3D Free-Surface Characterization of Hydraulic Jumps Downstream of a Vertical Drop Using an RGB-D Depth Camera

Abstract Vertical drop structures typically dissipate energy through a hydraulic jump formed immediately downstream of the drop toe, where strong aeration, splashing, and free-surface unsteadiness make conventional measurements difficult. This technical note evaluates the capability of an Intel RealSense D435if depth and color (red, green, blue) (RGB-D) depth camera, operating at 90 fps, to characterize the free surface of a hydraulic jump downstream of a 0.50 m vertical drop in a 0.80-m-wide laboratory flume. Experiments were conducted for unit discharges <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q equals 0.089 en dash 0.127 normal m cubed divided by normal s divided by normal m" display="inline" overflow="scroll"> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.089</mml:mn> <mml:mo>–</mml:mo> <mml:mn>0.127</mml:mn> <mml:mtext> </mml:mtext> <mml:msup> <mml:mi mathvariant="normal">m</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo stretchy="false">/</mml:mo> <mml:mi mathvariant="normal">s</mml:mi> <mml:mo stretchy="false">/</mml:mo> <mml:mi mathvariant="normal">m</mml:mi> </mml:math> , corresponding to inflow Froude numbers <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F r 1 equals 4.55 en dash 5.19" display="inline" overflow="scroll"> <mml:mi>F</mml:mi> <mml:msub> <mml:mi>r</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>4.55</mml:mn> <mml:mo>–</mml:mo> <mml:mn>5.19</mml:mn> </mml:math> . Mean free-surface profiles derived from the camera were validated against the characteristic depths <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y" display="inline" overflow="scroll"> <mml:mi>y</mml:mi> </mml:math> associated with local void fractions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C equals 0.5" display="inline" overflow="scroll"> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C equals 0.9" display="inline" overflow="scroll"> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.9</mml:mn> </mml:math> , denoted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y 50" display="inline" overflow="scroll"> <mml:msub> <mml:mi>y</mml:mi> <mml:mn>50</mml:mn> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y 90" display="inline" overflow="scroll"> <mml:msub> <mml:mi>y</mml:mi> <mml:mn>90</mml:mn> </mml:msub> </mml:math> , respectively, obtained from single-tip conductivity-probe measurements along the channel centerline. Within the main roller region, the camera-derived profiles remained between the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y 50" display="inline" overflow="scroll"> <mml:msub> <mml:mi>y</mml:mi> <mml:mn>50</mml:mn> </mml:msub> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y 90" display="inline" overflow="scroll"> <mml:msub> <mml:mi>y</mml:mi> <mml:mn>90</mml:mn> </mml:msub> </mml:math> envelopes, indicating that the RGB-D sensor can resolve the mean aerated free surface under highly disturbed conditions. An auxiliary comparison between single-tip conductivity-probe and conductivity wire gauge measurements of the equivalent clear-water depth yielded agreement within 7.3%, supporting the internal consistency of the intrusive validation data. Three-dimensional reconstruction of the hydraulic jump revealed marked transverse nonuniformity in the free-surface fluctuation field. Peak fluctuations did not occur systematically along the channel centerline; instead, the largest values were found at off-centerline locations and reached up to 8.9% above the corresponding centerline peaks. These findings show that centerline-only measurements may underestimate the governing fluctuation envelope and that RGB-D imaging provides a practical basis for assessing free-surface variability, freeboard requirements, and sidewall design in stilling regions downstream of vertical drops.