scholarly journals CALCULATIONS OF WAVES FORMED FROM SURFACE CAVITIES

1976 ◽  
Vol 1 (15) ◽  
pp. 63 ◽  
Author(s):  
Charles L. Mader
Keyword(s):  
Water Waves ◽  
Wave Motion ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Critical Depth ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Tsunami Waves ◽  
Long Wave

The wave motion resulting from cavities in the ocean surface was investigated using both the long wave, shallow water model and the incompressible Navier-Stokes equations. The fluid flow resulting from the calculated collapse of the cavities is significantly different for the two models. The experimentally observed flow resulting from explosively formed cavities is in better agreement with the flow calculated using the incompressible Navier-Stokes model. The resulting wave motions decay rapidly to deep water waves. Large cavities located under the surface of the ocean will be more likely to result in Tsunami waves than cavities on the surface. This is contrary to what has been suggested by the upper critical depth phenomenon.

A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue

2008 ◽  
Vol 601 ◽  
pp. 189-198 ◽  
Author(s):  
ASLAN R. KASIMOV
Keyword(s):  
Surface Tension ◽  
Hydraulic Jump ◽  
Stokes Equations ◽  
Critical Value ◽  
Water Model ◽  
Navier Stokes ◽  
Jump Conditions ◽  
Shallow Water Model ◽  
Finite Radius ◽  
Navier Stokes Equations

We propose a theory of a steady circular hydraulic jump based on the shallow-water model obtained from the depth-averaged Navier–Stokes equations. The flow structure both upstream and downstream of the jump is determined by considering the flow over a plate of finite radius. The radius of the jump is found using the far-field conditions together with the jump conditions that include the effects of surface tension. We show that a steady circular hydraulic jump does not exist if the surface tension is above a certain critical value. The solution of the problem provides a basis for the hydrodynamic stability analysis of the hydraulic jump. An analogy between the hydraulic jump and a detonation wave is pointed out.

scholarly journals Shallow water model for pollutant distribution in the Ypacarai Lake

2021 ◽  
Vol 26 (2) ◽  
pp. 54-76
Author(s):  
Diego Bareiro ◽  
Enrique O’Durnin ◽  
Laura Oporto ◽  
Christian Schaerer
Keyword(s):  
Shallow Water ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Wind Velocities ◽  
The Impact

In this paper, we analyze the distribution of a non-reactive contaminant in Ypacarai Lake. We propose a shallow-water model that considers wind-induced currents, inflow and outflow conditions in the tributaries, and bottom effects due to the lakebed. The hydrodynamic is based on the depth-averaged Navier-Stokes equations considering wind stresses as force terms which are functions of the wind velocity. Bed (bottom) stress is based on Manning's equation, the lakebed characteristics, and wind velocities. The contaminant transportation is modeled by a 2D convection-diffusion equation taking into consideration water level. Comparisons between the simulation of the model, analytical solutions, and laboratory results confirm that the model captures the complex dynamic phenomenology of the lake. In the simulations, one can see the regions with the highest risk of accumulation of contaminants. It is observed the effect of each term and how it can be used them to mitigate the impact of the pollutants.    

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

scholarly journals Study of the stability of a thin liquid layer in the Landau–Levich problem

2020 ◽  
pp. 48-55
Author(s):  
A. V. Lyushnin ◽  
◽  
K. A. Permyakova ◽  
Keyword(s):  
Liquid Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Liquid Layer ◽  
Wave Approximation ◽  
Long Wave ◽  
Interphase Boundaries ◽  
The Stability ◽  
Long Wave Approximation

The stability of the liquid layer in the Landay–Levich problem is theoretically investigated. The free energy of this layer is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of two electric layers at both interphase boundaries. In the framework of long-wave approximation, the stability of such a system with respect to perturbations is studied in the system of Navier–Stokes equations. A stability map is provided for different layer thicknesses.

scholarly journals COMPARISON OF DIFFERENT METHODS FOR GENERATION AND ABSORPTION OF WATER WAVES

2019 ◽  
Vol 18 (1) ◽  
pp. 71 ◽  
Author(s):  
J. M. P. Conde
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Numerical Models ◽  
Experimental Studies ◽  
Wave Generation ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Wave Absorption ◽  
Water Level Rise

The knowledge of water wave characteristics (generation, propagation, transformation and breaking) is fundamental for hydrodynamic studies and the design of ocean, coastal and port structures. In addition to the small-scale experimental studies, the use of numerical models is also a very important tool in hydrodynamic studies. To have reliable numerical results a proper validation is required. The main objective of this paper is to compare different methods of wave generation and wave absorption in a numerical flume, and to find what is the most suited to simulate non-breaking regular wave propagation in a two-dimensional flume in deep water condition. The numerical simulations were made using the OpenFOAM® software package. Two solvers, waves2Foam and IHFoam/OlaFlow, the utility GroovyBC and a mesh stretching technique are compared. These numerical codes solve the transient Navier-Stokes equations and use a VoF (Volume of Fluid) method to identify the free surface. A solution dependence study with the methods of wave generation and wave absorption is presented. The results are also compared with the theoretical wave and experimental data. The results show that the different methods of generation produce waves similar to the theoretical and the experimental ones, only slightly differences were visible. The three method of wave dissipation considered produce very different results: IHFoam/OlaFlow is not able to dissipate the wave tested; the mesh stretching technique is able to dissipate the waves but produces a water level rise; the waves2Foam solver is able to dissipate properly the wave tested.

scholarly journals Recent Results from Analysis of Flow Structures and Energy Modes Induced by Viscous Wave around a Surface-Piercing Cylinder

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Agostino Lauria ◽  
Leonardo Primavera
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
The Subject ◽  
Run Up ◽  
Velocity Pressure

Due to its relevance in ocean engineering, the subject of the flow field generated by water waves around a vertical circular cylinder piercing the free surface has recently started to be considered by several research groups. In particular, we studied this problem starting from the velocity-potential framework, then the implementation of the numerical solution of the Euler equations in their velocity-pressure formulation, and finally the performance of the integration of the Navier-Stokes equations in primitive variables. We also developed and applied methods of extraction of the flow coherent structures and most energetic modes. In this work, we present some new results of our research directed, in particular, toward the clarification of the main nonintuitive character of the phenomenon of interaction between a wave and a surface-piercing cylinder, namely, the fact that the wave exerts its maximum force and exhibits its maximum run-up on the cylindrical obstacle at different instants. The understanding of this phenomenon becomes of crucial importance in the perspective of governing the entity of the wave run-up on the obstacle by means of wave-flow-control techniques.

scholarly journals Simulations of oil spread on a water surface

2000 ◽  
Vol 214 (6) ◽  
pp. 889-900
Author(s):  
Y Liu ◽  
H Liu ◽  
H Zhang ◽  
G Miao
Keyword(s):  
Water Waves ◽  
Wave Reflection ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Advection Equation ◽  
Navier Stokes Equations ◽  
Oil Slick ◽  
Smooth Plane ◽  
Wavy Surfaces ◽  
Set Up

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called σ transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

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