From: Erik Mosselman To: Cc: erik mosselman Subject: Rivers-List: Rivers List: Regime Theory Date: 03 July 2000 10:49 Dear fellow river researchers, Thanks for the reactions to my earlier comments on Regime Theory. Below follows a reaction to the latest messages from Dr. Roger Bettess and Dr. Robert Millar. The considerations below underly my conviction that, indeed, the equilibrium values for specified inputs are not unique but can take a range. Hence I do believe that in case of a set of identical test channels with the same boundary conditions but different initial conditions (i.e. some underwide channels and some overwide channels), the resulting equilibrium channels will not be identical. (1) Processes of bank erosion differ essentially from processes of bank advance. Hence equations for bank advance are different from the equations of bank erosion, quite unlike the situation for the equations of bed erosion and bed sedimentation. In the simplest bank erosion models, the rate of bank retreat is proportional to the excess bank shear stress (or near-bank flow velocity) above some critical threshold shear stress (or flow velocity). Models of bank advance are less developed, but tentatively they could also be expressed in a way that the rate of bank advance is proportional to some bank shear stress "shortage" under a certain critical threshold shear stress. Given the different nature of the two processes, it would be a great coincidence if these two threshold values would be identical. It is more likely that the two thresholds are different, unless proven otherwise. That implies that there is a range of bank shear stresses for which neither bank erosion nor bank advance occurs. This leads to the possibility of multiple equilibria, depending on the initial conditions. (2) Blench (1969, Mobile-bed fluviology, University of Alberta Press, Edmonton) based his reasoning on theoretical insight as well as field experience with alluvial irrigation canals in the Punjab. He writes in his Section 7.18: "If the attack exceeds some limit then the sides will erode till the attack drops to what they can withstand. If the attack falls short of a lower limit then materials from the total load can deposit on the sides, and the channel breadth will decrease. If the attack is between these limits nothing will happen to the sides". (3) Field data always show a large variation around their so-called "regime value". This variation is usually explained away as being due to fluctuations about the supposed single equilibrium, caused in part by adjustment to past events and in part by the unsteadiness of discharge and sediment supply. However, the completeness of this explanation has never been demonstrated. (4) Small test channels and alluvial irrigation canals may still be fairly simple, but real rivers have different mechanisms of bank erosion and bank advance, operating on different scales of time and space). For those rivers it will be extremely hard to distinguish between the effects of natural variations and multivaluedness of equilibria. (5) My experience with channels in the braided Brahmaputra-Jamuna River in Bangladesh is that growing channels have a smaller width-to-depth ratio than dying channels. Admittedly, those channels are never in equilibrium, but this difference in shape provides at least circumstantial evidence that also equilibria can be different, depending on whether they result from a growing or a diminishing channel. (6) I disagree with the suggestion that equilibrium conditions can be found by averaging over suitably long periods, so that fluctuations tend to average out. My opinion has been worded well by Blench (1969), who writes the following in his Section 4.13: "A statistical mean has no physical significance in its own right although, in a particular context, it may happen to have it. There is occasional non-technical misconception that a mean, particularly an arithmetic one, must have some special dynamical significance". (6) I am very critical about extremal hypotheses which imply an "optimum state" as a single equilibrium. My arguments for that can be found in the following recent discussion: Mosselman, E. (2000), River width adjustment. I: Processes and mechanisms. Journal of Hydraulic Engineering, ASCE, Vol.126, No.2, pp.159-160. I am looking forward to more reactions. Best regards, Erik Mosselman