On surface flow induced by internal waves generated by a slender body moving at low internal Froude number in a sharply stratified fluid

2021 ◽  
Vol 239 ◽  
pp. 109755
Author(s):  
Jun Zhang ◽  
Zhichong Yao ◽  
Fangwen Hong ◽  
Genshui Zhou ◽  
Debao Gao ◽  
...  
Keyword(s):  
Froude Number ◽  
Internal Waves ◽  
Stratified Fluid ◽  
Surface Flow ◽  
Slender Body ◽  
Internal Froude Number

scholarly journals A limitation on Long's model in stratified fluid flows

1971 ◽  
Vol 48 (1) ◽  
pp. 161-179 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Froude Number ◽  
Barrier Height ◽  
Density Gradient ◽  
Dynamic Pressure ◽  
Fluid Flows ◽  
Critical Value ◽  
Stratified Fluid ◽  
Lee Wave ◽  
Finite Barrier ◽  
Internal Froude Number

The flow of a continuously stratified fluid into a contraction is examined, under the assumptions that the dynamic pressure and the density gradient are constant upstream (Long's model). It is shown that a solution to the equations exists if and only if the strength of the contraction does not exceed a certain critical value which depends on the internal Froude number. For the flow of a stratified fluid over a finite barrier in a channel, it is further shown that, if the barrier height exceeds this same critical value, lee-wave amplitudes increase without bound as the length of the barrier increases. The breakdown of the model, as implied by these arbitrarily large amplitudes, is discussed. The criterion is compared with available experimental results for both geometries.

Intrusion into a stratified fluid

1976 ◽  
Vol 74 (3) ◽  
pp. 547-560 ◽  
Author(s):  
P. C. Manins
Keyword(s):  
Froude Number ◽  
Kinematic Viscosity ◽  
Salt Water ◽  
Stratified Fluid ◽  
Buoyancy Frequency ◽  
Homogeneous Fluid ◽  
Order Unity ◽  
Internal Froude Number ◽  
Half Thickness

Preliminary measurements have been made of the debouching of homogeneous fluid from a broad source at its equilibrium depth into a linearly stratified tank of salt water. With c the velocity of the nose of the intrusion, h its half-thickness near the source, N the environmental buoyancy frequency and v the kinematic viscosity of the fluid, it is shown for 100 [lsim ] Re ≡ 2ch/ν [lsim ] 500 that the intrusion becomes practically steady under an inertia-buoyancy balance. The internal Froude number Fr = c/Nh is shown to be of order unity. Forward-propagating disturbances and the ends of the tank are inferred to play an important part in the flow.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

Side Forces on a Ship’s Hull

1988 ◽  
Vol 32 (03) ◽  
pp. 203-207
Author(s):  
W. S. Hunter ◽  
P. N. Joubert
Keyword(s):  
Froude Number ◽  
Asymptotic Expansions ◽  
Experimental Results ◽  
Slender Body ◽  
Flat Plates ◽  
Slender Body Theory ◽  
Towing Tank ◽  
Side Force ◽  
Low Froude Number ◽  
Body Theory

Side forces on a ship traveling at small yaw angles are predicted using slender-body theory. The approach uses the method of matched asymptotic expansions, with a cascade of flat plates as a model for the submarine portion of the ship's hull. Resulting predictions of side force coefficients are then compared with experimentally measured values derived from towing tank tests of a typical (tanker) hull. Correlation between theoretical and experimental results was very good for yaw angles less than 8 deg at low Froude number (Fn = 0.134).

Time-Domain Hydroelasticity Theory of Ships Responding to Waves

1997 ◽  
Vol 41 (04) ◽  
pp. 286-300
Author(s):  
Jinzhu Xia ◽  
Zhaohui Wang
Keyword(s):  
Time Domain ◽  
Separation Of Variables ◽  
Mathematical Formulation ◽  
Rigid Motion ◽  
Surface Flow ◽  
Slender Body ◽  
Irregular Waves ◽  
Restoring Force ◽  
Slender Body Theory ◽  
Body Theory

A time-domain linear theory of fluid-structure interaction between floating structures and the incident waves is presented. The structure is assumed to be elastic and represented by general separation of variables, whereas the fluid is described as an initial boundary value problem of potential free surface flow. The general interface boundary condition is used in the mathematical formulation of the fluid motion around the flexible structure. The general time-domain theory is simplified to a slender-body theory for the analysis of wave-induced global responses of monohull ships. The structure is represented by a nonuniform beam, while the generalized hydrodynamic coefficients can be obtained from two-dimensional potential flow theory. The linear slender body theory is generalized to treat the nonlinear loading effects of rigid motion and structural response of ships traveling in rough seas. The nonlinear hydrostatic restoring force and hydrodynamic momentum action are considered. A numerical solution is presented for the slender body theory. Numerical examples are given for two ship cases with different geometry features, a warship hull and the S175 containership with two different bow flare forms. The predicted results include linear and nonlinear rigid motions and structural responses of ships advancing in regular and irregular waves. The results clearly demonstrate the importance and the magnitude of nonlinear effects in ship motions and internal forces. Numerical calculations are compared with experimental results of rigid and elastic material ship model tests. Good agreement is obtained.

scholarly journals Two infinite-Froude-number cusped free-surface flows due to a submerged line source or sink

1986 ◽  
Vol 28 (2) ◽  
pp. 260-270 ◽  
Author(s):  
I. L. Collings
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Ideal Fluid ◽  
Line Source ◽  
Steady Motion ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Flow Problems

AbstractSolutions are found to two cusp-like free-surface flow problems involving the steady motion of an ideal fluid under the infinite-Froude-number approximation. The flow in each case is due to a submerged line source or sink, in the presence of a solid horizontal base.

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.

Flows generated by the periodic horizontal oscillations of a sphere in a linearly stratified fluid

1994 ◽  
Vol 263 ◽  
pp. 245-270 ◽  
Author(s):  
Qiang Lin ◽  
D. L. Boyer ◽  
H. J. S. Fernando
Keyword(s):  
Flow Field ◽  
Flow Regime ◽  
Numerical Models ◽  
Stokes Number ◽  
Stratified Fluid ◽  
Circular Cylinders ◽  
Wave Flow ◽  
Motion Field ◽  
Attached Flow ◽  
Internal Froude Number

The flow field induced by a sphere oscillating horizontally in a linearly stratified fluid is studied using a series of laboratory experiments. The resulting flows are shown to depend on the Stokes number β, the Keulegan–Carpenter number KC and the internal Froude number Fr. For Fr [clubs ] 0.2, it is shown that the nature of the resulting flow field is approximately independent of Fr and, based on this observation, a flow regime diagram is developed in the (β, KC)-plane. The flow regimes include: (i) fully-attached flow; (ii) attached vortices; (iii) local vortex shedding; and (iv) standing eddy pair. An internal-wave flow regime is also identified but, for such flows, the motion field is a function of Fr as well. Some quantitative measures are given to allow for future comparisons of the present results with analytical and/or numerical models. Wherever possible, the results are compared with the experiments of Tatsuno & Bearman (1990) on right circular cylinders oscillating in homogeneous fluids.

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