Using Tracer Variance Decay to Quantify Variability of Salinity Mixing in the Hudson River Estuary

Abstract

The salinity distribution in estuaries is controlled by the mixing of salt and fresh water, which is driven by many factors including tidal amplitude, freshwater inflow, bathymetry, wind stress, and waves. The timing and location of the mixing are dependent on stratification and shear in the water column, which vary tidally (Simpson et al., 1990) and over the spring neap cycle (Bowen & Geyer, 2003). There have been many previous approaches to identify and quantify the mechanisms of estuarine mixing. Early studies focused on constant and parameterized values of eddy diffusivity (Hansen & Rattray, 1965; Lerczak et al. 2006). However, the eddy diffusivity is not in itself a measure of estuarine mixing but rather of the turbulence that would cause mixing in the presence of a vertical gradient. Several recent studies of estuarine mixing (Burchard & Rennau, 2008; MacCready et al., 2018; Wang & Geyer, 2018) have proposed that the destruction of salinity variance provides the appropriate measure of the mixing of salt in an estuary. This destruction of scalar variance has long been addressed in context with turbulent microstructure as the quantity χ s (Nash & Moum, 2002). Not only does χ s relate directly to the irreversible process that formally represents mixing (in context with the entropy of mixing, Gregg, 1984), but it also has particular significance in context with estuaries in that the strength of the exchange flow is directly proportional to the volume integral of χ s (Mac-Cready et al., 2018).

Impact of Evaporation and Precipitation on Estuarine Mixing

“…To test the derived relations (32)-( 35) in a numerical model, we employ a 2D model similar to the setup of Warner et al (2005) and Burchard et al (2019), and a realistic threedimensional model of the Persian Gulf, also known as Arabian Gulf. The model of our choice is the General Estuarine Transport Model (GETM; Burchard and Bolding 2002), a coastal ocean model, solving the hydrostatic Boussinesq equations (Klingbeil et al 2018).…”

Freshwater Composition and Connectivity of the Connecticut River Plume During Ambient Flood Tides

“…Plume-averaged tracer budgets are valuable for analyzing plume evolution as a whole, but combine together horizontal and vertical processes as well as processes occurring in different regions of the plume. Future analysis of the Connecticut River plume should explore the decomposition of tracer variance into its horizontal and vertical parts, as introduced in Li et al (2018) and applied in other studies (e.g., Wang and Geyer, 2018;Warner et al, 2020). The vertical tracer variance is particularly useful since it is directly related to stratification and it may be more readily applied to understanding biogeochemical processes in plumes.…”

“…The vertical tracer variance is particularly useful since it is directly related to stratification and it may be more readily applied to understanding biogeochemical processes in plumes. Analyzing spatial variations of tracer variance and budget terms as in Li et al (2018) and other works (e.g., Warner et al, 2020) would help highlight important areas for variance advection and dissipation. The multiple tracer approach applied in the present study already allows for distinguishing between near-field and far-field plume regions.…”

“…Analysis of salinity variance has been applied to studying mixing in estuaries and coastal waters (e.g., Burchard and Rennau, 2008;Li et al, 2018;MacCready et al, 2018;Wang and Geyer, 2018;Burchard, 2020;Warner et al, 2020). Analogous tracer variance analysis is applied to the freshwater tracers described above.…”

“…K is written as a scalar in (4) for simplicity (as in MacCready et al, 2018), but a more detailed representation involves a diagonal diffusivity tensor with different horizontal and vertical eddy diffusivities (e.g., Li et al, 2018). Alternately, horizontal diffusion is sometimes considered negligible and only vertical diffusion is included (e.g., Warner et al, 2020). The final integrand in (4) represents the tracer mixing per unit volume; it is symbolized with χ in some prior studies (e.g., Wang and Geyer, 2018;Burchard, 2020).…”