Mayim Chayim

Living Waters: Rivers, Geomorphology, and Consulting

Notes in Leopold's et al. Fluvial Processes Book

Berkeley, Thursday, April 9, 2026 2:08 AM

Currently, I am at about a 38% of progress of this book, Fluvial Processes in Geomorphology, written by the fathers of this discipline: Luna Leopold, Gordon Wolman, and John Miller. the book was originally published in 1964.

Of course, while I need to get some sleep. i was thinking on providing this space for asking questions, and some learned lessons while I read the book.

The goal is not to make the reading too long, but rather break down things that I would need to spend more time with them, or additional questions, as a result of the reading. I might add additional literature.

It is great to learn how movable are rivers' beds, as on chapter 6, which talks about water and sediments in channels, and with some clear detail of the grain size distribution from the headwaters, in West Fork Rock Creek near Red Lodge, Montana, all the way downstream through the Mississippi River to the Gulf of Mexico.

I start this continuos post with chapter seven. I will make a section, so easier later to find where the information is.

Chapter 7. Channel Form and Process

First of all and hard to miss, there is a beautiful so true quote from Shakespeare:

Rain added to a river that is rank

Perforce will force it overflow its bank.

Shakespeare. Venus and Adonis (as cited by Leopold et al. 1964)

The quote talks about breaking points or tipping points. Rank in the Shakespearean time could have been interpreted as swollen or saturated in this case. Gemini help with some of the interpretation of that key word to understand better the context.

Ok. On that context I will start with some parts I need to understand better, which is within the shape of the channel, and particularly talks about forces of motion of grains of sand.

For instance, if I see right away the equation below, and it has been a while in recent times that I work with this kind of equations. i didn't grasp right away its meaning. That is why I might need to break it down:

σρσMgsinϕ=σρσMgcosϕtanαeq. (1)\frac{\sigma - \rho}{\sigma} Mg \sin \phi = \frac{\sigma - \rho}{\sigma} Mg \cos \phi \tan \alpha \qquad \qquad \text{eq. (1)}

Gemini again helped typing the equation above quite fast in LaTeX.

So, here eq. (1), which is rather a numerical order I am using for this text. The following term:

σρσMg\frac{\sigma - \rho}{\sigma} Mg

is the immersed weight of the grain of sand.

g is of course gravity.

M: is the mass of the particle (Grain of sand). Getting some help of the book and Gemini here.

M, I needed to clarify, but further I had to clarify the following:

σ (sigma): Density of the particle (the grain of sand).

ρ (rho): Density of the fluid (water).

But then why it is over sigma?