Drag work

[KarstModel]

Does Fornari et al. (2015)'s equation of motion yield similar velocity calculations as the ones we use? Considering the concept of the reference area, are the particles only influenced by the velocity of the fluid in the cell they travel through? I think we need to consider the size of the particles--especially with large particles that would "take-up" multiple cells--and determine which cells of fluid flow influence the particle's motion.

1. Invoke the actual diameter of the particle and have fluid influence it just at its edges.
2. Vary the area of influence

[ddoubleprime]

doesn't Lamb just apply a small normally distributed perturbation to the impact velocities to account for this? I'm not convinced we need to be addressing the full tractions on the surface of every particle to get a good-enough estimate of Cd.

[KarstModel]

            a = (1 - (rho_w/rho_s)) * g - ((3 * rho_w * drag_coef) * (wrel**2) /(4 * rho_s * D))  
        pi_w = sediment_location[h, 4] + (drag * w_water[int(z_idx), int(x_idx)]) + (a * dt)

v = v_0 + drag v_water + [(1 - rho_f/rho_p) g - (3 rho_f C_D * v_rel*2)/(8 rho_p a)] dt = (Fornari et al. eqn. 3.6) + v_0 + drag * v_water

It looks like we are doubling the influence of the water. I'm going to delete the second term from the code. Revised vertical velocity will look like:

v = v_0 + [(1 - rho_f/rho_p) g - (3 rho_f C_D v_rel*2)/(4 rho_p D)] dt

[ddoubleprime]

aha. I was wondering about that. I think I ended up doubling the water's work on horizontal as well, so the trajectories were more downstream and realizing but both sets of velocities too high! This will likely address (if not resolve) issue#12 as well.

[KarstModel]

I don't see the doubling in the horizontal. Velocities are slower now but still way too fast. I have not merged these changes from explore-velocities to main.

[ddoubleprime]

the horz doubling might have been on my other branch, no worries.

How fast is the water going where it is downwelling? (w_water)? small particles are going faster, implying that the downwelling is pulling them more than the big ones - which it should. Is the downward water velocity faster or slower than the settling speed for that particle size? and does the calculation treat the signs right in that case?

[KarstModel]

I don't know how fast anything is going right now. I broke the darthabrader :(

If you look at the version in the explore-velocities branch, you can see how I've changed the drag implementation. It should slow things down but I don't know whether it does or not. I elaborated on the rationale behind it on Slack.

Too tired to troubleshoot . I was careful about keeping tracks of signs when I derived things. Trig makes it good.

[KarstModel]

slight progress in troubleshooting new drag algorithm. it's stuck in a loop at the first grain's initial location.

[KarstModel]

I abandoned the approach I was using here in favor of the one presented by Ferguson, RI, and M Church. “A Simple Universal Equation for Grain Settling Velocity.” Journal of Sedimentary Research 74, no. 6 (2004): 933–937. Code running again. Interesting oscillatory behavior from upwelling.