5:15 PM - 7:15 PM
[HGM04-P12] Verification of the Equation of the Flight Distance of a Sand Particle over Wind Ripples in the Nishimori Model by using Numerical Analysis
Keywords:Wind Ripples, Dunes, Numerical Analysis, Finite Difference Method, Cellular Automaton
The morphology of sand ripples and dunes has been investigated physically for about a century, but various questions remain open. In particular, nonlinear coarsening through collisions and merging of individual dunes makes the problem difficult. This study is based on a qualitative model of the formation of ripples and dunes proposed by Nishimori and Ouchi (1993) [1]. We hereafter refer to this model as "the Nishimori model." The model uses different equations of sand transports for ripples and dunes. In the saltation model of sands for ripples, the flight distance is assumed to be a linear function of the bed height at the position where the sand leaves the ground.
We attempted to improve the equation for saltation in the Nishimori model in order to make the model more quantitative. We mechanically calculated the sand flight distance, which is the difference between the take-off and landing positions of saltating sand particles. First, we numerically solved the equations of an incompressible fluid in a two-dimensional vertical plane since the wind blows a sand particle over ripples. The shape of the boundary between the fluid and the underlying sand bed was assumed to be sinusoidal, and the influence of saltating sand particles on the flow field was ignored. We used the finite difference method to obtain a steady flow field. Second, we solved the equation of motion of a sand particle in the flow field obtained in the previous step. The forces acting on the sand particle are the gravity and the drag based on Stokes' law. The magnitude of the initial velocity of the sand particle when it leaves the ground was assumed to be the friction velocity. The direction of the initial velocity was assumed to be a parameter, which was set at 10°, 20°, 30° and 40° measured from the ground.
Figure 1 shows the resulting flight distance. The horizontal axis represents the bed height where the sand particle leaves the ground, and the vertical axis represents the flight distance of the sand particle. The brightness of color represents the direction of the initial velocity. The darker the color is, the larger the angle between the initial velocity and the ground is. The solid light blue line is a curve fitted with an exponential function of the bed height for all points. A positive correlation exists between the bed height and the flight distance, suggesting that the flight distance model in the Nishimori model was qualitatively reasonable. We applied the exponential model of the flight distance to the Nishimori model to find a ripple pattern. The patterns obtained with the new and original equations were qualitatively similar but somewhat different in shape. A comparison of ripple patterns with new and original equations will be reported in this meeting. The Nishimori model predicts that the ripple wavelength is approximately 4/3 times the average flight distance, which was confirmed for the model with the new equation of the flight distance. The flight distance increased as the initial angle of a sand particle increased because the higher the particle is thrown in the air, the longer it is blown by the wind. The results of applying a directional distribution of the initial sand velocity to the Nishimori model will be reported in this meeting.
References
[1] Nishimori･Ouchi (1993) "Dynamics of Wind-blown Sand Bed -Ripples and Dunes-", Bussei Kenkyu 61(1):32-43. (in Japanese)
We attempted to improve the equation for saltation in the Nishimori model in order to make the model more quantitative. We mechanically calculated the sand flight distance, which is the difference between the take-off and landing positions of saltating sand particles. First, we numerically solved the equations of an incompressible fluid in a two-dimensional vertical plane since the wind blows a sand particle over ripples. The shape of the boundary between the fluid and the underlying sand bed was assumed to be sinusoidal, and the influence of saltating sand particles on the flow field was ignored. We used the finite difference method to obtain a steady flow field. Second, we solved the equation of motion of a sand particle in the flow field obtained in the previous step. The forces acting on the sand particle are the gravity and the drag based on Stokes' law. The magnitude of the initial velocity of the sand particle when it leaves the ground was assumed to be the friction velocity. The direction of the initial velocity was assumed to be a parameter, which was set at 10°, 20°, 30° and 40° measured from the ground.
Figure 1 shows the resulting flight distance. The horizontal axis represents the bed height where the sand particle leaves the ground, and the vertical axis represents the flight distance of the sand particle. The brightness of color represents the direction of the initial velocity. The darker the color is, the larger the angle between the initial velocity and the ground is. The solid light blue line is a curve fitted with an exponential function of the bed height for all points. A positive correlation exists between the bed height and the flight distance, suggesting that the flight distance model in the Nishimori model was qualitatively reasonable. We applied the exponential model of the flight distance to the Nishimori model to find a ripple pattern. The patterns obtained with the new and original equations were qualitatively similar but somewhat different in shape. A comparison of ripple patterns with new and original equations will be reported in this meeting. The Nishimori model predicts that the ripple wavelength is approximately 4/3 times the average flight distance, which was confirmed for the model with the new equation of the flight distance. The flight distance increased as the initial angle of a sand particle increased because the higher the particle is thrown in the air, the longer it is blown by the wind. The results of applying a directional distribution of the initial sand velocity to the Nishimori model will be reported in this meeting.
References
[1] Nishimori･Ouchi (1993) "Dynamics of Wind-blown Sand Bed -Ripples and Dunes-", Bussei Kenkyu 61(1):32-43. (in Japanese)