Slope-induced tidal straining: Analysis of rotational effects

AbstractThe dependency of the estuarine circulation on the depth-to-width ratio of a periodically, weakly stratified tidal estuary is systematically investigated here for the first time. Currents, salinity, and other properties are simulated by means of the General Estuarine Transport Model (GETM) in cross-sectional slice mode, applying a symmetric Gaussian-shaped depth profile. The width is varied over four orders of magnitude. The individual along-channel circulation contributions from tidal straining, gravitation, advection, etc., are calculated and the impact of the depth-to-width ratio on their intensity is presented and elucidated. It is found that the estuarine circulation exhibits a distinct maximum in medium-wide channels (intermediate depth-to-width ratio depending on various parameters), which is caused by a maximum of the tidal straining contribution. This maximum is related to a strong tidal asymmetry of eddy viscosity and shear created by secondary strain-induced periodic stratification (2SIPS): in medium channels, transverse circulation generated by lateral density gradients due to laterally differential longitudinal advection induces stable stratification at the end of the flood phase, which is further increased during ebb by longitudinal straining (SIPS). Thus, eddy viscosity is low and shear is strong in the entire ebb phase. During flood, SIPS decreases the stratification so that eddy viscosity is high and shear is weak. The circulation resulting from this viscosity–shear correlation, the tidal straining circulation, is oriented like the classical, gravitational circulation, with riverine outflow at the surface and oceanic inflow close to the bottom. In medium channels, it is about 5 times as strong as in wide (quasi one-dimensional) channels, in which 2SIPS is negligible.

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The Relative Importance of Wind Straining and Gravitational Forcing in Driving Exchange Flows in Tidally Energetic Estuaries

Journal of Physical Oceanography ◽

10.1175/jpo-d-18-0014.1 ◽

2019 ◽

Vol 49 (3) ◽

pp. 723-736 ◽

Cited By ~ 5

Author(s):

Xaver Lange ◽

Hans Burchard

Keyword(s):

Cross Sections ◽

Steady State Solution ◽

Estuarine Circulation ◽

Wind Forcing ◽

Tidal Mixing ◽

Exchange Flow ◽

Tidal Straining ◽

Tidal Estuaries ◽

Lateral Circulation ◽

Wedderburn Number

AbstractIn straight tidal estuaries, residual overturning circulation results mainly from a competition between gravitational forcing, wind forcing, and friction. To systematically investigate this for tidally energetic estuaries, the dynamics of estuarine cross sections is analyzed in terms of the relation between gravitational forcing, wind stress, and the strength of estuarine circulation. A system-dependent basic Wedderburn number is defined as the ratio between wind forcing and opposing gravitational forcing at which the estuarine circulation changes sign. An analytical steady-state solution for gravitationally and wind-driven exchange flow is constructed, where tidal mixing is parameterized by parabolic eddy viscosity. For this simple but fundamental situation, is calculated, meaning that the up-estuary wind forcing needs to be 15% of the gravitational forcing to invert estuarine circulation. In three steps, relevant physical processes are added to this basic state: (i) tidal dynamics are resolved by a prescribed semidiurnal tide, leading to caused by tidal straining; (ii) lateral circulation is added by introducing cross-channel bathymetry, smoothly increasing from 0.47 (flat bed) to 1.3 (parabolic bed) due to an increasing effect of lateral circulation on estuarine circulation; and (iii) full dynamics of a real tidally energetic inlet with highly variable forcing, where results from a two-dimensional linear regression.

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Residual Transport of Suspended Material by Tidal Straining near Sloping Topography

Journal of Physical Oceanography ◽

10.1175/jpo-d-15-0218.1 ◽

2016 ◽

Vol 46 (7) ◽

pp. 2083-2102 ◽

Cited By ~ 11

Author(s):

Kirstin Schulz ◽

Lars Umlauf

Keyword(s):

Slope Angle ◽

Critical Threshold ◽

Suspended Material ◽

Tidal Straining ◽

Velocity Amplitude ◽

Residual Currents ◽

Differential Heating ◽

Freshwater Runoff ◽

Special Cases ◽

Wide Range

AbstractTidal straining is known to have an important impact on the generation of residual currents and the transport of suspended material in estuaries and the coastal ocean. Essential for this process is an externally imposed horizontal density gradient, typically resulting from either freshwater runoff or differential heating. Here, it is shown that near sloping topography, tidal straining may effectively transport suspended material across isobaths even if freshwater runoff and differential heating do not play a significant role. A combined theoretical and idealized modeling approach is used to illustrate the basic mechanisms and implications of this new process. The main finding of this study is that, for a wide range of conditions, suspended material is transported upslope by a pumping mechanism that is in many respects similar to classical tidal pumping. Downslope transport may also occur, however, only for the special cases of slowly sinking material in the vicinity of slopes with a slope angle larger than a critical threshold. The effective residual velocity at which suspended material is transported across isobaths is a significant fraction of the tidal velocity amplitude (up to 40% in some cases), suggesting that suspended material may be transported over large distances during a single tidal cycle.

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The impact of tidal straining on the cycle of turbulence in a partially stratified estuary

Continental Shelf Research ◽

10.1016/j.csr.2004.08.003 ◽

2005 ◽

Vol 25 (1) ◽

pp. 51-64 ◽

Cited By ~ 75

Author(s):

J.H. Simpson ◽

E. Williams ◽

L.H. Brasseur ◽

J.M. Brubaker

Keyword(s):

Tidal Straining ◽

Stratified Estuary ◽

The Impact

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Effects of tidal straining on the semidiurnal cycle of dissipation in the Rhine region of freshwater influence: Comparison of model and measurements

Journal of Geophysical Research Atmospheres ◽

10.1029/2006jc004002 ◽

2008 ◽

Vol 113 (C1) ◽

Cited By ~ 13

Author(s):

Alejandro J. Souza ◽

Neil R. Fisher ◽

John H. Simpson ◽

M. John Howarth

Keyword(s):

Tidal Straining ◽

Freshwater Influence

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Tidal Straining, Density Currents, and Stirring in the Control of Estuarine Stratification

Estuaries ◽

10.2307/1351581 ◽

1990 ◽

Vol 13 (2) ◽

pp. 125 ◽

Cited By ~ 522

Author(s):

J. H. Simpson ◽

J. Brown ◽

J. Matthews ◽

G. Allen

Keyword(s):

Density Currents ◽

Tidal Straining ◽

Estuarine Stratification

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Quantifying the Contributions of Tidal Straining and Gravitational Circulation to Residual Circulation in Periodically Stratified Tidal Estuaries

Journal of Physical Oceanography ◽

10.1175/2010jpo4270.1 ◽

2010 ◽

Vol 40 (6) ◽

pp. 1243-1262 ◽

Cited By ~ 112

Author(s):

Hans Burchard ◽

Robert D. Hetland

Keyword(s):

Water Column ◽

Strouhal Number ◽

Richardson Number ◽

Eddy Viscosity ◽

Estuarine Circulation ◽

Turbulence Closure ◽

Closure Model ◽

Tidal Straining ◽

Gravitational Circulation ◽

Turbulence Closure Model

Abstract This numerical modeling study quantifies for the first time the contribution of various processes to estuarine circulation in periodically stratified tidal flow under the impact of a constant horizontal buoyancy gradient. The one-dimensional water column equations with periodic forcing are first cast into nondimensional form, resulting in a multidimensional parameter space spanned by the modified inverse Strouhal number and the modified horizontal Richardson number, as well as relative wind speed and wind direction and the residual runoff. The along-tide momentum equation is then solved for the tidal-mean velocity profile in such a way that it is equated to the sum of the contributions of tidal straining (resulting from the temporal correlation between eddy viscosity and vertical shear), gravitational circulation (resulting from the depth-varying forcing by a constant horizontal buoyancy gradient), wind straining, and depth-mean residual flow (resulting from net freshwater runoff). This definition of tidal straining does not only account for tidal asymmetries resulting from horizontal buoyancy gradients but also from wind straining and residual runoff. For constant eddy viscosity, the well-known estuarine circulation analytical solution with polynomial residual profiles is directly obtained. For vertically parabolic and constant-in-time eddy viscosity, a new analytic solution with logarithmic residual profiles is found, showing that the intensity of the gravitational circulation scales with the horizontal Richardson number. For scenarios with realistic spatially and temporally varying eddy viscosity, a numerical water column model equipped with a state-of-the-art two-equation turbulence closure model is applied to quantify the individual contributions of the various processes to estuarine circulation. The fundamental outcome of this study is that, for irrotational flow with periodic stratification and without wind forcing and residual runoff, the tidal straining is responsible for about two-thirds and gravitational circulation is responsible for about one-third of the estuarine circulation, proportionally dependent on the horizontal Richardson number, and weakly dependent on the Strouhal number. This new and robust result confirms earlier estimates by H. Burchard and H. Baumert, who suggested that tidal straining is the major generation mechanism for estuarine turbidity maxima. However, a sensitivity analysis of the model results to details of the turbulence closure model shows some uncertainty with respect to the parameterization of sheared convection during flood. Increasing down-estuary wind straining and residual runoff reduce the quantitative contribution of tidal straining. For relatively small horizontal Richardson numbers, the tidal straining contribution to estuarine circulation may even be reversed by down-estuary wind straining.

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