Wave Propagation in Flows Across Junctions Between Rigid and Flexible Walls

2002 ◽  
Author(s):  
P. W. Carpenter ◽  
P. K. Sen ◽  
S. Hegde ◽  
C. Davies
Keyword(s):  
Wave Propagation ◽  
Channel Flow ◽  
Incident Wave ◽  
Wave System ◽  
Transmitted Waves ◽  
Generic Problem ◽  
Flexible Walls ◽  
Walled Channel ◽  
Spatially Homogeneous ◽  
Tollmien Schlichting

The generic problem considered is the propagation of vortical waves across junctions between one wave-bearing medium and another. It is assumed that the eigensolutions are known for the corresponding spatially homogeneous problems. The task is how to determine the amplitudes of the reflected and transmitted waves given the amplitude of the incident wave. In general, there may be more than one incident, reflected or transmitted wave. It is shown how this sort of problem may be solved in terms of the homogeneous eigensolutions by drawing an analogy between the junction and a wave-driver. The particular illustrative problem studied is that of a Tollmien-Schlichting wave, propagating along a rigid-walled channel flow, that is incident on a section of the channel where the walls consist of compliant panels. It is shown how the wave system over the compliant panels and the amplitude of the Tollmien-Schlichting wave leaving the compliant section may be determined in terms of the incident wave. The technique developed for this problem is considered to be generic.

Ship Motions in Shallow Water

1970 ◽  
Vol 14 (04) ◽  
pp. 317-328 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Incident Wave ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Exciting Force ◽  
Ship Motions ◽  
Wave System ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients

The problem discussed concerns small motions of a ship, in all six degrees of freedom, but at zero speed of advance, due to an incident wave system in shallow water of depth comparable with the ship's draft. The problem is completely formulated for an arbitrary ship, and is partially solved for the case when the ship is slender and the wavelength much greater than the water depth. Sample numerical computations of heave, pitch, and sway added mass and damping coefficients and the sway exciting force are presented.

The effect of boundaries on wave propagation in a liquid-filled porous solid: V. Transmission across a plane interface

1964 ◽  
Vol 54 (1) ◽  
pp. 409-416
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Interface ◽  
Plane Body ◽  
Cross Sectional ◽  
Material Constants ◽  
Transmitted Waves

abstract The passage of plane body waves across a plane interface from one to another, contiguous, porous aggregate is examined, with particular attention paid to motions involving wave lengths large in comparison with cross-sectional pore dimensions. The results are obtained for a rather general set of boundary conditions which take account of possible resistance to flow due to partial nonalignment of pores at the interface. It is found that when certain conditions of equality of material constants for the two media are met one or more of the reflected and transmitted waves are extinguished.

scholarly journals Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

2016 ◽  
Vol 178 ◽  
pp. 158-166 ◽  
Author(s):  
Armen G. Hayrapetyan ◽  
Jörg B. Götte ◽  
Karen K. Grigoryan ◽  
Stephan Fritzsche ◽  
Rubik G. Petrosyan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Electromagnetic Wave Propagation ◽  
Time Varying ◽  
Dielectric Media ◽  
Spatially Homogeneous

Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks

1979 ◽  
Vol 83 (1-2) ◽  
pp. 17-24 ◽  
Author(s):  
Guy Boillatt ◽  
Tommaso Ruggeri
Keyword(s):  
Shock Wave ◽  
General Theory ◽  
Shock Front ◽  
Incident Wave ◽  
Reflection And Transmission ◽  
Transmitted Waves ◽  
Discontinuity Waves ◽  
Weak Shocks

SynopsisAn incident wave creates a discontinuity in the acceleration of the shock front. The amplitudes of the reflected and transmitted waves are also determined. Special attention is given to the case of the weak shocks and the characteristic shocks.

Nonlinear interaction of oblique three-dimensional Tollmien-Schlichting waves and longitudinal vortices, in channel flows and boundary layers

1992 ◽  
Vol 436 (1898) ◽  
pp. 585-602 ◽  
Keyword(s):  
Boundary Layers ◽  
Channel Flow ◽  
Nonlinear Interaction ◽  
Vortex Flow ◽  
Blow Up ◽  
Three Dimensional ◽  
Channel Flows ◽  
Nonlinear Evolution Equations ◽  
Longitudinal Vortex ◽  
Tollmien Schlichting

The present theoretical article considers the nonlinear interaction of oblique three dimensional Tollmien-Schlichting waves and induced or input longitudinal vortex motion, mainly for channel flow at large Reynolds numbers. Both the waves and the vortices are controlled by viscous-inviscid balancing but their respective flow structures are rather different because of the different typical timescales involved. This leads to the vortex-wave interaction being governed by nonlinear evolution equations on the vortex timescale, even though the wave amplitudes are notably small. The analogue in boundary-layer transition, addressed in a previous paper, is also re-considered here. Computational and analytical properties of the interaction equations for both channel flows and boundary layers are investigated, along with certain connections with companion studies of other vortex-wave interactions in channel flow. The nonlinear interactions in channel flow are found to lead to finitetime blow-up in amplitudes or to sustained vortex flow at large scaled times, depending on the input conditions. In particular, increasing the input amplitudes of the vortex or the wave can readily provoke blow-up even in the linearly stable regime; whereas in the case of sustained vortex flow new physical effects come into play on slightly longer timescales. Again, a very interesting feature is that the blowup response is found to be confined to a small range of wave angles near 45° relative to the original flow direction.

Simulations of natural transition in viscoelastic channel flow

2017 ◽  
Vol 820 ◽  
pp. 232-262 ◽  
Author(s):  
Sang Jin Lee ◽  
Tamer A. Zaki
Keyword(s):  
Growth Rate ◽  
Drag Reduction ◽  
Channel Flow ◽  
Secondary Instability ◽  
Transition To Turbulence ◽  
Newtonian Flow ◽  
Final State ◽  
Periodic State ◽  
Nonlinear Amplification ◽  
Tollmien Schlichting

Orderly, or natural, transition to turbulence in dilute polymeric channel flow is studied using direct numerical simulations of a FENE-P fluid. Three Weissenberg numbers are simulated and contrasted to a reference Newtonian configuration. The computations start from infinitesimally small Tollmien–Schlichting (TS) waves and track the development of the instability from the early linear stages through nonlinear amplification, secondary instability and full breakdown to turbulence. At the lowest elasticity, the primary TS wave is more unstable than the Newtonian counterpart, and its secondary instability involves the generation of $\unicode[STIX]{x1D6EC}$-structures which are narrower in the span. These subsequently lead to the formation of hairpin packets and ultimately breakdown to turbulence. Despite the destabilizing influence of weak elasticity, and the resulting early transition to turbulence, the final state is a drag-reduced turbulent flow. At the intermediate elasticity, the growth rate of the primary TS wave matches the Newtonian value. However, unlike the Newtonian instability mode which reaches a saturated equilibrium condition, the instability in the polymeric flow reaches a periodic state where its energy undergoes cyclical amplification and decay. The spanwise size of the secondary instability in this case is commensurate with the Newtonian $\unicode[STIX]{x1D6EC}$-structures, and the extent of drag reduction in the final turbulent state is enhanced relative to the lower elasticity condition. At the highest elasticity, the exponential growth rate of the TS wave is weaker than the Newtonian flow and, as a result, the early linear stage is prolonged. In addition, the magnitude of the saturated TS wave is appreciably lower than the other conditions. The secondary instability is also much wider in the span, with weaker ejection and without hairpin packets. Instead, streamwise-elongated streaks are formed and break down to turbulence via secondary instability. The final state is a high-drag-reduction flow, which approaches the Virk asymptote.

Shallow Wave Propagation in Open Channel Flow

1977 ◽  
Vol 103 (12) ◽  
pp. 1461-1476 ◽  
Author(s):  
Victor Miguel Ponce ◽  
Daryl B. Simons
Keyword(s):  
Wave Propagation ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow
Sign in / Sign up

Export Citation Format

Share Document