On submarine sand-waves and tidal lee-waves

Abstract
A simplified analysis is made of the stability of long waves in a sand bed under deep, slow, and steady (or slowly varying) water flow. Allowing for vertical variation in density and shear, the linearized hydrodynamical equations yield a symmetrical flow whose only action is to impart a slow phase velocity to existing sand-waves without altering their amplitude. The only mechanism found under which sand-waves could grow under the assumed conditions is that of a stationary wave train in the lee of a permanent obstacle. The lee-waves require density gradients greater than a certain minimum, independently of any stability due to shear. Application of this model to tidal flow in the Summer thermocline over the Continental Shelf west of Brittany yields a spectrum of wave-building increments which agrees in general wavelength and shape with that of sand-waves measured on La Chapelle Bank (47 degrees 41$^{\prime}$N, 7 degrees 13$^{\prime}$W). Changes in amplitude of a few sand-grain diameters per year would be expected. Thermal stratification would be insufficient for the same mechanism to generate waves in the North Sea, but the possibility of density gradients due to suspended sediment is suggested as a likely factor of importance.

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