An operational linear lee wave model for arbitrary basic flow and two-dimensional topography

1971 ◽  
Vol 97 (411) ◽  
pp. 30-60 ◽  
Author(s):  
I. Vergeiner
Keyword(s):  
Wave Model ◽  
Basic Flow ◽  
Two Dimensional ◽  
Lee Wave

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals Development of Two-Dimensional Non-Hydrostatic Wave Model Based on Central-Upwind Scheme

2020 ◽  
Vol 8 (7) ◽  
pp. 505
Author(s):  
Gangfeng Wu ◽  
Ying-Tien Lin ◽  
Ping Dong ◽  
Kefeng Zhang
Keyword(s):  
Hydrostatic Pressure ◽  
Large Scale ◽  
Wave Model ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Practical Engineering ◽  
Hydrostatic Model ◽  
Good Agreement ◽  
Biconjugate Gradient

In this study, a two-dimensional depth-integrated non-hydrostatic wave model is developed. The model solves the governing equations with hydrostatic and non-hydrostatic pressure separately. The velocities under hydrostatic pressure conditions are firstly obtained and then modified using the biconjugate gradient stabilized method. The hydrostatic front approximation (HFA) method is used to deal with the wave breaking issue, and after the wave breaks, the non-hydrostatic model is transformed into the hydrostatic shallow water model, where the non-hydrostatic pressure and vertical velocity are set to zero. Several analytical solutions and laboratory experiments are used to verify the accuracy and robustness of the developed model. In general, the numerical simulations are in good agreement with the theoretical or experimental results, which indicates that the model is able to simulate large-scale wave motions in practical engineering applications.

Coupling PSE and FLUENT to Predict Laminar-Turbulent Transition in Boundary Layers

2013 ◽  
Vol 432 ◽  
pp. 168-172
Author(s):  
Y. Zhou ◽  
Y.H. Fang
Keyword(s):  
Flat Plate ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Basic Flow ◽  
Two Dimensional ◽  
S Wave ◽  
S Waves ◽  
Turbulent Transition ◽  
Transition Criterion ◽  
Laminar Turbulent Transition

In this paper, the coupling method of PSE and FLUENT was experimented for predicting the laminar-turbulent transition. The software FLUENT was used to get the basic flow over a flat plate. A two-dimensional T-S wave and a pair of three-dimensional T-S waves were fed in at the entrance. The transition criterion was verified by DNS results. The availability of the coupling methodology has been evaluated.

Maximum power from a turbine farm in shallow water

2013 ◽  
Vol 714 ◽  
pp. 634-643 ◽  
Author(s):  
Chris Garrett ◽  
Patrick Cummins
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Momentum Equation ◽  
Basic Flow ◽  
Maximum Power ◽  
Two Dimensional ◽  
Dominant Term ◽  
Tidal Flows ◽  
Linear Friction

AbstractThe maximum power that can be obtained from a confined array of turbines in steady or tidal flows is considered using the two-dimensional shallow-water equations and representing the turbine farm by a uniform local increase in friction within a circle. Analytical results supported by dimensional reasoning and numerical solutions show that the maximum power depends on the dominant term in the momentum equation for flows perturbed on the scale of the farm. If friction dominates in the basic flow, the maximum power is a fraction (half for linear friction and 0.75 for quadratic friction) of the dissipation within the circle in the undisturbed state; if the advective terms dominate, the maximum power is a fraction of the undisturbed kinetic energy flux into the front of the turbine farm; if the acceleration dominates, the maximum power is similar to that for the linear frictional case, but with the friction coefficient replaced by twice the tidal frequency.

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