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26-872: Lion Island is an island that is located at the mouth to the Hawkesbury River in Broken Bay on the Central Coast of the state of New South Wales , Australia. The island is located just off Pearl Beach and is part of the Central Coast Council local government area. It is a descriptive name because it resembles a Sphinx , a mythical figure of a crouching lion. The island was originally named Mount Elliott Island by Governor Arthur Phillip in 1789, because it resembled Gibraltar where his friend, General Elliott, had inflicted defeats on French and Spanish fleets. This name continued to be used by cartographers until

52-531: A = 0. {\displaystyle {\frac {\partial {\mathbf {a} }}{\partial t}}+\left({\mathbf {u} }\cdot \nabla \right){\mathbf {a} }=0.} Here, a {\displaystyle \mathbf {a} } is a vector field instead of the scalar field ψ {\displaystyle \psi } . Solutions to the advection equation can be approximated using numerical methods , where interest typically centers on discontinuous "shock" solutions and necessary conditions for convergence (e.g.

78-500: A vector field , and the transported material is described by a scalar field showing its distribution over space. Advection requires currents in the fluid, and so cannot happen in rigid solids. It does not include transport of substances by molecular diffusion . Advection is sometimes confused with the more encompassing process of convection , which is the combination of advective transport and diffusive transport. In meteorology and physical oceanography , advection often refers to

104-469: A lake without significant bulk water flow, the ink would simply disperse outwards from its source in a diffusive manner, which is not advection. Note that as it moves downstream, the "pulse" of ink will also spread via diffusion. The sum of these processes is called convection . The advection equation for a conserved quantity described by a scalar field ψ ( t , x , y , z ) {\displaystyle \psi (t,x,y,z)}

130-405: Is advected by a known velocity vector field . It is derived using the scalar field's conservation law , together with Gauss's theorem , and taking the infinitesimal limit. One easily visualized example of advection is the transport of ink dumped into a river. As the river flows, ink will move downstream in a "pulse" via advection, as the water's movement itself transports the ink. If added to

156-429: Is constant along a streamline . If a vector quantity a {\displaystyle \mathbf {a} } (such as a magnetic field ) is being advected by the solenoidal velocity field u {\displaystyle \mathbf {u} } , the advection equation above becomes: ∂ a ∂ t + ( u ⋅ ∇ )

182-402: Is energy or enthalpy . Here the fluid may be any material that contains thermal energy, such as water or air . In general, any substance or conserved, extensive quantity can be advected by a fluid that can hold or contain the quantity or substance. During advection, a fluid transports some conserved quantity or material via bulk motion. The fluid's motion is described mathematically as

208-487: Is expressed by a continuity equation : ∂ ψ ∂ t + ∇ ⋅ ( ψ u ) = 0 , {\displaystyle {\frac {\partial \psi }{\partial t}}+\nabla \cdot \left(\psi {\mathbf {u} }\right)=0,} where vector field u = ( u x , u y , u z ) {\displaystyle \mathbf {u} =(u_{x},u_{y},u_{z})}

234-402: Is the flow velocity and ∇ {\displaystyle \nabla } is the del operator. If the flow is assumed to be incompressible then u {\displaystyle \mathbf {u} } is solenoidal , that is, the divergence is zero: ∇ ⋅ u = 0 , {\displaystyle \nabla \cdot {\mathbf {u} }=0,} and

260-443: Is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is also a fluid. The properties that are carried with the advected substance are conserved properties such as energy . An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity

286-432: Is uncertain about which terminology best describes their particular system. In meteorology and physical oceanography , advection often refers to the horizontal transport of some property of the atmosphere or ocean , such as heat , humidity or salinity, and convection generally refers to vertical transport (vertical advection). Advection is important for the formation of orographic clouds (terrain-forced convection) and

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312-898: The CFL condition ). Numerical simulation can be aided by considering the skew-symmetric form of advection 1 2 u ⋅ ∇ u + 1 2 ∇ ( u u ) , {\displaystyle {\tfrac {1}{2}}{\mathbf {u} }\cdot \nabla {\mathbf {u} }+{\tfrac {1}{2}}\nabla ({\mathbf {u} }{\mathbf {u} }),} where ∇ ( u u ) = ∇ ⋅ [ u u x , u u y , u u z ] . {\displaystyle \nabla ({\mathbf {u} }{\mathbf {u} })=\nabla \cdot [{\mathbf {u} }u_{x},{\mathbf {u} }u_{y},{\mathbf {u} }u_{z}].} Since skew symmetry implies only imaginary eigenvalues , this form reduces

338-622: The Plym River ), Sidmouth (i.e. mouth of the Sid River ), and Great Yarmouth (i.e. mouth of the Yare River ); in Celtic, the term is Aber or Inver . Due to rising sea levels as a result of climate change, the coastal cities are at heightened risk of flooding. Sediment starvation in the river compounds this concern. Advection In the field of physics , engineering , and earth sciences , advection

364-417: The "blow up" and "spectral blocking" often experienced in numerical solutions with sharp discontinuities. The term advection often serves as a synonym for convection , and this correspondence of terms is used in the literature. More technically, convection applies to the movement of a fluid (often due to density gradients created by thermal gradients), whereas advection is the movement of some material by

390-655: The 1920s. In 1956, the Lion Island Fauna Reserve was established on the island. In 1977, it was reclassified as the Lion Island Nature Reserve , a protected nature reserve under the National Parks and Wildlife Act 1967 and is administered by the NSW National Parks & Wildlife Service . The nature reserve covers all of the island, an area of approximately 8 hectares (20 acres). Due to

416-534: The Eastern end of Lion Island is composed of Hawkesbury Sandstone . The shores of the island are composed of the older Narrabeen Group of sandstones and shales . In 2005, a documentary film claimed erroneously that the wreckage of a Japanese midget submarine , which disappeared after the attack on Sydney Harbour in 1942, was buried under sand on the seabed, just east of Lion Island. The wreck has since been located near Bungan Head . Mouth (river) If

442-470: The National Parks and Wildlife Service Regional Manager, and is restricted to conservation, education and research purposes. No recreational facilities are provided on the island. On the evening of 25 August 2018 it was reported that Lion Island was fully engulfed in flames following a lightning strike. Further reports in relation to the impact on the island and the island's fauna are expected. The cap at

468-516: The above equation reduces to ∂ ψ ∂ t + u ⋅ ∇ ψ = 0 {\displaystyle {\frac {\partial \psi }{\partial t}}+{\mathbf {u} }\cdot \nabla \psi =0} In particular, if the flow is steady , then u ⋅ ∇ ψ = 0 {\displaystyle {\mathbf {u} }\cdot \nabla \psi =0} which shows that ψ {\displaystyle \psi }

494-587: The island's significant biodiversity it was added to the Australian National Heritage List in December 2006. The island is a breeding habitat for shearwaters and is free of feral cats and foxes . The island has a weed infestation problem that includes Bitou Bush and Lantana . Lion Island contains the largest population of Australian little penguins in the Sydney area. In 2007, the population

520-520: The little penguin population on Granite Island in South Australia . In 2012, penguin researchers observed that penguins' feeding trips were much longer than those taken by the population on Bowen Island in the Jervis Bay Territory . In 2021, efforts were made to clear storm debris that had washed up ahead of penguin breeding season. Public access to the island is by permit, provided by

546-454: The mouth of a river, the change in flow conditions can cause the river to drop any sediment it is carrying. This sediment deposition can generate a variety of landforms , such as deltas , sand bars , spits , and tie channels. Landforms at the river mouth drastically alter the geomorphology and ecosystem. Along coasts, sand bars and similar landforms act as barriers, sheltering sensitive ecosystems that are enriched by nutrients deposited from

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572-514: The river water has a higher density than the surface of the receiving water, the river water will plunge below the surface. The river water will then either form an underflow or an interflow within the lake. However, if the river water is lighter than the receiving water, as is typically the case when fresh river water flows into the sea, the river water will float along the surface of the receiving water as an overflow. Alongside these advective transports, inflowing water will also diffuse . At

598-460: The river. However, the damming of rivers can starve the river of sand and nutrients, creating a deficit at the river's mouth. As river mouths are the site of large-scale sediment deposition and allow for easy travel and ports, many towns and cities are founded there. Many places in the United Kingdom take their names from their positions at the mouths of rivers, such as Plymouth (i.e. mouth of

624-411: The transport of some property of the atmosphere or ocean , such as heat , humidity (see moisture ) or salinity . Advection is important for the formation of orographic clouds and the precipitation of water from clouds, as part of the hydrological cycle . The advection equation is a first-order hyperbolic partial differential equation that governs the motion of a conserved scalar field as it

650-472: The velocity of the fluid. Thus, although it might seem confusing, it is technically correct to think of momentum being advected by the velocity field in the Navier-Stokes equations, although the resulting motion would be considered to be convection. Because of the specific use of the term convection to indicate transport in association with thermal gradients, it is probably safer to use the term advection if one

676-457: Was approximately 300 breeding pairs and appeared to be stable. A more recent study has suggested that the colony has been in steep decline since the 1990s. No primary cause of the decline has been identified. By comparison, the nearby colony at Manly is believed to be stable. Lion Island supports mammalian predators, namely water rats, which have been observed running along the water's edge at night. Rat nest depredation has been proven to impact

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