scholarly journals The structure of low-Froude-number lee waves over an isolated obstacle

2011 ◽  
Vol 689 ◽  
pp. 3-31 ◽  
Author(s):  
Stuart B. Dalziel ◽  
Michael D. Patterson ◽  
C. P. Caulfield ◽  
Stéphane Le Brun
Keyword(s):  
Froude Number ◽  
Three Dimensional ◽  
Classical Problem ◽  
Quantitative Agreement ◽  
Horizontal Flow ◽  
Lee Waves ◽  
Theoretical Predictions ◽  
Low Froude Number ◽  
Linearized Theory ◽  
Over The Top

AbstractWe present new insight into the classical problem of a uniform flow, linearly stratified in density, past an isolated three-dimensional obstacle. We demonstrate how, for a low-Froude-number obstacle, simple linear theory with a linearized boundary condition is capable of providing excellent quantitative agreement with laboratory measurements of the perturbation to the density field. It has long been known that such a flow may be divided into two regions, an essentially horizontal flow around the base of the obstacle and a wave-generating flow over the top of the obstacle, but until now the experimental diagnostics have not been available to test quantitatively the predicted features. We show that recognition of a small slope that develops across the obstacle in the surface separating these two regions is vital to rationalize experimental measurements with theoretical predictions. Utilizing the principle of stationary phase and causality arguments to modify the relationship between wavenumbers in the lee waves, linearized theory provides a detailed match in both the wave amplitude and structure to our experimental observations. Our results demonstrate that the structure of the lee waves is extremely sensitive to departures from horizontal flow, a detail that is likely to be important for a broad range of geophysical manifestations of these waves.

A Contribution to Study on the Lift of Ventilated Supercavitating Vehicle With Low Froude Number

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Yu Kaiping ◽  
Zhou Jingjun ◽  
Min Jingxin ◽  
Zhang Guang
Keyword(s):  
Numerical Simulations ◽  
Froude Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Gravitational Effect ◽  
Gas Leakage ◽  
Supercavitating Vehicle ◽  
Numerical Predictions ◽  
Low Froude Number

A ventilated cavity was investigated using three-dimensional numerical simulation and cavitation water tunnel experiments under the condition of low Froude number. A two-fluid multiphase flow model was adopted in numerical predictions. The drag between the different phases and gravitational effect, as well as the compressibility of gas, was considered in the numerical simulations. By comparing the ventilated coefficient computational results of three different turbulence models with the Epshtein formula, the shear-stress-transport turbulence model was finally employed. The phenomenon of double-vortex tube gas-leakage was observed in both numerical simulations and experiments. Based on the validity of the numerical method, the change law of the lift coefficient on the afterbody was given by numerical predictions and accorded well with experimental results. The cause for the appearance of an abrupt increase in lift was difficult to get from experiments for the hard measurement, whereas the numerical simulations provided some supplements to analyze the reasons. The distribution of lift coefficient on the afterbody had important significance to the design of underwater vehicles.

Numerical study of surface thermal signatures of lee waves excited by moving underwater sphere at low Froude number

2021 ◽  
pp. 109314
Author(s):  
Cheng-An Wang ◽  
Duo Xu ◽  
Ji-Peng Gao ◽  
Jian-Yu Tan ◽  
Zhi-Quan Zhou
Keyword(s):  
Froude Number ◽  
Numerical Study ◽  
Lee Waves ◽  
Low Froude Number

The rise and fall of turbulent fountains: a new model for improved quantitative predictions

2010 ◽  
Vol 657 ◽  
pp. 265-284 ◽  
Author(s):  
G. CARAZZO ◽  
E. KAMINSKI ◽  
S. TAIT
Keyword(s):  
Steady State ◽  
Froude Number ◽  
Turbulent Flows ◽  
Scaling Laws ◽  
Quantitative Agreement ◽  
Industrial Applications ◽  
Clear Understanding ◽  
New Model ◽  
Major Interest ◽  
Theoretical Predictions

Turbulent fountains are of major interest for many natural phenomena and industrial applications, and can be considered as one of the canonical examples of turbulent flows. They have been the object of extensive experimental and theoretical studies that yielded scaling laws describing the behaviour of the fountains as a function of source conditions (namely their Reynolds and Froude numbers). However, although such scaling laws provide a clear understanding of the basic dynamics of the turbulent fountains, they usually rely on more or lessad hocdimensionless proportionality constants that are scarcely tested against theoretical predictions. In this paper, we use a systematic comparison between the initial and steady-state heights of a turbulent fountain predicted by classical top-hat models and those obtained in experiments. This shows scaling agreement between predictions and observations, but systematic discrepancies regarding the proportionality constant. For the initial rise of turbulent fountains, we show that quantitative agreement between top-hat models and experiments can be achieved by taking into account two factors: (i) the reduction of entrainment by negative buoyancy (as quantified by the Froude number), and (ii) the fact that turbulence is not fully developed at the source at intermediate Reynolds number. For the steady-state rise of turbulent fountains, a new model (‘confined top-hat’) is developed to take into account the coupling between the up-flow and the down-flow in the steady-state fountain. The model introduces three parameters, calculated from integrals of experimental profiles, that highlight the dynamics of turbulent entrainment between the up-flow and the down-flow, as well as the change of buoyancy flux with height in the up-flow. The confined top-hat model for turbulent fountains achieves good agreement between theoretical predictions and experimental results. In particular, it predicts a systematic increase of the ratio between the initial and steady-state heights of turbulent fountains as a function of their source Froude number, an observation that was not handled properly in previous models.

1503 Three-dimensional velocity-field measurement of inflow phenomenon in buoyant jet at low Froude number

2013 ◽  
Vol 2013.50 (0) ◽  
pp. 150301-150302
Author(s):  
Atsushi MAEDA ◽  
Ai ISHIZUKA ◽  
Ryuta WATANABE ◽  
Takayuki YAMAGATA ◽  
Nobuyuki FUJISAWA
Keyword(s):  
Velocity Field ◽  
Froude Number ◽  
Field Measurement ◽  
Three Dimensional ◽  
Buoyant Jet ◽  
Low Froude Number ◽  
Velocity Field Measurement

Tilt-induced instability of a stratified vortex

2008 ◽  
Vol 596 ◽  
pp. 1-20 ◽  
Author(s):  
NICOLAS BOULANGER ◽  
PATRICE MEUNIER ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Froude Number ◽  
Three Dimensional ◽  
Axial Flow ◽  
Companion Paper ◽  
Shear Instability ◽  
Critical Layer ◽  
Theoretical Predictions ◽  
Layer Region ◽  
Sudden Decrease ◽  
Dimensional Instability

This experimental and theoretical study considers the dynamics and the instability of a Lamb–Oseen vortex in a stably stratified fluid. In a companion paper, it was shown that tilting the vortex axis with respect to the direction of stratification induces the formation of a rim of strong axial flow near a critical radius when the Froude number of the vortex is larger than one.Here, we demonstrate that this tilt-induced flow is responsible for a three-dimensional instability. We show that the instability results from a shear instability of the basic axial flow in the critical-layer region. The theoretical predictions for the wavelength and the growth rate obtained by a local stability analysis of the theoretical critical-layer profile are compared to experimental measurements and a good agreement is observed. The late stages of the instability are also analysed experimentally. In particular, we show that the tilt-induced instability does not lead to the destruction of the vortex, but to a sudden decrease of its Froude number, through the turbulent diffusion of its core size, when the initial Froude number is close to 1. A movie is available with the online version of the paper.

scholarly journals New gravity–capillary waves at low speeds. Part 1. Linear geometries

2013 ◽  
Vol 724 ◽  
pp. 367-391 ◽  
Author(s):  
Philippe H. Trinh ◽  
S. Jonathan Chapman
Keyword(s):  
Froude Number ◽  
Fourier Transforms ◽  
Capillary Flow ◽  
Asymptotic Series ◽  
Bond Number ◽  
Capillary Waves ◽  
Low Froude Number ◽  
Linearized Theory ◽  
The Waves ◽  
Exponential Asymptotics

AbstractWhen traditional linearized theory is used to study gravity–capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear nature of the obstruction, asymptotic expansions in the low-Froude-number or low-Bond-number limits can be derived, but here, the solutions invariably predict a waveless surface at every order. This is because the waves are in fact, exponentially small, and thus beyond-all-orders of regular asymptotics; their formation is a consequence of the divergence of the asymptotic series and the associated Stokes Phenomenon. By applying techniques in exponential asymptotics to this problem, we have discovered the existence of new classes of gravity–capillary waves, from which the usual linear solutions form but a special case. In this paper, we present the initial theory for deriving these waves through a study of gravity–capillary flow over a linearized step. This will be done using two approaches: in the first, we derive the surface waves using the standard method of Fourier transforms; in the second, we derive the same result using exponential asymptotics. Ultimately, these two methods give the same result, but conceptually, they offer different insights into the study of the low-Froude-number, low-Bond-number problem.

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