scholarly journals ENERGY LOSSES UNDER WAVE ACTION

1970 ◽  
Vol 1 (12) ◽  
pp. 16 ◽  
Author(s):  
P.D. Treloar ◽  
A. Brebner
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wave Height ◽  
Dissipation Function ◽  
Wave Action ◽  
Energy Losses ◽  
Boundary Layer Equations ◽  
Wave Height Attenuation ◽  
Prandtl Boundary Layer ◽  
Made In

Wave-height attenuation measurements were made in two identical flumes of different widths and the results used to separate bottom energy losses from sidewall energy losses These energy losses, in the form of rates of energy dissipation, were then compared with their theoretical values as calculated by solving the linearized Prandtl boundary layer equations and evaluating the Rayleigh dissipation function Using these results, an adjusted formula for the wave-height attenuation modulus was determined.

scholarly journals Wave energy dissipation in the mangrove vegetation off Mumbai, India

2017 ◽  
Author(s):  
Samiksha S. Volvaiker ◽  
Ponnumony Vethamony ◽  
Prasad K. Bhaskaran ◽  
Premanand Pednekar ◽  
MHamsa Jishad ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Drag Coefficient ◽  
Wave Height ◽  
Wave Attenuation ◽  
Coastal Region ◽  
Measured Data ◽  
Vegetation Density ◽  
Mangrove Vegetation ◽  
Wave Height Attenuation ◽  
Set Up

Abstract. Coastal regions of India are prone to sea level rise, cyclones, storm surges and human induced activities, resulting in flood, erosion, and inundation. The primary aim of the study is to estimate wave attenuation by mangrove vegetation using SWAN model in standalone mode, as well as SWAN nested with WW3 model for the Mumbai coastal region. To substantiate the model results, wave measurements were carried out during 5–8 August 2015 at 3 locations in a transect normal to the coast using surface mounted pressure level sensors under spring tide conditions. The measured data presents wave height attenuation of the order of 52 %. The study shows a linear relationship between wave height attenuation and gradual changes in water level in the nearshore region, in phase with the tides. Model set-up and sensitivity analyses were conducted to understand the model performance to vegetation parameters. It was observed that wave attenuation increased with an increase in drag coefficient (Cd), vegetation density, and stem diameter. For a typical set-up for Mumbai coastal region having vegetation density of 0.175 per m2, stem diameter of 0.3 m and drag coefficient varying from 0.4 to 1.5, the model reproduced attenuation, ranging from 49 to 55 %, which matches well with the measured data. Spectral analysis performed for the cases with and without vegetation very clearly portrays energy dissipation in the vegetation area as well as spectral changes. This study has the potential of improving the quality of wave prediction in vegetation areas, especially during monsoon season and extreme weather events.

Potential Systems and Nonlocal Conservation Laws of Prandtl Boundary Layer Equations on the Surface of a Sphere

2017 ◽  
Vol 72 (4) ◽  
pp. 351-357 ◽  
Author(s):  
R. Naz
Keyword(s):  
Boundary Layer ◽  
Conservation Laws ◽  
Linear Combination ◽  
Conservation Law ◽  
Local Conservation ◽  
Boundary Layer Equations ◽  
Potential System ◽  
Nonlocal Conservation Laws ◽  
Prandtl Boundary Layer ◽  
Nonlocally Related Systems

Abstract:The potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere have been investigated. The multiplier approach yields two local conservation laws for the Prandtl boundary layer equations on the surface of a sphere. Two potential variables ψ and ϕ are introduced corresponding to first and second conservation law. Moreover, another potential variable p is introduced by considering the linear combination of both conservation laws. Two level one potential systems involving a single nonlocal variable ψ or ϕ are constructed. One level two potential system involving both nonlocal variables ψ and ϕ is established. The nonlocal variable p is utilised to derive a spectral potential system. The nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere are derived by computing the local conservation laws of its potential systems. The nonlocal conservation laws are utilised to derive the further nonlocally related systems.

scholarly journals Wave energy dissipation in the mangrove vegetation off Mumbai, India

2018 ◽  
Author(s):  
Samiksha S. Volvaiker ◽  
Ponnumony Vethamony ◽  
Prasad K. Bhaskaran ◽  
Premanand Pednekar ◽  
Mhamsa Jishad ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Drag Coefficient ◽  
Wave Height ◽  
Wave Energy ◽  
Coastal Region ◽  
Measured Data ◽  
Vegetation Density ◽  
Mangrove Vegetation ◽  
Wave Height Attenuation ◽  
Set Up

Abstract. Coastal regions of India are prone to sea level rise, cyclones, storm surges and human induced activities, resulting in flood, erosion and inundation. The primary aim of the study is to estimate wave energy attenuation by mangrove vegetation using SWAN model, and validate the model results with measurements for the Mumbai coastal region. Wave measurements were carried out during 5–8 August 2015 at 3 locations in a transect normal to the coast using surface mounted pressure level sensors in spring tide conditions. The measured data presents wave height attenuation of the order of 52 %. The study shows a linear relationship between wave height attenuation and gradual changes in water level in the nearshore region, in phase with the tides. Model set-up and sensitivity analyses were conducted to understand the model performance to vegetation parameters. It was observed that wave attenuation increases with an increase in drag coefficient, vegetation density and stem diameter. For a typical set-up for Mumbai coastal region having vegetation density of 0.175 per m2, stem diameter of 0.3 m and drag coefficient varying from 0.4 to 1.5, the model reproduced attenuation, ranging from 49 to 55 %, which matches well with the measured data. Spectral analysis performed for the cases with and without vegetation very clearly portrays energy dissipation in the vegetation area. This study has the potential of improving the quality of wave prediction in vegetation areas, especially during monsoon season and extreme weather events.

Oscillatory solutions of the Falkner-Skan equation

1985 ◽  
Vol 397 (1813) ◽  
pp. 415-418 ◽  
Keyword(s):  
Boundary Layer ◽  
Periodic Solution ◽  
Incompressible Flow ◽  
Symbolic Dynamics ◽  
Similarity Solutions ◽  
Oscillatory Solutions ◽  
Smale Horseshoe ◽  
Boundary Layer Equations ◽  
Prandtl Boundary Layer ◽  
Infinitely Many Periodic Solutions

The Falkner-Skan equation for similarity solutions of the Prandtl boundary-layer equations for incompressible flow is analysed for both positive and negative values of the parameter β . For β < — 1 branches of solutions with any number of intervals of overshoot are found analytically, and confirm recent numerical results. For β > 1 we have proved that there is a periodic solution. We conjecture that for β > 2 there are infinitely many periodic solutions and that a form of ‘symbolic dynamics’, of the kind associated with a Smale ‘horseshoe map’ can be constructed. We have shown this rigorously for β close to 2.

Solution of the Incompressible Turbulent Boundary-Layer Equations With Heat Transfer

1970 ◽  
Vol 92 (1) ◽  
pp. 133-141 ◽  
Author(s):  
T. Cebeci ◽  
A. M. O. Smith ◽  
G. Mosinskis
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Incompressible Flows ◽  
Reynolds Shear Stress ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Incompressible Turbulent Boundary Layer ◽  
Implicit Finite Difference ◽  
Stress Term ◽  
Made In

The boundary-layer equations for laminar and turbulent incompressible flows about two-dimensional and axisymmetric flows are solved by an implicit finite-difference method. An eddy-viscosity concept is used to eliminate the Reynolds shear-stress term, and an eddy-conductivity concept is used to eliminate the time mean of the product of fluctuating velocity and temperature. Several flows have been computed by this method, and comparisons with experimental data and with the Bradshaw-Ferriss method are made. In general, the agreement is quite good.

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