Kevin McIlhany, Grant Gillary, Reza Malek-Madani Normal Mode Analysis of the Chesapeake Bay using COMSOL MultiPhysics Abstract A Normal Mode Analysis (NMA) of the Chesa- peake Bay was performed using Neumann boundary con- ditions and COMSOL MultiPhysics (formerly known as FEMLAB). The lowest 100 eigenstates were calculated and compared to a finite difference solution. Based on the normal modes derived numerically, surface current vector fields can be calculated. The vector fields of the Chesa- peake Bay provide tools for the solution of problems such as the diffusion of pollutants, tracking of crab spat, particle transport (bio-terrorism), as well as providing a basis set for decomposing real-time currents. Given the difficulty of the boundary, attempts to measure the error in the calcu- lation included tests for orthogonality within the basis set, convergence of the eigenvalue as a function of grid cho- sen and a comparison to a finite difference calculation for a similar sized grid. Keywords Normal Mode Analysis · NMA · Chesapeake Bay · COMSOL MultiPhysics · FEMLAB 1 Introduction The study of computational fluid dynamics has a rich his- tory and the community is still very active. The govern- ing equations, Navier-Stokes, have yet to be analytically K. McIlhany (presenter) Physics Dept. Tel.: 410-293-6667 Fax: 410-293-3729 E-mail: mcilhany@usna.edu R. Malek-Madani Mathematics Dept. Tel.: 410-293-2504 Fax: 410-293-2507 E-mail: rmm@usna.edu United States Naval Academy 572 Holloway Rd. Annapolis, MD 21402 G. Gillary Oxford University Computing Laboratory E-mail: Grant.Gillary@comlab.ox.ac.uk Wolfson Building, Parks Road Oxford, OX1 3QD,UK solved and the question remains whether the complete so- lution to fluid flow is even achievable from theoretical grounds. To this end, solutions to flow related problems have necessarily been numerical by nature and solved on computers. The practical goal of achieving near-realtime fluid flows is almost technologically realized through the use of programs such as FEMLAB. One approach to understanding flow related problems is to employ the same techniques used by the signal pro- cessing sector. Given a basis set which fully describes the characteristic modes of a system (the eigenmodes), one can analyze the state of a system by decomposing the state into amplitudes related to the eigenmodes. The resulting power spectrum for one dimensional data sets such as time series has proven to be a tremendous tool for many ap- plications. Signal identification and classification repre- sent the simplest of applications. Given a power spectrum, one may speculate that the eigenmodes should evolve in time governed by rules which allows one to forecast sig- nals based on the time evolution of the intensities for each eigenmode. For one dimensional eigenvalue problems, the Fourier series and its associated transform have been the toolset of choice for signal processing for the last fifty years. With increasing computer power, numerical solutions to the eigenvalue problem in higher dimensions are be- coming common-place. The need for computation of eigen- modes is similar to signal processing. When studying a system, having a knowledge of the basis set allows one to describe the state of that system in its most compact language. The numerical aspects of this paper were moti- vated by a method for completing surface current velocity fields called Normal Mode Analysis (NMA) [Eremeev et al. 1992][1] [2],[Lipphardt et al. 2000][3] . There have been two studies in recent years [2],[3] which have tested methods for filling in gaps in the veloc- ity field for the data they obtained. Eremeev et al. used the data received from autonomous drifting buoys (ADB) in the Black Sea to extrapolate velocity fields for this closed body of water using what was later termed by Lipphardt’s group as Normal Mode Analysis. Eremeev and his collab- orators found that this process allowed one to model the large scale currents measured by the ADBs with a rela-