Analytical Solution for 3D Tidal Flow with Vertically Varying Eddy Viscosity

2019 ◽  
Vol 18 (4) ◽  
pp. 771-783 ◽  
Author(s):  
Yang Chen ◽  
Wensheng Jiang ◽  
Shizuo Feng
Keyword(s):  
Analytical Solution ◽  
Eddy Viscosity ◽  
Tidal Flow

Analytical solution for the vertical structure of an estuarine tidal flow type

2000 ◽  
Vol 27 (5) ◽  
pp. 607-612 ◽  
Author(s):  
Sylvain Guillou ◽  
Nathaly Barbry ◽  
Jean-Claude Brun-Cottan
Keyword(s):  
Analytical Solution ◽  
Vertical Structure ◽  
Tidal Flow ◽  
Flow Type

Footprint Analysis: A Closed Analytical Solution Based On Height-Dependent Profiles Of Wind Speed And Eddy Viscosity

1999 ◽  
Vol 93 (3) ◽  
pp. 395-409 ◽  
Author(s):  
H.-D. Haenel ◽  
L. Grünhage
Keyword(s):  
Wind Speed ◽  
Analytical Solution ◽  
Eddy Viscosity ◽  
Footprint Analysis

scholarly journals The Role of Wave-Induced Coriolis–Stokes Forcing on the Wind-Driven Mixed Layer

2005 ◽  
Vol 35 (4) ◽  
pp. 444-457 ◽  
Author(s):  
Jeff A. Polton ◽  
David M. Lewis ◽  
Stephen E. Belcher
Keyword(s):  
Analytical Solution ◽  
Observational Data ◽  
Mixed Layer ◽  
Analytical Solutions ◽  
Eddy Viscosity ◽  
Large Eddy Simulations ◽  
Current Profile ◽  
Large Eddy ◽  
The Mean ◽  
Mean Current

Abstract The interaction between the Coriolis force and the Stokes drift associated with ocean surface waves leads to a vertical transport of momentum, which can be expressed as a force on the mean momentum equation in the direction along wave crests. How this Coriolis–Stokes forcing affects the mean current profile in a wind-driven mixed layer is investigated using simple models, results from large-eddy simulations, and observational data. The effects of the Coriolis–Stokes forcing on the mean current profile are examined by reappraising analytical solutions to the Ekman model that include the Coriolis–Stokes forcing. Turbulent momentum transfer is modeled using an eddy-viscosity model, first with a constant viscosity and second with a linearly varying eddy viscosity. Although the Coriolis–Stokes forcing penetrates only a small fraction of the depth of the wind-driven layer for parameter values typical of the ocean, the analytical solutions show how the current profile is substantially changed through the whole depth of the wind-driven layer. It is shown how, for this oceanic regime, the Coriolis–Stokes forcing supports a fraction of the applied wind stress, changing the boundary condition on the wind-driven component of the flow and hence changing the current profile through all depths. The analytical solution with the linearly varying eddy viscosity is shown to reproduce reasonably well the effects of the Coriolis–Stokes forcing on the current profile computed from large-eddy simulations, which resolve the three-dimensional overturning motions associated with the turbulent Langmuir circulations in the wind-driven layer. Last, the analytical solution with the Coriolis–Stokes forcing is shown to agree reasonably well with current profiles from previously published observational data and certainly agrees better than the standard Ekman model. This finding provides evidence that the Coriolis–Stokes forcing is an important mechanism in controlling the dynamics of the upper ocean.

Analytical Solution of Two Gradient-Diffusion Models Applied to Turbulent Couette Flow

1984 ◽  
Vol 106 (2) ◽  
pp. 211-216 ◽  
Author(s):  
F. S. Henry ◽  
A. J. Reynolds
Keyword(s):  
Kinetic Energy ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Central Region ◽  
Eddy Viscosity ◽  
Diffusion Models ◽  
Gradient Diffusion ◽  
Wall Boundary Conditions ◽  
Model Equations

Two widely used gradient-diffusion models of turbulence, when applied to fully-developed Couette flow, are shown to reduce to a set of equations that can be solved analytically. The solutions reveal that both models predict the turbulence kinetic energy to be constant across the entire central region in which the modeling is applied. The implications for the prediction of velocity and eddy viscosity are explored. It is found that the point at which the model equations are matched to the near-wall boundary conditions is an important parameter of the solution.

scholarly journals An Analytical Solution for Investigating the Characteristics of Tidal Wave and Surge Propagation Associated with Non-Tropical and Tropical Cyclones in the Humen Estuary, Pearl River

Water ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2375
Author(s):  
Zhuo Zhang ◽  
Fei Guo ◽  
Di Hu ◽  
Dong Zhang
Keyword(s):  
Analytical Solution ◽  
Analytical Model ◽  
Spring Tide ◽  
Tidal Flow ◽  
Storm Surges ◽  
Tidal Wave ◽  
Numerical Results ◽  
Pearl River ◽  
Tidal Waves ◽  
Astronomical Tide

The Humen Estuary, one of the largest outlets of the Pearl River, is a long and wide tidal channel with a considerable tidal flow every year. Storm surges, always superposing spring tide, travel from the estuary and endanger the safety of people living around the river. However, little research has quantified the relationship between the hydraulic characteristics and the geometry features in this estuary. In this regard, an analytical model, combined with a numerical model, is applied to investigate the characteristics of tidal waves and surge propagations in the estuary. Given the geometric, topographic, and tidal parameters at the mouth of the estuary, the tidal damping and wave celerity can be computed. The numerical results were used to calibrate and verify the analytical model. The results indicate that the analytical model can describe the astronomical tidal dynamics very well in correspondence with the numerical results. However, the analytical model cannot predict the tide well when a tropical cyclone-induced surge is superimposed on the astronomical tide. The reason is that this model does not take the wind stress and the pressure depression into account. After reducing Manning’s coefficient, we found that the analytical results could be close to the numerical results. Finally, we analyzed the characteristics of the tidal wave in the Humen Estuary using the analytical solution and its parameters.

Analytical solution to the 3D tide-induced Lagrangian residual current in a narrow bay with vertically varying eddy viscosity coefficient

2020 ◽  
Vol 70 (6) ◽  
pp. 759-770
Author(s):  
Yang Chen ◽  
Yanxing Cui ◽  
Xiaoxuan Sheng ◽  
Wensheng Jiang ◽  
Shizuo Feng
Keyword(s):  
Analytical Solution ◽  
Eddy Viscosity ◽  
Viscosity Coefficient ◽  
Residual Current ◽  
Narrow Bay ◽  
Lagrangian Residual Current ◽  
Eddy Viscosity Coefficient

The optimum position for a tidal power barrage in the Severn estuary

2009 ◽  
Vol 636 ◽  
pp. 497-507 ◽  
Author(s):  
R. C. T. RAINEY
Keyword(s):  
Analytical Solution ◽  
Numerical Models ◽  
Tidal Flow ◽  
Point Of View ◽  
Tidal Power ◽  
Severn Estuary ◽  
Tidal Waves ◽  
Optimum Position ◽  
The Difference ◽  
Power Point

G. I. Taylor's approximate analytical solution for the tidal flow in the Severn estuary is extended to find the optimum location for a tidal power barrage, from the power point of view. It appears to be at the lowest point in the estuary, between Ilfracombe and Gower – contrary to earlier computations. The analytical solution shows that barrages radiate tidal waves out to sea, which highlights the important role of the far-field boundary condition in absorbing them. This appears to have been neglected in numerical models, which may explain the difference from the earlier results.

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