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

2019 ◽  
Vol 49 (3) ◽  
pp. 723-736 ◽  
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.

Analysis of Tidal Straining as Driver for Estuarine Circulation in Well-Mixed Estuaries

2012 ◽  
Vol 42 (2) ◽  
pp. 261-271 ◽  
Author(s):  
Hans Burchard ◽  
Henk M. Schuttelaars
Keyword(s):  
Pressure Gradient ◽  
Internal Pressure ◽  
Velocity Component ◽  
Eddy Viscosity ◽  
Estuarine Circulation ◽  
Vertical Shear ◽  
Tidal Straining ◽  
Lateral Circulation ◽  
Channel Velocity ◽  
Lateral Advection

Abstract Tidal straining, which can mathematically be described as the covariance between eddy viscosity and vertical shear of the along-channel velocity component, has been acknowledged as one of the major drivers for estuarine circulation in channelized tidally energetic estuaries. In this paper, the authors investigate the role of lateral circulation for generating this covariance. Five numerical experiments are carried out, starting with a reference scenario including the full physics and four scenarios in which specific key physical processes are neglected. These processes are longitudinal internal pressure gradient forcing, lateral internal pressure gradient forcing, lateral advection, and the neglect of temporal variation of eddy viscosity. The results for the viscosity–shear covariance are correlated across different experiments to quantify the change due to neglect of these key processes. It is found that the lateral advection of vertical shear of the along-channel velocity component and its interaction with the tidally asymmetric eddy viscosity (which is also modified by the lateral circulation) is the major driving force for estuarine circulation in well-mixed tidal estuaries.

Impact of the Depth-to-Width Ratio of Periodically Stratified Tidal Channels on the Estuarine Circulation

2015 ◽  
Vol 45 (8) ◽  
pp. 2048-2069 ◽  
Author(s):  
Elisabeth Schulz ◽  
Henk M. Schuttelaars ◽  
Ulf Gräwe ◽  
Hans Burchard
Keyword(s):  
Eddy Viscosity ◽  
Transport Model ◽  
Stable Stratification ◽  
Estuarine Circulation ◽  
Width Ratio ◽  
Cross Sectional ◽  
Tidal Straining ◽  
The Individual ◽  
Periodic Stratification ◽  
The Impact

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.

Three-dimensional destabilization of Stuart vortices: the influence of rotation and ellipticity

1999 ◽  
Vol 387 ◽  
pp. 205-226 ◽  
Author(s):  
P. G. POTYLITSIN ◽  
W. R. PELTIER
Keyword(s):  
Cross Sections ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Steady State Solution ◽  
Vorticity Distribution ◽  
Columnar Vortex ◽  
Elliptical Instability ◽  
The Stability ◽  
Dimensional Instability ◽  
Stuart Vortices

We investigate the influence of the ellipticity of a columnar vortex in a rotating environment on its linear stability to three-dimensional perturbations. As a model of the basic-state vorticity distribution, we employ the Stuart steady-state solution of the Euler equations. In the presence of background rotation, an anticyclonic vortex column is shown to be strongly destabilized to three-dimensional perturbations when background rotation is weak, while rapid rotation strongly stabilizes both anticyclonic and cyclonic columns, as might be expected on the basis of the Taylor–Proudman theorem. We demonstrate that there exist three distinct forms of three-dimensional instability to which strong anticyclonic vortices are subject. One form consists of a Coriolis force modified form of the ‘elliptical’ instability, which is dominant for vortex columns whose cross-sections are strongly elliptical. This mode was recently discussed by Potylitsin & Peltier (1998) and Leblanc & Cambon (1998). The second form of instability may be understood to constitute a three-dimensional inertial (centrifugal) mode, which becomes the dominant mechanism of instability as the ellipticity of the vortex column decreases. Also evident in the Stuart model of the vorticity distribution is a third ‘hyperbolic’ mode of instability that is focused on the stagnation point that exists between adjacent vortex cores. Although this short-wavelength cross-stream mode is much less important in the spectrum of the Stuart model than it is in the case of a true homogeneous mixing layer, it nevertheless does exist even though its presence has remained undetected in most previous analyses of the stability of the Stuart solution.

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

2010 ◽  
Vol 40 (6) ◽  
pp. 1243-1262 ◽  
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.

scholarly journals The Point on the Theoretical Changes of Surface Chemistry During Massive Star Evolution

1988 ◽  
Vol 108 ◽  
pp. 79-85
Author(s):  
André Maeder
Keyword(s):  
Surface Chemistry ◽  
Cross Sections ◽  
Massive Star ◽  
Main Sequence ◽  
Tidal Mixing ◽  
Main Sequence Stars ◽  
Star Evolution ◽  
Cno Abundances ◽  
Massive Star Evolution ◽  
Nuclear Processing

For main sequence stars, the central nuclear processing generally has no effect on surface abundances. Later in the evolution, the newly synthetized elements may be revealed at the stellar surface by processes such as mass loss, convective dredge-up, overshooting, diffusion, rotational and tidal mixing, etc. The changes of CNO abundances are the most conspicuous and the easiest to observe spectroscopically; some abundance ratios like C/N, O/N may undergo changes by more than 102. On the whole, surface chemistry is a most powerful diagnostics of stellar evolution, model assumptions and nuclear cross sections.

Construction of net isopleth plots in cross-sections of tidal estuaries

1984 ◽  
Vol 42 (3) ◽  
pp. 503-508 ◽  
Author(s):  
Björn Kjerfve ◽  
Harvey E. Seirn
Keyword(s):  
Cross Sections ◽  
Tidal Estuaries
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