An intercomparison of internal solitary waves in the Bay of Biscay and resulting from Korteweg-de Vries-Type theory

A recently developed Korteweg-de Vries (KdV)-type theory is used to study the formation of internal ‘solitary’ waves from internal tides in the Bay of Biscay, and detailed comparisons are made with observations. The theory is for a continuously-stratified fluid, and includes both first order non-linearity and dispersion, as well as the earth's rotation without restriction at the lowest order. We investigate and compare the detailed structure of the waves, paying particular attention to the horizontal and vertical velocity fields, as well as to the more usual characteristics, since it appears this has not been undertaken before. The comparison shows that the simplified but often-used ‘KdV physics’ is able to reproduce almost all features of the observed solitary waves, such as wavelengths, amplitudes, phase speeds, and horizontal velocity structure, with reasonable success. The magnitude of the vertical velocities, however, is significantly underestimated by the theory, although their qualitative structure is reproduced. The comparison also indicates that the internal solitary waves in nature are likely to produce significant mixing of the seasonal thermocline.