Shoreline Advance
A sediment surface advancing into an ocean basin.
The Left simulation is into a constant depth ocean. The Right into an oean with a subsiding trench.
Constant Depth Subsiding Trench
Theory
Above is a schematic of a fluvial sediment surface--with a "cliff" face shoreline-- advancing into a subsiding ocean basin
h(x,y,t) is the height of the sediment above sea-level
G(x,y,t) is the depth of the sediment below sea-level
A prescribed sediment flux, q(x,t) on y = 0 (an upland sediment production)is transported across the fluvial surface and deposits to advance the shoreline. In addition to the sediment flux the advance of the shoreline is controlled by the nature of the subsidence and the changes in ocean depth.
Building on the ground breaking work of
- Swenson et al. European Journal of Applied Mathenatics, 11, 433-452, 2000.
who showed that this problem can be described by an analogy to the melting Stefan problem
- Voller et al. Int J. heat and Fludi Flow, 16,641-654, 2006.
show that teh advance of a "cliff faced" shoreline can be described by the single domain enthalpy model
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where n is a diffusivity. This formulation allows for the solution on a fixed grid.
The important and essential difference between this and an enthalpy solution for a basic melting problem is that the latent heat term G(x,y,t) is NOT a constant but rather a function of space and time
The simulations at the top of this page use this model. The domain is square plan-view ocean basin, 100x100.Sediemnt is supplied q = 1 at the mid point on the side y = 0. A unit n=1 is assumed.
In addition to the papers noted above further models and refinements can be found in
- Wonsuck Kim, John B. Swenson, Chris Paola , and Vaughan R. Voller. J. Geophys. Res. 111, F04013, 2006.
- Chris Paola and Vaughan Voller, JGR-Earth Surface, 110, 2005.
- Wonsuck Kim, Chris Paola, Vaughan R. Voller and John B.Swenson, Journal of Sedimentary Research,76, 270-283,2006.
- John Swenson, Chris Paola, Lincoln Pratson, Vaughan Voller, A. Brad Murray. JGR , 110, 2005
- V.R. Voller, J.B Swenson, and C. Paola. Int. J. Heat Mass Trans., 47, 5387-5390, 2004.
- J.G. Marr, J. Swenson, C. Paola and V.R. Voller. Basin Research 12, 381-398, 2000.