Transcritical flow over obstacles and holes: forced Korteweg–de Vries framework

2019 ◽  
Vol 881 ◽  
pp. 660-678 ◽  
Author(s):  
Roger H. J. Grimshaw ◽  
Montri Maleewong
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Vries Equation ◽  
Solitary Wave Solution ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Main Concern ◽  
Oncoming Flow ◽  
Transcritical Flow ◽  
De Vries

This paper extends a previous study of free-surface flow over two localised obstacles using the framework of the forced Korteweg–de Vries equation, to an analogous study of flow over two localised holes, or a combination of an obstacle and a hole. Importantly the terminology obstacle or hole can be reversed for a stratified fluid and refers more precisely to the relative polarity of the forcing and the solitary wave solution of the unforced Korteweg–de Vries equation. As in the previous study, our main concern is with the transcritical regime when the oncoming flow has a Froude number close to unity. In the transcritical regime at early times, undular bores are produced upstream and downstream of each forcing site. We then describe the interaction of these undular bores between the forcing sites, and the outcome at very large times.

Transcritical flow over two obstacles: forced Korteweg–de Vries framework

2016 ◽  
Vol 809 ◽  
pp. 918-940 ◽  
Author(s):  
Roger H. J. Grimshaw ◽  
Montri Maleewong
Keyword(s):  
Froude Number ◽  
Numerical Study ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Control Flow ◽  
Main Concern ◽  
Undular Bore ◽  
Second Stage ◽  
Third Stage ◽  
De Vries

We consider free-surface flow over two localised obstacles using the framework of the forced Korteweg–de Vries equation in a suite of numerical simulations. Our main concern is with the transcritical regime when the oncoming flow has a Froude number close to unity. The flow behaviour can be characterised by the Froude number and the maximum heights of the obstacles. In the transcritical regime at early times, undular bores are produced upstream and downstream of each obstacle. Our main aim is to describe the interaction of these undular bores between the obstacles, and to find the outcome at very large times. We find that the flow development can be defined in three stages. The first stage is described by the well-known development of undular bores upstream and downstream of each obstacle. The second stage is the interaction between the undular bore moving downstream from the first obstacle and the undular bore moving upstream from the second obstacle. The third stage is the very large time evolution of this interaction, when one of the obstacles controls criticality. For equal obstacle heights, our analytical and numerical results indicate that either one of the obstacles can control flow criticality, that being the first obstacle when the flow is slightly subcritical and the second obstacle otherwise. For unequal obstacle heights the larger obstacle controls criticality. The results obtained here complement a recent numerical study using the fully nonlinear, but non-dispersive, shallow water equations.

Steady free-surface flow over spatially periodic topography

2015 ◽  
Vol 781 ◽  
Author(s):  
B. J. Binder ◽  
M. G. Blyth ◽  
S. Balasuriya
Keyword(s):  
Free Surface ◽  
Bound States ◽  
Asymptotic Theory ◽  
Vries Equation ◽  
Solution Space ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Bed Topography ◽  
Spatially Periodic ◽  
Autonomous Dynamical Systems

Two-dimensional free-surface flow over a spatially periodic channel bed topography is examined using a steady periodically forced Korteweg–de Vries equation. The existence of new forced solitary-type waves with periodic tails is demonstrated using recently developed non-autonomous dynamical-systems theory. Bound states with two or more co-existing solitary waves are also identified. The solution space for varying amplitude of forcing is explored using a numerical method. A rich bifurcation structure is uncovered and shown to be consistent with an asymptotic theory based on small forcing amplitude.

scholarly journals Numerical solution of a free surface flow problem over an obstacle

2019 ◽  
Vol 106 (120) ◽  
pp. 135-148
Author(s):  
Samira Beyoud ◽  
Dahbia Boukari-Hernane
Keyword(s):  
Free Surface ◽  
Flow Problem ◽  
Vries Equation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Inviscid Fluid ◽  
Subcritical Case ◽  
Runge Kutta Method ◽  
Different Shapes ◽  
Gravity Acceleration

We consider a free surface flow problem of an incompressible and inviscid fluid, perturbed by a topography placed on the bottom of a channel. We suppose that the flow is steady, bidimensional and irrotational. We neglect the effects of the superficial tension but we take into account the gravity acceleration g. The main unknown of our problem is the equilibrium free surface of the flow; its determination is based on the Bernoulli equation which is transformed as the forced Korteweg-de Vries equation. The problem is solved numerically via the fourth-order Runge-Kutta method for the subcritical case, and the finite difference method for the supercritical case. The results obtained are illustrated by several figures, where the height h of the obstacle, and the value of the Froude number F of the flow, are varied. Note that different shapes of the obstacle have been considered.

scholarly journals Laminar free-surface flow into a vertical cylinder

1975 ◽  
Vol 3 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Thomas G. Smith ◽  
J.O. Wilkes
Keyword(s):  
Free Surface ◽  
Vertical Cylinder ◽  
Free Surface Flow ◽  
Surface Flow

Free-Surface Flow Simulations With Interactively Moving Bodies

2017 ◽  
Author(s):  
Arthur E. P. Veldman ◽  
Henk Seubers ◽  
Peter van der Plas ◽  
Joop Helder
Keyword(s):  
Free Surface ◽  
Free Fall ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Numerical Solution Method ◽  
Flow Simulations ◽  
Floating Object ◽  
Offshore Industry ◽  
Floating Objects ◽  
Moving Bodies

The simulation of free-surface flow around moored or floating objects faces a series of challenges, concerning the flow modelling and the numerical solution method. One of the challenges is the simulation of objects whose dynamics is determined by a two-way interaction with the incoming waves. The ‘traditional’ way of numerically coupling the flow dynamics with the dynamics of a floating object becomes unstable (or requires severe underrelaxation) when the added mass is larger than the mass of the object. To deal with this two-way interaction, a more simultaneous type of numerical coupling is being developed. The paper will focus on this issue. To demonstrate the quasi-simultaneous method, a number of simulation results for engineering applications from the offshore industry will be presented, such as the motion of a moored TLP platform in extreme waves, and a free-fall life boat dropping into wavy water.

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