Exact Ray‐Theory Solutions for Two‐Dimensional Velocity Variation

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.

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Numerical simulation of converging nonlinear wavefronts

Journal of Fluid Mechanics ◽

10.1017/s0022112098003310 ◽

1999 ◽

Vol 385 ◽

pp. 1-20 ◽

Cited By ~ 10

Author(s):

PHOOLAN PRASAD ◽

K. SANGEETA

Keyword(s):

Numerical Simulation ◽

Linear Theory ◽

Amplitude Distribution ◽

Two Dimensional ◽

Ray Theory ◽

Initial Shape ◽

Weakly Nonlinear ◽

Polytropic Gas ◽

Uniform State

The propagation of a two-dimensional weakly nonlinear wavefront into a polytropic gas in a uniform state and at rest has been studied. Successive positions of the wavefront and the distribution of amplitude on it are obtained by solving a system of conservation forms of the equations of weakly nonlinear ray theory (WNLRT) using a TVB scheme based on the Lax–Friedrichs flux. The predictions of the WNLRT are found to be qualitatively quite different from the predictions of the linear theory. The linear wavefronts leading to the formation of caustics are replaced by nonlinear wavefronts with kinks. By varying the initial shape of the wavefront and the amplitude distribution on it, the formation and separation of kinks on the wavefront has been studied.

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Ray theory for scattering by two-dimensional quasiperiodic plane finite arrays

IEEE Transactions on Antennas and Propagation ◽

10.1109/8.486307 ◽

1996 ◽

Vol 44 (3) ◽

pp. 375-382 ◽

Cited By ~ 29

Author(s):

L.B. Felsen ◽

E.G. Ribas

Keyword(s):

Two Dimensional ◽

Ray Theory

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Stability analysis of stratified shear flows with a monotonic velocity profile without inflection points. Part 2. Continuous density variation

Journal of Fluid Mechanics ◽

10.1017/s0022112008004278 ◽

2008 ◽

Vol 617 ◽

pp. 301-326 ◽

Cited By ~ 11

Author(s):

S. M. CHURILOV

Keyword(s):

Velocity Profile ◽

Shear Flows ◽

Oscillation Mode ◽

Lower Boundary ◽

Ideal Incompressible Fluid ◽

Velocity Variation ◽

Two Dimensional ◽

Instability Domain ◽

Minimum Width ◽

Inflection Points

We investigate stability with respect to two-dimensional (independent of z) disturbances of plane-parallel shear flows with a velocity profile Vx=u(y) of a rather general form, monotonically growing upwards from zero at the bottom (y=0) to U0 as y → ∞ and having no inflection points, in an ideal incompressible fluid stably stratified in density in a layer of thickness ℓ, small as compared to the scale L of velocity variation. In terms of the ‘wavenumber k – bulk Richardson number J’ variables, the upper and lower (in J) boundaries of instability domains are found for each oscillation mode. It is shown that the total instability domain has a lower boundary which is convex downwards and is separated from the abscissa (k) axis by a strip of stability 0 < J < J0(−)(k) with minimum width J*=O(ℓ2/L2) at kL=O(1). In other words, the instability domain configuration is such that three-dimensional (oblique) disturbances are first to lose their stability when the density difference across the layer increases. Hence, in the class of flows under consideration, it is a three- not two-dimensional turbulence that develops as a result of primary instability.

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Effect of Axial Velocity Variation in Aerofoil Cascades

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1971_013_015_02 ◽

1971 ◽

Vol 13 (2) ◽

pp. 92-99 ◽

Cited By ~ 1

Author(s):

S. Soundranayagam

Keyword(s):

Wind Tunnel ◽

Incompressible Flow ◽

Axial Velocity ◽

Three Dimensional ◽

Velocity Variation ◽

Two Dimensional ◽

Dimensional Flow ◽

Two Dimensional Flow ◽

Wind Tunnel Data ◽

Flow Through

The effect of the variation of axial velocity in the incompressible flow through a cascade of aerofoils is discussed and it is shown that changes take place in the flow angles and in the blade circulation. A method is proposed by which the effect of axial velocity variation on a known two-dimensional flow or alternatively the two-dimensional equivalent of a flow with axial velocity variation can be calculated. The method is very easy to apply. The deviation may increase or decrease depending on the change in blade circulation and the stagger. An increase in apparent deflection through the cascade can be accompanied by a reduction in the blade force. The method would be particularly useful for the interpretation of cascade wind tunnel data and in the design of impeller stages where three-dimensional flows occur.

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