Theoretical sketches on fluvial and tidal morphodynamics

The dynamic interaction between a sediment-carrying fluid and the erodible Earth's surface is responsible for the formation of a variety of sedimentary patterns. These morphological features manifest across a broad range of spatial and temporal scales, often showing a high degree of regularity. Here, the attention is restricted to some fluvial and tidal sedimentary patterns. While fluvial patterns populate streams flowing downhill from mountain valleys to low-lying plains, tidal patterns form in coastal regions like estuaries, lagoons, and deltas. Recognizing that morphological patterns share the same basic elements, the development of simplified mechanistic models that relies on universal mathematical approaches like dimensional analysis and perturbation methods is pursued. In first place, several morphodynamic problems focusing on multi-thread streams are addressed. In these patterns, the downstream routing of water and sediment is fundamentally directed by channel bifurcations, morphological features where a main thread splits into two smaller anabranches. It is investigated the potential role of tides in controlling the long-term equilibrium state of riverine deltas. To this aim, an idealized tree-like delta network with multiple bifurcations is formulated. It is shown how, even if controlled by few simple interactions, the model behaves as a complex system, where tides can be either a stabilizing or a destabilizing factor for the asymptotic equilibrium state. Then, it is discussed how river bifurcations can be interpreted as a classical phase transition phenomena like the spontaneous magnetization of a ferromagnetic material. This is shown through a fully analytical treatment, which ultimately allows to explicitly compute the flow distribution and bed topography at the bifurcation node. Subsequently, it is explored the role of sediment heterogeneity on stability conditions and equilibrium configurations of fluvial bifurcations, by extending a consolidated modeling framework to deal with mixtures. Ultimately, the spatial structure of looping systems is examined. Indeed, sometimes multi-thread patterns display flow splitting among two smaller anabranches that reconnect further downstream at a channel confluence. Through a systematic field data analysis, it is shown that the average length of the anabranches is not randomly distributed, but follows quasi-universal relations regardless of the specific climatic and geologic context of single rivers. These relations indicate that the length of channel anabranches is slope-invariant and directly proportional to bankfull hydraulic geometry variables (i.e., width and depth) of the main thread. A mechanistic justification of the observed relations is then proposed on the basis of a recent theoretical framework, which is found on the idea of a two-way morphodynamic interaction occurring between bifurcation and confluence nodes. The central part of the thesis analyzes the formation of both free and forced alternate bars, namely meso-scale bedforms characterized by a repetitive sequence of scour pools and sediment deposits. While free bars arise spontaneously due to an instability of the fluid-bed interface, forced bars are triggered by external factors affecting the boundary conditions of the system. Initially, the study of free bars development is restricted to coastal settings as tidal channels, which are distinguished by the absence of a fluvial source of freshwater and sediment, and estuaries, namely rivers debouching into open sea. It is shown how the study of tidal bars formation in these environments can be framed within the same theoretical framework. Then, it is analyzed the influence of sediment sorting on fluvial forced bars. The analysis enables to underline the close relationship between forced bars formation and channel bifurcations in sediment mixtures. The last part of the thesis deals with meandering streams flowing through permafrost floodplains. When the river banks are composed by perennially frozen material, a problem then arises of defining proper reference hydraulic and thermodynamic conditions that can represent the long-term migration of the stream. Through a simplified statistical approach, an erodibility coefficient, which retains the seasonal variability of flow and thermal regime, and physically embodying the cumulative effect of thermo-mechanical processes as ablation, is defined. The analytical model is tested on some Alaskan rivers. A preliminary qualitative analysis suggests that theoretical predictions are in good agreement with field data.