On the Vertical Structure of Tidal Flow in River Estuaries

Abstract

A technique is developed for calculating the distribution with depth of current and shearing stress in tidal estuaries. The effect of turbulence is introduced by a coefficient of eddy viscosity which is a prescribed function of the depth coordinate, and the predictions are compared with observation and existing theory. Using parameters representative of the Humber estuary, the resultant current profiles are found to be in reasonable agreement with recent measurements. The friction coefficient k (used in the Lorentz linearization of the quadratic friction law) has a value consistent with that determined by other methods.

Analytical solutions to two‐ and three‐dimensional periodic flows for numerical model testing

“…From (21), it is realized that the horizontal turbulent viscosity terms defined by Blumberg and Mellor [7] are equivalent to those of the first formulation but with twice the value on the horizontal turbulent viscosity coefficient. As adopted by Johns and Odd [2] and Guillou et al [6], an analytical form for the vertical turbulent viscosity is employed, assuming a quadratic variation over the depth:…”

“…Analytical solutions to the periodic flow problems in Cartesian and cylinder coordinates were proposed, for example, by Ippen [1], Johns and Odd [2], Lynch and Gray [3], Chen [4], Lynch 191 and Officer [5], and Guillou et al [6]. Ippen [1] developed an analytical solution to 1D tidal flow describing the propagation of the gravity wave without bottom friction and horizontal turbulent viscosity.…”

“…Ippen [1] developed an analytical solution to 1D tidal flow describing the propagation of the gravity wave without bottom friction and horizontal turbulent viscosity. Johns and Odd [2] introduced a vertical structure for the tidal flow in the analytical solution. Lynch and Gray [3] and Chen [4] proposed analytical solutions to the 1D tidal flow, including bottom friction but neglecting the horizontal turbulent viscosity.…”

“…Lynch and Officer [5] developed analytical test cases for 3D tidal flow in cylinder coordinates. Recently, Guillou et al [6] improved the analytical solution proposed by Johns and Odd [2] and Chen [4] by taking into account the bottom friction effects on the free surface elevation with regard to phase delay and the vertical velocity profile.…”

Note on a 2DH finite element model of tidal flow of the North Passage of the partially-mixed Changjiang River estuary, China

“…Tidal computation in estuarine and coastal waters has been attempted since the 1920s (Taylor, 1921a, b;Doodson and Corkan, 1932;Grace, 1931Grace, , 1936Grace, , 1937Proudman, 1925Proudman, , 1946Proudman, , 1955aProudman, , 1955bProudman, , 1957aProudman, , 1957bPillsbury, 1956;Otter and Day, 1960;Agnew, 1961;Rossiter, 1961;Johns, 1960Johns, , 1967Johns, , 1968Johns, , 1969Johns, , 1970Dronkers, 1964;Ippen, 1964;Hunt, 1964;Rossiter and Lennon, 1965;Banks, 1974;Flather and Heaps, 1975;Blumberg, 1977;Henry et al, 1984;Tee, 1988;Cheng, 1988;El-Sabh and Murty, 1990;Muchow and Garvine, 1991;Tan, 1992;Scarlatos, 1993Scarlatos, , 1996Liang et al, 2006;Liu et al, 2007;and Shi, 2009a, b). Four principal types of shallow water (coastal and estuarine) numerical models have been used up to now: 1) one-dimensional (Dronkers, 1964;Uncles and Jordan, 1980;Uncles, 1981aUncles, , 1981b…”