Introduction 7
Material and methods 13
1.1 The study area 13
2.2 The one-dimensional water column model 16
2.3 One-dimensional analysis: one-dimensional dynamic equations 17
2.4 Simpson number 18
2.5 ADCP data 19
Results 21
3.1 Idealized one-dimensional GOTM model simulations 21
3.2 Density salinity gradient magnitude 22
3.3 Relative direction effect of the density salinity gradient 22
3.3.1 Relative direction of the density salinity gradient a = 0° 23
3.3.2 Relative direction of the density salinity gradient a = 45° 24
3.3.3 Relative direction of the density salinity gradient a = 90° 25
3.3.4 Relative direction of the density salinity gradient a = 135° 26
3.3.5 Relative direction of the density salinity gradient a = 180° 27
3.3.6 Relative direction of the density salinity gradient a = 225° 28
3.3.7 Relative direction of the density salinity gradient a = 270° 29
3.3.8 Relative direction of the density salinity gradient a = 315° 30
3.4 Sensitivity analysis of the density salinity gradient magnitude effect 34
3.4.1 Velocity direction response to the density salinity gradient moving
from the south-west (a = 225°) 35
3.4.2 Velocity direction response to the density salinity gradient moving
from the south (a = 270°) 36
3.4.3 Velocity direction response to the density salinity gradient moving
from the south-east (a = 315°) 37
3.4.4 Salinity response to the density salinity gradient moving
from the south-west (a = 225°) 39
3.4.5 Salinity response to the density salinity gradient moving from the south (a =
270°) 40
3.4.6 Salinity response to the density salinity gradient moving
from the south-east (a = 315°) 41
3.5 Sensitivity analysis of the tidal current velocity magnitude 43
3.5.1 Response to the density salinity gradient = -1.6 x 10-4 psu m 1 moving from the
south (a = 270°) and tidal current velocity = 0.3 m s 1 44
3.5.2 Response to the density salinity gradient = -1.6 x 10 4 psu m 1 moving from the
south (a = 270°) and tidal current velocity = 0.8 m s-1 45
3.5.3 Response to the density salinity gradient = -2.0 x 10~4 psu m 1 moving from the
south-west (a = 225°) and tidal current velocity = 0.3 m s-1 46
3.5.4 Response to the density salinity gradient = -2.0 x 10~4 psu m 1 moving from the
south-west (a = 225°) and tidal current velocity = 0.8 m s-1 47
Discussion 49
4.1 Comparison the GOTMsimulation results to the ADCP data 50
4.2 Quantifying of tidal straining phenomenon by Simpson number 54
Conclusions 57
Acknowledgements 59
References 60
Tidal straining is a phenomenon of temporal variations in stratification and mixing resulting from the interaction of longitudinal density gradients with the horizontal tidal velocity. As a result, the theory predicts stronger and weaker stratification during ebb/low tide and flood/high tide, respectively. In more detail, this oceanographic process is represented in Fig.1, where freshwater input from rivers induces substantial horizontal gradients of density in estuaries and the surrounding waters. These density gradients drive a shear flow circulation with low-density water flowing offshore at the surface and higher density water moving shoreward at the bottom (Simpson et al. 1990).
Tidal straining phenomenon is investigated in this study based on forecasting of the ADCP, obtained during the HE-417 expedition in the German Bight from the 13 th of March until 18th of March in 2014, organized by Marum research center.
According to sensitivity analysis of the density salinity gradient strength and its direction, the specifications of the GOTM model, which can represent the real conditions where the ADCP data was obtained, are: water depth is kept to a constant mean value of H = 30 m. A tidal period is fixed to reproduce the semidiurnal M2 tide, with T = 44714 s. The density salinity gradient magnitude dxS is -1.6 x 10-4 psu m-1 directed from the south (a = 270°) and tidal current velocity is equal to 0.5 m s’1. In this case, the water column is decoupled in the velocity direction parameter and the threshold of the Simpson number is 0.576, which represents the SIPS regime in the water column.
The counter rotation driven by the density salinity gradient strength and its direction is pronounced if the density salinity gradient is big, for example -1.6 x 10-4 psu m’1, and vanishes when the density salinity gradient strength is equal or smaller than -1.2 x 10-4 psu m-1. Furthermore, the appearance of the counter rotation depends on the density salinity gradient direction. It is more significant if the density salinity gradient moves perpendicular towards the tidal current velocity. In addition, bed roughness does not change the velocity rotation in the water column.
Tidal straining is induced in the water column when the density salinity gradient strength is -1.2 x 10-4 psu m-1 or bigger. Therefore, it is highly induced by the density salinity gradient strength. Tidal straining can be characterized by the Simpson number, which in this study, was estimated that for 0.432 or lower values, the tidal straining is insignificant or absent and for 0.576 or bigger, the tidal straining is pronounced.
Furthermore, variation between permanent stratification and SIPS in the water column is determined by the density salinity gradient direction. In this case, SIPS appears in the water column when the density salinity gradient is perpendicular directed towards the tidal current. On the other hand, permanent stratification appears when the density salinity gradient moves from the sides. In addition, the duration of the permanent stratification and SIPS depends on the duration of shear as a result of the friction interaction of saline and less saline water flow.
The GOTM model cannot produce stable results if tidal current velocity is small (0.3 m s-1 and less). In this case, friction between upper and lower layer becomes very small during the entire tidal cycle, such that the exchange flow will not be damped and the GOTM will consider the steady forcing of the exchange flow by the density gradient. As a result, the GOTM model will not produce a tidally periodic simulation, since the exchange flow will further increase during each tidal cycle.
