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Velocities

The fluid velocity is shown in figures 7-31 - 7-38 at tex2html_wrap_inline12457 for the four waves shown in table 7-1.

   table6335
Table: The four waves in figures 7-31 - 7-38

   figure6359
Figure 7-31: Horizontal velocity contour plot for wave (1) with tex2html_wrap_inline12323 , tex2html_wrap_inline12193 , tex2html_wrap_inline12453 and f = 1.4 at tex2html_wrap_inline12457 .

   figure6369
Figure 7-32: Vertical velocity contour plot for wave (1) with tex2html_wrap_inline12323 , tex2html_wrap_inline12193 , tex2html_wrap_inline12453 and f = 1.4 at tex2html_wrap_inline12457 .

   figure6379
Figure 7-33: Horizontal velocity contour plot for wave (2) with tex2html_wrap_inline12323 , tex2html_wrap_inline12193 , tex2html_wrap_inline12473 and f = 1.05 at tex2html_wrap_inline12457 .

   figure6389
Figure 7-34: Vertical velocity contour plot for wave (2) with tex2html_wrap_inline12323 , tex2html_wrap_inline12193 , tex2html_wrap_inline12473 and f = 1.05 at tex2html_wrap_inline12457 .

   figure6399
Figure 7-35: Horizontal velocity contour plot for wave (3) with tex2html_wrap_inline12323 , tex2html_wrap_inline12193 , tex2html_wrap_inline12493 and f = 1.86 at tex2html_wrap_inline12457 .

   figure6409
Figure 7-36: Vertical velocity contour plot for wave (3) with tex2html_wrap_inline12323 , tex2html_wrap_inline12193 , tex2html_wrap_inline12493 and f = 1.86 at tex2html_wrap_inline12457 .

   figure6419
Figure 7-37: Horizontal velocity contour plot for wave (4) with tex2html_wrap_inline12323 , tex2html_wrap_inline12511 , tex2html_wrap_inline12453 and f = 1.4 at tex2html_wrap_inline12457 .

   figure6429
Figure 7-38: Vertical velocity contour plot for wave (4) with tex2html_wrap_inline12323 , tex2html_wrap_inline12511 , tex2html_wrap_inline12453 and f = 1.4 at tex2html_wrap_inline12457 .

All four waves have g in the range tex2html_wrap_inline16703 . The value of g affects both the magnitude and the shape of the velocity profile since tex2html_wrap_inline12301 is a function of g. Wave (1) has a relatively low viscosity and the lower fluid is significantly denser than the top fluid. Wave (2) also has a relatively low viscosity and the two fluids are of similar densities varying by only 5%. Wave (3) has the same viscosity as the first two waves but the density difference is considerable, the ratio of the densities is 1.86. Wave (4) has the same density distribution as wave (1) but the viscosity is five times larger. For each wave the velocity is symmetric about and tex2html_wrap_inline12305 . The velocities are not symmetric about x = 0, although the contour plots are similar in both fluids. The difference is greatest when there is a large density difference corresponding to a large value of f. The magnitudes of the velocities are different for each wave. Wave (2) has velocities considerable smaller than the other waves. These lower velocities are shown in figures 7-33 and 7-34 where the contour lines are distorted slightly near the interface. This is due to small, spurious interface velocities which have been observed for the lattice Boltzmann model and which are due to the finite space and time steps [38]. This is not observed for the other waves where the velocities are higher. For each wave the magnitudes of u and w are similar. The vertical velocity peaks at z = 0 to a slightly higher value than the peak horizontal velocity, which occurs slightly above and below the interface. In wave (1) and wave (3) u peaks close to the interface, the contours for the higher magnitudes have an elliptical appearance, the semi-major axis parallel to the interface. The contours for the lower magnitudes appear more triangular in shape with the base near the interface and the opposite angle considerably rounded. Waves (2) and (4), on the other hand, have u peaking further from the interface. The high magnitude contours are much more circular and the lower magnitude contours are almost rectangular with curved corners. The lower magnitude contours for the vertical velocity are elliptical for all the waves, the semi-major axis is perpendicular to the interface. The higher magnitude contours for waves (2) and (4) are approximately circular while for waves (1) and (3) they are more elliptical in the same sense as the horizontal velocity.




next up previous contents
Next: Velocity Variation Across a Up: Interfacial Standing Wave Simulations Previous: Continuously Varying Density at

James Buick
Tue Mar 17 17:29:36 GMT 1998