TY - JOUR
T1 - Nonlinear waves on a coupled density front
AU - Paldor, Nathan
PY - 1986/12
Y1 - 1986/12
N2 - It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed. In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.
AB - It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed. In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.
UR - http://www.scopus.com/inward/record.url?scp=84963178460&partnerID=8YFLogxK
U2 - 10.1080/03091928608210095
DO - 10.1080/03091928608210095
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AN - SCOPUS:84963178460
SN - 0309-1929
VL - 37
SP - 171
EP - 191
JO - Geophysical and Astrophysical Fluid Dynamics
JF - Geophysical and Astrophysical Fluid Dynamics
IS - 3
ER -