scholarly journals Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Darryl D. Holm ◽  
Erwin Luesink
Keyword(s):  
Fluid Dynamics ◽  
Shallow Water ◽  
Asymptotic Expansions ◽  
Three Dimensional ◽  
Water Dynamics ◽  
Nonlinear Wave Propagation ◽  
Entire Family ◽  
Variational Framework ◽  
Current Interaction ◽  
Circulation Theorem

AbstractHolm (Proc R Soc A Math Phys Eng Sci 471(2176):20140963, 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin’s circulation theorem, while also allowing for dispersive nonlinear wave propagation, both within a stratified fluid and at its free surface. The present paper combines asymptotic expansions and vertical averaging with the stochastic variational framework to formulate a new approach for developing stochastic parametrisation schemes for nonlinear waves in fluid dynamics. The approach is applied to two sequences of shallow water models which descend from Euler’s three-dimensional fluid equations with rotation and stratification under approximation by asymptotic expansions and vertical averaging. In the entire family of nonlinear stochastic wave–current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.

scholarly journals A variational formulation of vertical slice models

2013 ◽  
Vol 469 (2155) ◽  
pp. 20120678 ◽  
Author(s):  
C. J. Cotter ◽  
D. D. Holm
Keyword(s):  
Three Dimensional ◽  
Boussinesq Equations ◽  
Subsequent Evolution ◽  
Boussinesq Model ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Variational Framework ◽  
Vertical Slice ◽  
Error Testing ◽  
Circulation Theorem

A variational framework is defined for vertical slice models with three-dimensional velocity depending only on x and z . The models that result from this framework are Hamiltonian, and have a Kelvin–Noether circulation theorem that results in a conserved potential vorticity in the slice geometry. These results are demonstrated for the incompressible Euler–Boussinesq equations with a constant temperature gradient in the y -direction (the Eady–Boussinesq model), which is an idealized problem used to study the formation and subsequent evolution of weather fronts. We then introduce a new compressible extension of this model. Unlike the incompressible model, the compressible model does not produce solutions that are also solutions of the three-dimensional equations, but it does reduce to the Eady–Boussinesq model in the low Mach number limit. Hence, the new model could be used in asymptotic limit error testing for compressible weather models running in a vertical slice configuration.

Three-dimensional stromatolites from Maastrichtian–Danian Yacoraite Formation, Argentina: modelling and assessing hydrodynamic controls on growth patterns

2021 ◽  
pp. 1-17
Author(s):  
Patricio Guillermo Villafañe ◽  
Carlos Cónsole-Gonella ◽  
Paolo Citton ◽  
Ignacio Díaz-Martínez ◽  
Silvina de Valais
Keyword(s):  
Environmental Factors ◽  
Methodological Approach ◽  
Three Dimensional ◽  
Growth Patterns ◽  
External Morphology ◽  
Water Dynamics ◽  
Microbial Composition ◽  
Depositional Processes ◽  
Run Off ◽  
Internal Arrangement

Abstract Stromatolites are biogenic sedimentary structures formed by the interplay of biological (microbial composition) and environmental factors (local hydrodynamic conditions, clastic input and/or water chemistry). Well-preserved, three-dimensional (3D) fossil stromatolites are key to assessing the environmental factors controlling their growth and resulting morphology in space and time. Here, we report the detailed analysis of well-exposed, highly informative stromatolite build-ups from a single stratigraphic horizon within the Maastrichtian–Danian Yacoraite Formation (Argentina). This study focuses on the analysis of depositional processes driving intertidal to shallow subtidal stromatolites. Overall depositional architecture, external morphology and internal arrangement (mega, macro, meso and microstructures) of stromatolite build-ups were analysed and combined with 3D photogrammetric models, allowing us to decipher the links between stromatolite structure and tidal dynamics. Results suggest that external morphology and architecture of elongated and parallel clusters grew under the influence of run-off channels. The internal morphology exhibits columnar structures where the space between columns is interpreted as recharge or discharge channels. This work supports the theory that stromatolites can be used as a high-resolution tool in the assessment of water dynamics, and provides a new methodological approach and data for the dynamic reconstruction of intertidal stromatolite systems through the geological record.

The Effect of Bench Arrangements on the Natural Ventilation of a Multispan Greenhouse

2013 ◽  
Author(s):  
Sunita Kruger ◽  
Leon Pretorius
Keyword(s):  
Fluid Dynamics ◽  
Natural Ventilation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Low Velocity ◽  
Lower Velocity ◽  
Cfd Models ◽  
Temperature Distributions ◽  
Computational Fluid Dynamics Cfd ◽  
Plant Level

In this paper, the influence of various bench arrangements on the microclimate inside a two-span greenhouse is numerically investigated using three-dimensional Computational Fluid Dynamics (CFD) models. Longitudinal and peninsular arrangements are investigated for both leeward and windward opened roof ventilators. The velocity and temperature distributions at plant level (1m) were of particular interest. The research in this paper is an extension of two-dimensional work conducted previously [1]. Results indicate that bench layouts inside the greenhouse have a significant effect on the microclimate at plant level. It was found that vent opening direction (leeward or windward) influences the velocity and temperature distributions at plant level noticeably. Results also indicated that in general, the leeward facing greenhouses containing either type of bench arrangement exhibit a lower velocity distribution at plant level compared to windward facing greenhouses. The latter type of greenhouses has regions with relatively high velocities at plant level which could cause some concern. The scalar plots indicate that more stagnant areas of low velocity appear for the leeward facing greenhouses. The windward facing greenhouses also display more heterogeneity at plant level as far as temperature is concerned.

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