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Affine connections can be defined within Cartan's general framework. [7] In the modern approach, this is closely related to the definition of affine connections on the frame bundle. Indeed, in one formulation, a Cartan connection is an absolute parallelism of a principal bundle satisfying suitable properties.
The ocean plays a key role in the water cycle as it is the source of 86% of global evaporation. [2] The water cycle involves the exchange of energy, which leads to temperature changes. When water evaporates, it takes up energy from its surroundings and cools the environment. When it condenses, it releases energy and warms the environment.
Benthic-pelagic coupling are processes that connect the benthic zone and the pelagic zone through the exchange of energy, mass, or nutrients. These processes play a prominent role in both freshwater and marine ecosystems and are influenced by a number of chemical, biological, and physical forces that are crucial to functions from nutrient cycling to energy transfer in food webs.
A newer method that allows 1-D groundwater and surface water coupling in homogeneous soil layers and that is related to the Richards equation is the Finite water-content vadose zone flow method solution of the Soil Moisture Velocity Equation. In the case of uniform initial soil water content and deep, well-drained soil, some excellent ...
The pycnocline is the transitory region between a surface layer of water (warmer and less dense) and deeper layer of water (colder and more dense). Mixing occurs across the pycnocline, driven primarily by waves and shear. A pycnocline is the cline or layer where the density gradient ( ∂ρ / ∂z ) is greatest within
A hydrologic model is a simplification of a real-world system (e.g., surface water, soil water, wetland, groundwater, estuary) that aids in understanding, predicting, and managing water resources. Both the flow and quality of water are commonly studied using hydrologic models.
This definition should be taken as defining the torsion-free spin connection, since, by convention, the Christoffel symbols are derived from the Levi-Civita connection, which is the unique metric compatible, torsion-free connection on a Riemannian Manifold. In general, there is no restriction: the spin connection may also contain torsion.
Groundwater is water that is found underground in cracks and spaces in the soil, sand and rocks. Where water has filled these spaces is the phreatic (also called) saturated zone. Groundwater is stored in and moves slowly (compared to surface runoff in temperate conditions and watercourses) through layers or zones of soil, sand and rocks: aquifers.