On standing internal gravity waves of finite amplitude

Abstract

Two-dimensional internal gravity waves in a rectangular container are examined theoretically and experimentally in (a) fluids which contain a single density discontinuity and (b) fluids in which the density gradient is everywhere continuous. The fractional density difference between the top and bottom of the fluid is small.Good agreement is found between the observed and calculated wave profiles in case (a). Unlike surface standing waves, which tend to sharpen at their crests as the wave amplitude increases, and which eventually break at the crests when fluid accelerations become equal to that of gravity, internal wave crests are found to be flat and exhibit no instability. In the case (a) breaking is found to occur at the nodes of the interfacial wave, where the current shear, generated by the wave itself, is greatest. For sufficiently large wave amplitudes, a disturbance with the form of a vortex but with direction of rotation reversing twice every cycle, grows at the wave node and causes mixing. This instability is found to be followed by the generation of cross-waves, of which two different forms are observed.Several modes of oscillation can be generated and are observed in a fluid with constant density gradient. The wave frequencies and shape are well predicted by theory. The experiments failed to establish any limitation of the possible wave amplitudes.