Purely irrotational theories of the effect of the viscosity on the decay of free gravity waves

It is generally believed that the major effects of viscosity are associated with vorticity. This belief is not always well founded; major effects of viscosity can be obtained from purely irrotational analysis of flows of viscous fluids. Here we illustrate this point by comparing our irrotational solutions with Lamb's 1932 exact solution of the problem of the decay of free gravity waves. Excellent agreements, even in fluids 10$^{7}$ more viscous than water, are achieved for the decay rates $n(k)$ for all wavenumbers $k$, excluding a small interval around a critical value $k_{c}$ where progressive waves change to monotonic decay.