Kelvin Chan (kechan@mit.edu) & Daniel Rothman (dan@SEGOVIA.MIT.EDU)
54-627 EAPS, MIT, Cambridge, MA 02139, U.S.A.
We study natural topography by means of local transformations. A nonlinear local transform Alc [h(x)] of the elevation field h(x) is used to determine a macroscopic order parameter a(x). The vector field a(x) is related to the local dominant wavevector of the topography at a length scale lc. We also define s(x) = **h*Ls, the coarse-grained average slope at a length scale Ls. In more general settings, s(x) would be regarded as the local stress on the system and a(x) the response. For the case of topography, s(x) indicates the local direction of the flow while a(x) indicates the local anisotropy caused by directed erosion. We study the correlation *a(x); lc) · s(x; Ls)*x and discover that the local anisotropy defined on a small scale lc is most strongly correlated with the local slope field s(x) defined on a large scale Ls. This provides empirical evidence that small length scale fluctuations are correlated with large scale topographic structures and that processes of erosion operating at different scales may interact.
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