In this paper, we study the number of traveling wave families near a shear flow $(u,0)$ under the influence of Coriolis force, where the traveling speeds lie outside the range of $u$. Let $beta$ be the Rossby number. If the flow $u$ has at least one critical point at which $u$ attains its minimal (resp. maximal) value, then a unique transitional $beta$ value exists in the positive (resp. negative) half-line such that the number of traveling wave families near $(u,0)$ changes suddenly from finite one to infinity when $beta$ passes through it. If $u$ has no such critical points, then the number is always finite for positive (resp. negative) $beta$ values. This is true for general shear flows under a technical assumption, and for flows in class $mathcal{K}^+$ unconditionally. The sudden change of the number of traveling wave families indicates that nonlinear dynamics around the shear flow is much richer than the non-rotating case, where no such traveling waves exist.
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