Wave approach and shoreline response: identify the incorrect statement about nearshore hydrodynamics and sediment movement as waves reach the coast.

Introduction / Context:
As waves shoal and break near the coast, they generate setup (a rise in mean water level toward the shore), longshore currents, and cross-shore transport. Distinguishing correct from incorrect statements about these processes is fundamental in coastal morphology and engineering.

Given Data / Assumptions:

• Oblique waves can create a net drift (longshore current) in the direction of wave advance near breaking.
• Onshore winds enhance wave growth and can increase coastal water levels via wind setup.
• Backwash tends to remove finer particles seaward under certain conditions.

Concept / Approach:
Wave setup produces rising mean water level toward the shoreline, implying a hydraulic gradient that increases landward, not “falling” in the direction of the incoming wave. Therefore, the statement claiming a falling gradient in the direction of the wave is incorrect.

Step-by-Step Solution:
Check (A): Consistent with Stokes drift and longshore current—acceptable.Check (B): Onshore winds add energy and can raise local mean sea level—acceptable.Check (C): Incorrect—setup means the gradient increases toward shore, not falls.Check (D): Backwash carrying fines seaward is commonly observed—acceptable.

Verification / Alternative check:
Field measurements of surf-zone setup show higher mean levels near the shoreline compared to offshore during energetic wave conditions.

Why Other Options Are Wrong:

• They align with standard coastal process descriptions; only (C) contradicts observed gradients.

Common Pitfalls:

• Confusing instantaneous wave slopes with mean water level gradients (setup).

Final Answer:
A falling hydraulic gradient occurs in the direction of the wave