechanism for extracting energy from the barotropic tide. Turbulent buoyancy flux is strongest near the ridge in both observations and model results.

Calculating Estuarine Exchange Flow Using Isohaline Coordinates

A method for calculating subtidal estuarine exchange flow using an isohaline framework is described, and the results are compared with those of the more commonly used Eulerian method of salt flux decomposition. Concepts are explored using a realistic numerical simulation of the Columbia River estuary. The isohaline method is found to be advantageous because it intrinsically highlights the salinity classes in which subtidal volume flux occurs. The resulting expressions give rise to an exact formulation of the time-dependent Knudsen relation and may be used in calculation of the saltwater residence time. The volume flux of the landward transport, which can be calculated precisely using the isohaline framework, is of particular importance for problems in which the saltwater residence time is critical.

Estuarine salt flux through an isohaline surface

The salinity budget in an estuary is analyzed using an isohaline as the seaward bounding surface of the volume of integration. It is found that the rate of change of volume integrated salinity is governed by two processes: (1) the “drift” of the isohaline through the fluid, and (2) turbulent salt flux through the isohaline. This analysis highlights the role of turbulent salt flux in maintaining the salinity intrusion. In contrast, more standard budgets using a stationary, vertical cross section as the seaward end of the volume of integration attribute almost all along-estuary salt flux to advective processes such as the gravitational circulation. The isohaline budget is explored using an analytical model and using results from a three-dimensional numerical model. The numerical results highlight the complex spatial and temporal interplay between turbulent mixing and the shape of the isohaline. Averaging over a time period during which the freshwater volume behind the isohaline is constant reduces the isohaline budget to a balance of two terms: the time-mean, area-integrated turbulent salinity flux across the isohaline being equal to the mean river flow times the salinity of the isohaline.