The steady perturbation caused in a longshore flow by a bottom undulation is considered. The bedforms are assumed to be alongshore periodic, with crests in the cross‐shore direction and with a small amplitude in order for linear theory to be applicable. The inviscid shallow‐water equations are considered in order to investigate topographic resonance, that is, the condition under which the perturbation in the flow reaches a maximum. Since upstream edge waves held stationary by the mean flow are solutions to the homogeneous resonance equations, the existence of such flows gives rise to the existence of resonances of infinite amplitude (linear, inviscid theory). For a maximum local Froude number of the basic flow F of less than 1, the flow is found to behave subcritically according to classic channel flow theory. In addition, neither steady edge waves nor infinite amplitude resonances exist in this case. However, by numerical simulation, a finite maximum in the flow perturbation as a function of bedform wavelength is found. This topographic resonance is rather weak and wide banded. For a bedform height of 1% the local water depth, the perturbation on the flow may typically be 4% of the mean current. The resonant wavelength is between two and three times the distance of the peak longshore current to the shoreline, l_V, when the current profile has a maximum at some distance offshore, or nearly four times the cross‐shore length scale of the sandbars, l, for a flow profile monotonically increasing to a constant current far offshore. For F≳1 resonances of infinite amplitude are found. For every F, l_V, and l, there is an infinite set of resonant modes with an increasing cross‐shore complexity when the mode number increases, similarly to edge waves. The resonant wavelength increases with F and with l_V. Some implications on the growth of transverse sandbar families and cuspidal coast are discussed.

中文翻译：

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地形强迫作用下的近岸海流共振

在岸边引起的稳定扰动 流由底部起伏考虑。假定这些床形为沿岸周期性，波峰在跨岸方向，且振幅较小，以便线性理论适用。考虑无粘性浅水方程组是为了研究地形共振，也就是在这种情况下，流达到最大。由于上游边缘波平均保持静止流 是齐次共振方程的解，这样的存在 流 导致存在无限振幅的共振（线性，无粘性） 理论）。 对于基本的最大本地弗洛德数 流 F小于1，则流 被发现根据经典表现出次临界 渠道流 理论。另外，在这种情况下，既不存在稳定的边缘波也不存在无限的振幅共振。但是，通过数值模拟，流摄动随床形波长而变。这种形貌的共振是相当弱的和宽频带的。对于床形高度为局部水深1％的情况，流通常可能是平均电流的4％。谐振波长是峰值沿岸流的海岸线，两倍和三倍的距离之间升_V，当当前轮廓具有一定距离的最大海上，或砂棒的横岸长度尺度近四倍，升， 为一个流剖面单调增加到远洋的恒定电流。对于˚F无限幅度的≳1共振发现。对于每个F，L _V和L，都有一组无限的谐振模，当模数增加时，其跨岸复杂度会增加，类似于边波。谐振波长随F和I _V而增加。讨论了对横向沙洲家庭和尖齿海岸生长的一些影响。