scholarly journals Three-dimensional lee-wave pattern

1978 ◽  
Vol 104 (442) ◽  
pp. 947-957 ◽  
Author(s):  
B. Gjevik ◽  
T. Marthinsen
Keyword(s):  
Three Dimensional ◽  
Wave Pattern ◽  
Lee Wave

Stratified rotating flow over and around isolated three-dimensional topography

1987 ◽  
Vol 322 (1564) ◽  
pp. 213-241 ◽  
Keyword(s):  
Numerical Model ◽  
Three Dimensional ◽  
Wave Pattern ◽  
The Body ◽  
Lee Waves ◽  
Lee Wave ◽  
Long Time ◽  
Dynamical Parameters ◽  
The Right ◽  
Eddy Shedding

Laboratory and numerical experiments have been conducted on the flow of a linearly stratified rotating fluid past isolated obstacles of revolution (conical and cosinesquared profiles). Laboratory experiments are considered for a range of Rossby, Ekman and Burger numbers, the pertinent dynamical parameters of the system. In these experiments, inertial, Coriolis, pressure, viscous and buoyancy forces all play a significant role. Emphasis is given to examining the nature of the time development of the flow fields as well as its long-time behaviour, including eddy shedding. It is shown, for example, that increased stratification tends to diminish the steering effect of the obstacle, other parameters being fixed, at elevation levels above the topography. At levels below the top of the obstacle, increased stratification tends to force the fluid around rather than over the body and this, in turn, tends to develop vortex shedding at smaller Reynolds numbers than would occur in corresponding lower stratification cases. Data for the cone reveal that the Strouhal number for the eddy-shedding regime is relatively insensitive to the values of Ro , Ek and S for the range of parameters investigated. Stratification tends to induce lee waves in the topography wake, and the nature of this lee-wave pattern is modified by the presence of rotation. For example, it is demonstrated that for vertically upward rotation, the lee waves on the right, facing downstream, have a larger amplitude than their counterparts at the same location on the left. The steering effects, as predicted by a three-level quasigeostrophic numerical model, are shown to be in good agreement with the laboratory results for a narrow range of parameter space. The numerical model is used to examine the effects of rotation, friction and stratification in modifying the flow. The quasigeostrophic numerical simulations do not produce eddy shedding, and it is concluded that a full, primitive equation numerical model would be needed to explore this phenomenon.

Forcing of oceanic mean flows by dissipating internal tides

2012 ◽  
Vol 708 ◽  
pp. 250-278 ◽  
Author(s):  
Nicolas Grisouard ◽  
Oliver Bühler
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Wave Drag ◽  
Perturbation Series ◽  
Internal Tides ◽  
Time Averaging ◽  
Mean Flow ◽  
Wave Source ◽  
Lee Waves ◽  
Lee Wave

AbstractWe present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave–mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.

scholarly journals Numerical simulation of supersquare patterns in Faraday waves

2015 ◽  
Vol 772 ◽  
Author(s):  
L. Kahouadji ◽  
N. Périnet ◽  
L. S. Tuckerman ◽  
S. Shin ◽  
J. Chergui ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Outer Wall ◽  
Wave Pattern ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Critical Wavelength ◽  
Characteristic Wavelength ◽  
Cylindrical Domains ◽  
Lagrangian Tracking

We report the first simulations of the Faraday instability using the full three-dimensional Navier–Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid front-tracking/level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in square and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of Douady & Fauve (Europhys. Lett., vol. 6, 1988, pp. 221–226) and Douady (J. Fluid Mech., vol. 221, 1990, pp. 383–409) is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared with the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the centre.

scholarly journals FORCES ON A PONTOON IN THREE DIMENSIONAL WAVES

1970 ◽  
Vol 1 (12) ◽  
pp. 101
Author(s):  
J. Eie ◽  
A. Tratterberg ◽  
A. Torum
Keyword(s):  
Three Dimensional ◽  
Wave Pattern ◽  
Wave Forces ◽  
Deterministic Method ◽  
Laboratory Equipment ◽  
Floating Breakwater ◽  
Floating Bridges ◽  
Dimensional Wave

Wave forces on a long pontoon (floating breakwater, floating bridges etc.) depend to a large extent on the three dimensional wave pattern. There is no deterministic method for calculating wave forces for such structures in a three dimensional sea and laboratory equipment for testing long structures in irregular three dimensional waves does hardly exist.

scholarly journals The Impact of Finite-Amplitude Bottom Topography on Internal Wave Generation in the Southern Ocean

2014 ◽  
Vol 44 (11) ◽  
pp. 2938-2950 ◽  
Author(s):  
Maxim Nikurashin ◽  
Raffaele Ferrari ◽  
Nicolas Grisouard ◽  
Kurt Polzin
Keyword(s):  
Southern Ocean ◽  
Internal Wave ◽  
Linear Theory ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Wave Generation ◽  
Two Dimensional ◽  
Lee Wave ◽  
Internal Wave Generation

Abstract Direct observations in the Southern Ocean report enhanced internal wave activity and turbulence in a kilometer-thick layer above rough bottom topography collocated with the deep-reaching fronts of the Antarctic Circumpolar Current. Linear theory, corrected for finite-amplitude topography based on idealized, two-dimensional numerical simulations, has been recently used to estimate the global distribution of internal wave generation by oceanic currents and eddies. The global estimate shows that the topographic wave generation is a significant sink of energy for geostrophic flows and a source of energy for turbulent mixing in the deep ocean. However, comparison with recent observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean shows that the linear theory predictions and idealized two-dimensional simulations grossly overestimate the observed levels of turbulent energy dissipation. This study presents two- and three-dimensional, realistic topography simulations of internal lee-wave generation from a steady flow interacting with topography with parameters typical of Drake Passage. The results demonstrate that internal wave generation at three-dimensional, finite bottom topography is reduced compared to the two-dimensional case. The reduction is primarily associated with finite-amplitude bottom topography effects that suppress vertical motions and thus reduce the amplitude of the internal waves radiated from topography. The implication of these results for the global lee-wave generation is discussed.

scholarly journals Wave Characteristics of Falling Film on Inclination Plate at Moderate Reynolds Number

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Chuan Lu ◽  
Sheng-Yao Jiang ◽  
Ri-Qiang Duan
Keyword(s):  
Reynolds Number ◽  
Solitary Wave ◽  
Film Flow ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Two Dimensional ◽  
Irregular Wave ◽  
Moderate Reynolds Number ◽  
Pulse Spacing ◽  
Primary Pulse

Falling water film on an inclined plane is studied by shadowgraphy. The ranges of inclination angle and the film Reynolds number are, respectively, up to 21° and 60. Water is used as working fluid. The scenario of wave regime evolution is identified as three distinctive regimes, namely, initial quiescent smooth film flow, two-dimensional regular solitary wave pattern riding on film flow, and three-dimensional irregular wave pattern. Three characteristic parameters of two-dimensional solitary wave pattern, namely, inception length, primary pulse spacing, and propagation velocity, are examined, which are significant in engineering applications for estimation of heat and mass transfer on film flow. The present experimental data are well in agreement with the Koizumi correlations, the deviation from which is limited to 20% and 15%, respectively, for primary pulse spacing and propagation velocity. Through the scrutiny of the present experimental observation, it is concluded that wave evolution on film flow at the moderate Reynolds number is controlled by gravity and drag and the Rayleigh-Taylor instability that occurred on the steep front of primary pulse triggers the disintegration of continuous two-dimensional regular solitary wave pattern into three-dimensional irregular wave pattern.

scholarly journals Oblique wave groups in deep water

1984 ◽  
Vol 146 ◽  
pp. 1-20 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Deep Water ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Periodic Wave ◽  
Two Dimensions ◽  
Wave Groups ◽  
Oblique Wave ◽  
Parallel Lines ◽  
The Waves

Oblique wave groups consist of waves whose straight parallel lines of constant phase are oblique to the straight parallel lines of constant group phase. Numerical solutions for periodic oblique wave groups with envelopes of permanent shape are calculated from the equations for irrotational three-dimensional deep-water motion with nonlinear upper free-surface conditions. Two distinct families of periodic wave groups are found, one in which the waves in each group are in phase with those in all other groups, and the other in which there is a phase difference of π between the waves in consecutive groups. It is shown that some analytical solutions for oblique wave groups calculated from the nonlinear Schrödinger equation are in error because they ignore the resonant forcing of certain harmonics in two dimensions. Particular attention is given to oblique wave groups whose group-to-wave angle is in the neighbourhood of the critical angle tan−1√½, corresponding to waves on the boundary wedge of the Kelvin ship-wave pattern.

scholarly journals ADAPTIVE SIMULATION OF THE INTERNAL FLOW IN A ROCKET NOZZLE

2014 ◽  
Vol 44 (3) ◽  
pp. 267-276
Author(s):  
L. GARELLI ◽  
G. RIOS RODRIGUEZ ◽  
R. PAZ ◽  
M. STORTI
Keyword(s):  
Computational Cost ◽  
Three Dimensional ◽  
Internal Flow ◽  
Wave Pattern ◽  
Adaptation Strategy ◽  
Rocket Nozzle ◽  
Flow Problems ◽  
Pressure Distributions ◽  
Internal Shock ◽  
Unstructured Tetrahedral Meshes

This work is a first step in the understanding of the interaction process between internal shock waves and the flow transition inside of a rocket nozzle that develops during the engine start-up phase or when the nozzle is operated at overexpanded conditions. In many cases, this transition in the flow pattern produces side loads in the nozzle due to an asymmetric pressure distribution on the wall, being harmful for the rocket’s integrity. To understand this phenomenon, a numerical simulation is performed by solving the three-dimensional Euler equations on unstructured tetrahedral meshes. With this model the computational cost to solve the equations significantly increases, therefore parallel processing is required. Also, an unsteady h-adaptive refinement strategy is used jointly with a Streamline Upwind Petrov-Galerkin and a discontinuity capturing scheme, both to keep the size of the fluid flow problem bounded and to sharply resolve the shock wave pattern. The mesh adaptation strategy is introduced. Since its performance is a major concern in the solution of unsteady flow problems, some implementation issues about the data structure chosen to represent the mesh are discussed. Average pressure distributions computed at the wall and the axis of the nozzle for various pressure ratios are analyzed based on experimental and numerical results from other authors.

Bioprinting of Liquid Hydrogel Precursors in a Support Bath by Analyzing Two Key Features: Cell Distribution and Shape Fidelity

2018 ◽  
Author(s):  
Houzhu Ding ◽  
Robert C. Chang
Keyword(s):  
Three Dimensional ◽  
Wave Pattern ◽  
Performance Outcomes ◽  
3D Analysis ◽  
Cell Distribution ◽  
Spatiotemporal Mapping ◽  
Low Viscosity ◽  
Tissue Constructs ◽  
Gravity Effects ◽  
Quantitative Analyses

Microextrusion-based bioprinting within a support bath material is an emerging additive manufacturing technique for fabricating complex three-dimensional (3D) tissue constructs. However, there exists fundamental knowledge gaps in understanding the spatiotemporal mapping of cells within the bioprinted constructs and their shape fidelity when embedded in a support bath material. To address these questions, this paper advances quantitative analyses to systematically determine the spatial distribution for cell-laden filament-based tissue constructs as a function of the bio-ink properties. Also, optimal bio-ink formulations are investigated to fabricate complex 3D structures with superior shape integrity. Specifically, for a 1D filament printed in a support bath, cells suspended in low viscosity liquid hydrogel precursors are found to exhibit a characteristic non-uniform distribution as measured by a degree of separation (Ds) metric. In a 2D square wave pattern print, cells are observed to flow and aggregate downstream at certain positions along the in-plane print direction. In a 3D analysis, owing to the high cell density and gravity effects, a non-uniform cell distribution within a printed cylindrical structure is observed in the build direction. From the structural standpoint, the addition of CaCl2 to the support bath activates the hydrogel cross-linking process during printing, resulting in 3D prints with enhanced structural outcomes. This multidimensional print analysis provides evidence that, under the emerging bioprinting support bath paradigm, the printable parameter space can be extended to low viscosity liquid hydrogel precursor materials that can be systematically characterized and optimized for key process performance outcomes in cell distribution and shape fidelity.

Sign in / Sign up

Export Citation Format

Share Document