Interaction of a deformable free surface with statistically steady homogeneous turbulence

2010 ◽  
Vol 658 ◽  
pp. 33-62 ◽  
Author(s):  
XIN GUO ◽  
LIAN SHEN
Keyword(s):  
Free Surface ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Pseudospectral Method ◽  
Vertical Direction ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

Mechanistic Study of Upper Ocean Turbulence Interacting With Surface Waves

2010 ◽  
Author(s):  
Xin Guo ◽  
Di Yang ◽  
Yi Liu ◽  
Lian Shen
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Mechanistic Study ◽  
Navier Stokes Equations ◽  
Random Forcing ◽  
Set Up ◽  
Pseudo Spectral Method

We perform direct numerical simulations to simulate the interaction between surface waves and the turbulence underneath. The Navier–Stokes equations are simulated using a pseudo-spectral method in horizontal directions and a finite-difference method in vertical direction, with fully nonlinear viscous free-surface kinematic and dynamic boundary conditions at the free surface. We set up the turbulence and the waves by a random forcing method in the bulk flow and a pressure forcing method at the surface, which were recently developed by [1]. It is found that there are surface waves generated on the free surface due to the excitation by the turbulence. The surface elevation is sensitive to the effect of gravity and surface tension. In the presence of progressive waves at the free surface, the turbulent vortical structure is turned, stretched, and compressed periodically by the strain field of waves.

A Model for the Simulation of Steady Spilling Breaking Waves

2003 ◽  
Vol 47 (01) ◽  
pp. 13-23
Author(s):  
R. Muscari ◽  
A. Di Mascio
Keyword(s):  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Original Model ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Stable Algorithm ◽  
Surface Boundary Conditions

A numerical model for the simulation of two-dimensional spilling breaking waves is described. The model is derived from Cointe and Tulin's theory of steady breakers (Cointe & Tulin 1994), although some important changes have been introduced in order to obtain a stable algorithm when coupled with steady-state Reynolds averaged Navier-Stokes equations (RANSE) solvers. In particular, the shape of the breaker and its relation with the following wave height differ from the original model, and moreover, additional conditions for the tangential stress and the turbulent viscosity are proposed. The model has been implemented in a RANSE code, developed for the study of ship flows, through a modification in the free-surface boundary conditions below the breaker. This yields a simple but effective way to reproduce the breaker influence on the underlying flow. The algorithm was used for the simulation of the flow past a submerged hydrofoil. The numerical results are compared with the experimental data by Duncan (1983).

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Studies on Natural Convection Induced Flow and Thermal Behavior Inside Electronic Equipment Cabinet Model

2001 ◽  
Author(s):  
Masaru Ishizuka ◽  
Guoyi Peng ◽  
Shinji Hayama
Keyword(s):  
Natural Convection ◽  
Thermal Behavior ◽  
Body Surface ◽  
Stokes Equations ◽  
The Body ◽  
Electronic Equipment ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Induced Flow

Abstract In the present work, an important basic flow phenomena, the natural convection induced flow, is studied numerically. Three-dimensional Navier-Stokes equations along with the temperature equation are solved on the basis of finite difference method. Generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. Differential terms with respect to time are approximated by forward differences, diffusions terms are approximated by the implicit Euler form, convection terms in the Navier-Stokes equations are approximated by the third order upwind difference scheme. The heat flux at the body surface of heater is specified. The results of calculation showed a satisfactory agreement with the measured data and led to a good understanding of the overall flow and thermal behavior inside electronic equipment cabinet model which is very difficult, if not impossible, to gather by experiment.

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