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Coupled hydraulic and entropy relationships

Method indicator
Bottom-Up Hybrid Top-Down

Summary of key issues:

Issue Description
Description The technique explores the conditions that are likely to prevail close to dynamic equilibrium for open systems with flows of matter and energy. It also has the potential to be used to examine system behaviour.
Temporal applicability Typically applied over a scale of 10 to 100 years (short-term).
Spatial applicability Typically can be used throughout the whole estuary.
Links with other tools Can be used with Regime relationships, Accommodation space, expert geomorphological analysis, behaviour models, for example.
Data sources Hydraulic depth
High water levels
Low water levels
Tidal prism
Volume at LW
Surface area
Cross sectional area at mouth
Necessary software tools / skills Necessary software for modelling hydrodynamics such as Mike 11. Skills include a good understanding of the theory of Energy/Entropy as well as an understanding of modelling and geomorphology.
Typical analyses To look for perturbations from the most probable state, both in the existing regime and with any imposed changes (developments, sea level rise, etc).
Limitations The main use is as a diagnostic tool. The method has not yet been developed in a way that allows it to be used as a predictive tool.
Example applications Humber Estuary


The theoretical concept of minimum entropy production was first proposed by Prigogine (1955) and is excellently explained in general terms by Atkins (1984). The concept was applied to rivers by Leopold and Langbein (1962), who argued that the entropy production for the system, as a whole, should be a minimum. They combined this argument with conventional continuity, friction and sediment transport relationships and uniform energy per unit mass and uniform stream power to derive discharge relationships for the hydraulic geometry of a river, as summarised in Regime relationships. They noted that uniform energy would lead to a straight basin profile and minimum total work (entropy production) would give rise to a concave basin profile.

These concepts have been re-interpreted for the case of a bi-directional flow in an estuary and applied to a number of UK systems (Dun & Townend, 1998; Townend, 1999). The model is able to highlight the difference between systems, where some show a clear exponential upstream decay, whereas others show a more linear variation in the rate of energy dissipation. This reflects the interplay between minimum entropy production for the system as a whole and the fact that uniform work is but one way of achieving this most probable state, as identified by Leopold and Langbein (1962). Translating this into identifying the physical controls that determine the relative balance of this interplay is an aspect that still needs further research.

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Analysis and modelling

Last Modified on: 19 June 2011
Printed from the Estuary Guide on 26/05/2017 04:45:29