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Danielle Dowling, Kathleen McGovern

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Continuum Mechanics

Fluid Mechanics Solid Mechanics

Newtonian Non-Newtonian Plastic Elastic

Rheology

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Shear stress is stressthat is applied parallel

or tangential to theface of a material

This is why fluidstake the shape oftheir containers!

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Vorticity: The tendency for elements of a fluidto spin.

Where:Tau is the viscous stress tensorRho is the densityB is the body stressV is the velocity vector

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Conservation of Mass: Mass cannot be creatednor destroyed2.dM = i vi Ai dt - o vo Ao dt

= density (kg/m3)

v = speed (m/s)

A = area (m2)

dt = increment of time (s)

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Conservation of Energy: For incompressible,non-viscous fluids, the sum of the pressure,potential and kinetic energies per unit volumeis constant.

This takes the form of the Bernoulli equation, aspecial case of the Euler equation:

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Direction of Flow(Greenes Theorem)

Eulers FirstEquation!

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Modeling mean coastal circulationof variable depth, Gabriel Csanadyderived the arrested topographicwave equation by starting withEulers first equation:

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The general form of the continuity equation fora conserved quantity is:

Where v is any vector function describing theflux of Psi, and Psi is a conserved quantity.

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Where:Rho is the densityu is the fluid velocityTau is the stress tensorb is the body forces, such as gravity, CoriolisEffect, and centrifugal force

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Where:u and v are velocity componentsK is the kinematic viscosityf is a Coriolis parameterZeta is the dynamic heightg is the gravitational constant

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Where:F is the longshore component of the wind

stressh is the depthrv is the kinematic bottom stress

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Physically, the constraints dictate that near shore,the water moves along shore with the wind, while farfrom shore, it moves perpendicular to the wind. Thesolution of this equation determines the details of

how this transition takes place. It also determineshow far the coastal constraint on the flow reaches.

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Fluids can be modeled as continuousmaterials that obey basic principles ofphysics, such as conservation of mass andmomentum.

Using these principles, scientists have derivedequations that describe motion of coastalcirculation.

The arrested topographic wave equation is a

second order partial differential equation thatresembles the one-dimensional heatdiffusion equation.

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1 http://www.btinternet.com/~martin.chaplin/images/hyvisco2.jpg2http://docs.engineeringtoolbox.com/documents/182/law_mass_cons

ervation.png

3https://reader009.{domain}/reader009/html5/0419/5ad785394f76d/5ad7

4http://www.geohab.org/huntsman/csanady.html

5http://pong.tamu.edu/~rob/class/coastal_dyn/Reprints/csanady_JPO_1978.pdf

http://www.btinternet.com/~martin.chaplin/images/hyvisco2.jpghttp://docs.engineeringtoolbox.com/documents/182/law_mass_conservation.pnghttp://docs.engineeringtoolbox.com/documents/182/law_mass_conservation.pnghttp://www.av8n.com/physics/img48/flow.pnghttp://www.geohab.org/huntsman/csanady.htmlhttp://pong.tamu.edu/~rob/class/coastal_dyn/Reprints/csanady_JPO_1978.pdfhttp://pong.tamu.edu/~rob/class/coastal_dyn/Reprints/csanady_JPO_1978.pdfhttp://pong.tamu.edu/~rob/class/coastal_dyn/Reprints/csanady_JPO_1978.pdfhttp://pong.tamu.edu/~rob/class/coastal_dyn/Reprints/csanady_JPO_1978.pdfhttp://www.geohab.org/huntsman/csanady.htmlhttp://www.av8n.com/physics/img48/flow.pnghttp://docs.engineeringtoolbox.com/documents/182/law_mass_conservation.pnghttp://docs.engineeringtoolbox.com/documents/182/law_mass_conservation.pnghttp://www.btinternet.com/~martin.chaplin/images/hyvisco2.jpg

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