Moment Approximations and Model Cascades for Shallow Flow

Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates depth-averaging. While the shallow flow formulation is advantageous in terms of computational efficiency, it also comes at the price of losing vertical information such as the flow's velocity profile. This gives rise to a model error, which limits the shallow flow model's predictive power and is often not explicitly quantifiable. We propose the use of vertical moments to overcome this problem. The shallow moment approximation preserves information on the vertical flow structure while still making use of the simplifying framework of depth-averaging. In this article, we derive a generic shallow flow moment system of arbitrary order starting from a set of balance laws, which has been reduced by scaling arguments. The derivation is based on a fully vertically resolved reference model with the vertical coordinate mapped onto the unit interval. We specify the shallow flow moment hierarchy for kinematic and Newtonian flow conditions and present 1D numerical results for shallow moment systems up to third order. Finally, we assess their performance with respect to both the standard shallow flow equations as well as with respect to the vertically resolved reference model. Our results show that depending on the parameter regime, e.g. friction and slip, shallow moment approximations significantly reduce the model error in shallow flow regimes and have a lot of potential to increase the predictive power of shallow flow models, while keeping them computationally cost efficient

Shallow EDSLs and Object-Oriented Programming: Beyond Simple Compositionality

Context: Embedded Domain-Specific Languages (EDSLs) are a common and widely used approach to DSLs in various languages, including Haskell and Scala. There are two main implementation techniques for EDSLs: shallow embeddings and deep embeddings. Inquiry: Shallow embeddings are quite simple, but they have been criticized in the past for being quite limited in terms of modularity and reuse. In particular, it is often argued that supporting multiple DSL interpretations in shallow embeddings is difficult. Approach: This paper argues that shallow EDSLs and Object-Oriented Programming (OOP) are closely related. Gibbons and Wu already discussed the relationship between shallow EDSLs and procedural abstraction, while Cook discussed the connection between procedural abstraction and OOP. We make the transitive step in this paper by connecting shallow EDSLs directly to OOP via procedural abstraction. The knowledge about this relationship enables us to improve on implementation techniques for EDSLs. Knowledge: This paper argues that common OOP mechanisms (including inheritance, subtyping, and type-refinement) increase the modularity and reuse of shallow EDSLs when compared to classical procedural abstraction by enabling a simple way to express multiple, possibly dependent, interpretations. Grounding: We make our arguments by using Gibbons and Wu's examples, where procedural abstraction is used in Haskell to model a simple shallow EDSL. We recode that EDSL in Scala and with an improved OO-inspired Haskell encoding. We further illustrate our approach with a case study on refactoring a deep external SQL query processor to make it more modular, shallow, and embedded. Importance: This work is important for two reasons. Firstly, from an intellectual point of view, this work establishes the connection between shallow embeddings and OOP, which enables a better understanding of both concepts. Secondly, this work illustrates programming techniques that can be used to improve the modularity and reuse of shallow EDSLs

Nonclassical shallow water flows

This paper deals with violent discontinuities in shallow water flows with large Froude number $F$. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity may be described by a delta-shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step functioncomponents. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of \emph{O}($F^{-2}$) on a base with an \emph{O(1)} or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta-shock. The physical manifestation of this discontinuity is a small `tube' of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base

Attracting shallow donors: Hydrogen passivation in (Al,Ga,In)-doped ZnO

The hydrogen interstitial and the substitutional Al_Zn, Ga_Zn and In_Zn are all shallow donors in ZnO and lead to n-type conductivity. Although shallow donors are expected to repel each other, we show by first principles calculations that in ZnO these shallow donor impurities attract and form a complex, leading to a donor level deep in the band gap. This puts a limit on the n-type conductivity of (Al,Ga,In)-doped ZnO in the presence of hydrogen.Comment: 4 pages, 5 figure

A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems

We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake ecosystem model by augmenting the individual cognitive maps drawn by 8 scientists working in the area of shallow lake ecology. We calculated graph theoretical indices of the individual cognitive maps and the collective cognitive map produced by augmentation. The graph theoretical indices revealed internal cycles showing non-linear dynamics in the shallow lake ecosystem. The ecological processes were organized democratically without a top-down hierarchical structure. The steady state condition of the generic model was a characteristic turbid shallow lake ecosystem since there were no dynamic environmental changes that could cause shifts between a turbid and a clearwater state, and the generic model indicated that only a dynamic disturbance regime could maintain the clearwater state. The model developed herein captured the empirical behavior of shallow lakes, and contained the basic model of the Alternative Stable States Theory. In addition, our model expanded the basic model by quantifying the relative effects of connections and by extending it. In our expanded model we ran 4 simulations: harvesting submerged plants, nutrient reduction, fish removal without nutrient reduction, and biomanipulation. Only biomanipulation, which included fish removal and nutrient reduction, had the potential to shift the turbid state into clearwater state. The structure and relationships in the generic model as well as the outcomes of the management simulations were supported by actual field studies in shallow lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to understand the complex structure of shallow lake ecosystems as a whole and obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure

Earthquake slip surfaces identified by biomarker thermal maturity within the 2011 Tohoku-Oki earthquake fault zone.

Extreme slip at shallow depths on subduction zone faults is a primary contributor to tsunami generation by earthquakes. Improving earthquake and tsunami risk assessment requires understanding the material and structural conditions that favor earthquake propagation to the trench. We use new biomarker thermal maturity indicators to identify seismic faults in drill core recovered from the Japan Trench subduction zone, which hosted 50 m of shallow slip during the Mw9.1 2011 Tohoku-Oki earthquake. Our results show that multiple faults have hosted earthquakes with displacement ≥ 10 m, and each could have hosted many great earthquakes, illustrating an extensive history of great earthquake seismicity that caused large shallow slip. We find that lithologic contrasts in frictional properties do not necessarily determine the likelihood of large shallow slip or seismic hazard