An official website of the United States government
SUMMARY Tectonic plate motions predominantly result from a balance between the potential energy change of the subducting slab and viscous dissipation in the mantle, bending lithosphere and slab–upper plate interface. A wide range of observations from active subduction zones and exhumed rocks suggest that subduction interface shear zone rheology is sensitive to the composition of subducting crustal material—for example, sediments versus mafic igneous oceanic crust. Here we use 2-D numerical models of dynamically consistent subduction to systematically investigate how subduction interface viscosity influences large-scale subduction kinematics and dynamics. Our model consists of an oceanic slab subducting beneath an overriding continental plate. The slab includes an oceanic crustal/weak layer that controls the rheology of the interface. We implement a range of slab and interface strengths and explore how the kinematics respond for an initial upper mantle slab stage, and subsequent quasi-steady-state ponding near a viscosity jump at the 660-km-discontinuity. If material properties are suitably averaged, our results confirm the effect of interface strength on plate motions as based on simplified viscous dissipation analysis: a ∼2 order of magnitude increase in interface viscosity can decrease convergence speeds by ∼1 order of magnitude. However, the full dynamic solutions show a range of interesting behaviour including an interplay between interface strength and overriding plate topography and an end-member weak interface-weak slab case that results in slab break-off/tearing. Additionally, for models with a spatially limited, weak sediment strip embedded in regular interface material, as might be expected for the subduction of different types of oceanic materials through Earth’s history, the transient response of enhanced rollback and subduction velocity is different for strong and weak slabs. Our work substantiates earlier suggestions as to the importance of the plate interface, and expands the range of quantifiable links between plate reorganizations, the nature of the incoming and overriding plate and the potential geological record.
more »
« less
Efficient bending and lifting patterns in snake locomotion
We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation, we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10–100% higher.
more »
« less
- Award ID(s):
- 1811889
- PAR ID:
- 10373973
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 478
- Issue:
- 2266
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In order to improve the predictive abilities of weather and climate models, it is essential to understand the behaviour of wind stress at the ocean surface. Wind stress is contingent on small-scale interfacial dynamics typically not directly resolved in numerical models. Although skin friction contributes considerably to the total stress up to moderate wind speeds, it is notoriously challenging to measure and predict using physics-based approaches. This work proposes a supervised machine learning (ML) model that estimates the spatial distribution of the skin-friction drag over wind waves using solely wave elevation and wave age, which are relatively easy to acquire. The input–output pairs are high-resolution wave profiles and their corresponding surface viscous stresses collected from laboratory experiments. The ML model is built upon a convolutional neural network architecture that incorporates the Mish nonlinearity as its activation function. Results show that the model can accurately predict the overall distribution of viscous stresses; it captures the peak of viscous stress at/near the crest and its dramatic drop to almost null just past the crest in cases of intermittent airflow separation. The predicted area-aggregate skin friction is also in excellent agreement with the corresponding measurements. The proposed method offers a practical pathway for estimating both local and area-aggregate skin friction and can be easily integrated into existing numerical models for the study of air–sea interactions.more » « less
-
Viscosity determines the resistance of haemolymph flow through the insect body. For flying insects, viscosity is a major physiological parameter limiting flight performance by controlling the flow rate of fuel to the flight muscles, circulating nutrients and rapidly removing metabolic waste products. The more viscous the haemolymph, the greater the metabolic energy needed to pump it through confined spaces. By employing magnetic rotational spectroscopy with nickel nanorods, we showed that viscosity of haemolymph in resting hawkmoths (Sphingidae) depends on wing size non-monotonically. Viscosity increases for small hawkmoths with high wingbeat frequencies, reaches a maximum for middle-sized hawkmoths with moderate wingbeat frequencies, and decreases in large hawkmoths with slower wingbeat frequencies but greater lift. Accordingly, hawkmoths with small and large wings have viscosities approaching that of water, whereas hawkmoths with mid-sized wings have more than twofold greater viscosity. The metabolic demands of flight correlate with significant changes in circulatory strategies via modulation of haemolymph viscosity. Thus, the evolution of hovering flight would require fine-tuned viscosity adjustments to balance the need for the haemolymph to carry more fuel to the flight muscles while decreasing the viscous dissipation associated with its circulation.more » « less
-
We study small shocks of 1D scalar viscous conservation laws with uniformly convex flux and nonlinear dissipation. We show that such shocks are [Formula: see text] stable independently of the strength of the dissipation, even with large perturbations. The proof uses the relative entropy method with a spatially-inhomogeneous pseudo-norm.more » « less
-
Gusts of moderate and large magnitude induce flow separation and other complexities when they interact with the lifting surfaces of air vehicles. The presence of these nonlinear gusts are becoming ubiquitous in twenty-first-century air vehicles, where the classic potential flow–based methodologies applied in the past may no longer be valid. In this review, we define the parameter space for the presence of large-amplitude gusts and describe where and when these gusts may primarily be found. Recent research using modern experimental and computational techniques to define the limits of classical unsteady and indicial aerodynamic theories is summarized, with a focus on discrete transverse, streamwise (longitudinal), and vortex gust encounters. We propose areas where future research is needed to transition these studies of large-amplitude gust physics to real-time prediction and mitigation during flight.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2022.0312
