A depth measurement method in estuarine plume dyeing experiments

Abstract

The present invention belongs to the field of offshore engineering fluid mechanics experiments, and discloses a method for depth measurement in an estuary plume dyeing experiment. According to the ratio of the grayscale values ​​before and after dyed fresh water is added to the calibration tank and the corresponding depth value, a grayscale-depth calibration curve is obtained, and the calibration curve is used to inversely calculate the depth field of the plume in the normalized overhead image after the annular rotating tank introduces dyed fresh water, and a binary image is drawn to determine the plume contour, and the geometric parameters of the maximum width of the plume area are calculated. The present invention is of great significance to the calculation of the volume growth rate of the bulge in the laboratory plume experiment, and is of great significance to the laboratory plume experiment and the understanding of the real plume structure. The average error of the present invention in depth measurement and freshwater flow conservation calculation is within an acceptable range, and the operability is obvious and the reliability is strong.

Description

Technical Field

[0001] The invention relates to the field of offshore engineering fluid mechanics experiments, and in particular to a depth measurement method in an estuary plume dyeing experiment. Background Art

[0002] A river plume is a low-salinity body of water that forms nearshore after freshwater flows out of an estuary, creating a unique nearshore flow pattern. It typically forms a bulge protruding seaward near the estuary, generating longshore currents downstream (relative to the direction of Kelvin wave propagation). The estuary plume plays a crucial role in offshore flow patterns and the transport of nutrients, pollutants, and sediment from land to sea, making it a research hotspot in recent decades.

[0003] Estuarine ecosystems are a crucial component of marine ecosystems, characterized by high productivity and abundant resources. They provide a habitat for aquatic life and profoundly impact human activities in nearshore areas. For example, when a bulge is large, both pollutants and nutrients accumulate there, dramatically impacting the ecosystem in that area. This can also reduce the flow of downstream coastal currents, transporting less pollutants downstream and potentially benefiting human activities downstream. Another example is that during droughts, the decline in freshwater flow and the resulting reduction in offshore plumes can significantly reduce the number of species that rely on estuaries for their habitats, altering the ecology of local fish populations and further altering their composition and structure.

[0004] Many advanced technologies have been applied to measure plume structure. Particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) can only measure a single plane of the plume, not the three-dimensional flow field. Scanning LIF methods can address the spatial dimensionality issue, but also introduce significant experimental complexity. All of these methods have their limitations. For estuarine plume simulation experiments in a large-scale circular experimental annular rotating tank rotating about a central axis, a simple method is needed to calculate the depth field of the uplift near the freshwater source. Summary of the Invention

[0005] To address the shortcomings of the prior art, the present invention provides a depth measurement method for estuarine plume coloring experiments. This technique can be used for multiphase flow coloring experiments with a bird's-eye view. It is particularly practical in coastal plume model experiments and has been successfully used to determine the actual depth of estuarine plume coloring experiments. The plume volume and longshore transport calculated based on the depth field can verify the conservation relationship for freshwater flow. This improves the reliability, accuracy, and scientific nature of plume structure and dynamics analysis.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for measuring depth in an estuarine plume dyeing experiment, the method comprising the following steps:

[0008] Step 1: Salt water is injected into a circular rotating tank to a specified water level. Dyed fresh water is placed into a calibration tank fixed in advance on an acrylic plate. The image taken by the camera is grayscaled. Based on the ratio of the grayscale value I of the dyed fresh water in the calibration tank to the grayscale value I0 of the empty calibration tank and the corresponding depth value, a scatter plot of normalized grayscale and depth is drawn. An exponential function is used for nonlinear fitting to obtain a grayscale-depth calibration curve.

[0009] Step 2: Remove the calibration tank and continue to introduce dyed fresh water after the annular rotating tank is fully tempered. Use a camera to take pictures of the plume from above and from the side.

[0010] Step 3: Convert the image captured by the camera in step 2 into a grayscale image and perform normalization. Based on the grayscale-depth calibration curve obtained in step 1, inversely calculate the depth field of the plume in the grayscale image.

[0011] Step 4: Based on the depth field, a binary image is drawn to determine the plume contour and calculate geometric parameters such as width, area, and volume;

[0012] Step 5: Verify conservation of freshwater flow to determine the accuracy of the technique.

[0013] Furthermore, the step 1 is specifically as follows:

[0014] The experiments were conducted in a 1.5-meter-radius annular rotating tank. A "coast" was constructed using transparent acrylic panels. A diffuser connected to the rear of the "coast" simulated an "estuary" (with a constant flow area). A sloped topography was added to simulate the continental shelf terrain associated with estuarine plume conditions. Before each experiment, salt water (salinity controlled by the experimental parameter reduced gravity g') was injected into the annular rotating tank until the specified water level was reached.

[0015] 30mL of cherry red food dye was diluted to 40L with deionized water. After adding the dyed freshwater to a specific height in an empty calibration tank (with a right-angled trapezoidal cross-section), the tank was fixed near the "river mouth" to ensure that the water surface of the calibration tank was flush with the current water level while preventing the dyed freshwater in the tank from flowing out and mixing with the salt water during the rotation of the rotating tank, thereby interfering with the experiment. Because the corresponding depth value of each point in the calibration tank in the overhead image (the distance from the intersection of a vertical line with the water surface to the intersection of the line with the hypotenuse of the trapezoidal cross-section) is difficult to obtain directly, it is necessary to calculate it using a geometric similarity proportional formula.

[0016] The color image captured by the camera was grayscaled using the MATLAB command "rgb2gray." A scatter plot of normalized grayscale versus depth was plotted based on the ratio of the grayscale value I of the dyed freshwater in the tank to the grayscale value I0 of the corresponding pixel in the empty tank (to eliminate background interference in the captured area) and the corresponding normalized depth value h.

[0017] Based on the Lambert-Beer law, it is believed that the normalized grayscale and depth of the current plume experiment have the following exponential function relationship:

[0018]

[0019] Where I / I0 is the normalized grayscale value mentioned above; A, B, and D are coefficients to be determined. Since theoretically, when the normalized depth value h = 0, I / I0 = 1, and therefore D = 1-A, the original problem is transformed into a problem of solving A and B. This relationship converts the image grayscale value into the fluid depth value.

[0020] An exponential function curve was fitted using the "Curve Fitting" app in MATLAB. A series of subsequent camera images (primarily top-down views) were then used to convert normalized grayscale values ​​into depth values ​​based on the calibration curve.

[0021] Furthermore, the step 2 is specifically as follows:

[0022] Remove the calibration tank, and rotate the annular rotating tank 1 for at least 4 hours to meet tempering requirements before conducting various operating condition experiments. A constant-flow pump controls the inflow, continuously pumping dyed freshwater from the water supply tank to the diffuser. After capturing overhead and side-on images using a camera, grayscale the images as described in step 1. All images for each operating condition are divided by the first image of that condition to obtain a normalized grayscale to eliminate experimental background influences.

[0023] Furthermore, the step 3 is specifically as follows:

[0024] The normalized grayscale values ​​in the overhead image obtained in step 2 are back-calculated using the grayscale-depth calibration curve obtained in step 1 to obtain the depth value of each pixel. The average of the top 2% of depths is used as the maximum depth of the plume in the image (this value can be used to determine the contact relationship between the plume and the terrain). One-fifth of the maximum depth value is used as the boundary between the plume and the surrounding fluid.

[0025] Furthermore, the step 4 is specifically as follows:

[0026] The plume profile is determined based on the cutoff value in step 3, and a binary overhead image can be obtained. This image can determine parameters including the maximum width of the plume area.

[0027] The transverse section with the maximum depth value is selected. Since the geometric relationship between the introduced slope and the experimental annular rotating trough is known, a side view can be used to observe whether the contour intersects the terrain. This allows the plume's contact to be determined by inverting the standardized grayscale values ​​from the calibration curve. In this step, a GoPro camera is set up to capture the side view, allowing real-time tracking of the plume's contact. This also provides the maximum depth point and the instantaneous horizontal distance from that point to the wall, which can be compared with the maximum depth of the depth field captured by the side camera. The three depth values ​​are then cross-referenced to verify the reliability of the depth field method derived from the standardized grayscale inversion using the calibration curve.

[0028] Furthermore, the step 5 is specifically as follows:

[0029] “Freshwater flow conservation” means that the inflow of dyed freshwater is equal to the sum of the plume volume in the area photographed by the CCD camera and the coastal current transport outside the photographed area, that is,

[0030] V in =V bulge +∑Q′ fcc Δt

[0031] Where, the plume volume V bulge According to the depth field calculation obtained above, it is the sum of the product of the depth value of all pixels within the contour determined by the binary image and the unit area; the coastal current transport volume per unit time Q′ fcc The calculation formula is:

[0032]

[0033] Where α is the empirical coefficient in the interval (0.5, 0.8); f is the Coriolis parameter; S0 is the salinity of the ambient water; and the reduced gravity g′ = Δρ / ρ ambient =(ρ ambient -ρ inflow ) / ρ ambient (ρ ambient and ρ inflow refers to the density of the ambient water body and the inflow water body respectively); β is the positive correlation coefficient between the density difference and salinity difference between the ambient water body and the inflow water body; h i is the average longitudinal depth in the rectangular computational domain downstream of the plume, and N is the number of horizontal pixels in the computational domain.

[0034] The beneficial effects of the present invention are:

[0035] The present invention draws a grayscale-depth index relationship calibration curve based on a scatter plot of the normalized grayscale values ​​and corresponding depth values ​​of pixel points in the calibration slot. Based on the calibration curve, the maximum depth value of the plume in the overhead image under various working conditions is inversely calculated to determine the binary image of the plume contour. Finally, the accuracy of the maximum depth value of the plume is checked using the camera side view image and the theoretical formula.

[0036] The present invention provides a method for calculating the plume volume within the overhead imaging area, as well as a method for calculating the longshore current transport volume outside the overhead imaging area. This method is of great significance for the calculation of freshwater flow conservation in laboratory plume dyeing experiments, and is of great significance for the understanding of both laboratory experiments and real plumes.

[0037] The present invention has been verified through experiments, and the average errors in both depth measurement and freshwater flow conservation calculation are within an acceptable range. The method is simple and reliable, has strong operability, high reliability and high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a front view of the apparatus for the estuarine plume dyeing experiment in an embodiment of the present invention;

[0039] Figure 2 Schematic diagram of a calibration tank according to an embodiment of the present invention;

[0040] Figure 3a is a grayscale image taken from above in an embodiment of the present invention;

[0041] Figure 3b The depth field map is obtained by inverting the grayscale according to the grayscale-depth calibration curve in an embodiment of the present invention;

[0042] Figure 4 Schematic diagram of the relationship between normalized grayscale ratio and depth in an embodiment of the present invention;

[0043] Figure 5a exist Figure 3b The plume outline was added to the base;

[0044] Figure 5b for Figure 5a The corresponding binary image;

[0045] Figure 6 Schematic diagram of determining the contact relationship between the plume profile and the slope terrain in an embodiment of the present invention;

[0046] Figure 7 This is a relationship diagram for verifying the freshwater flow conservation equation in an embodiment of the present invention.

[0047] In the figure: 1. Annular rotating tank; 2. Camera; 3. Sloping terrain; 4. Acrylic plate; 5. Diffuser; 6. Calibration tank. DETAILED DESCRIPTION

[0048] The present invention will be further described below with reference to the accompanying drawings.

[0049] The present invention specifically comprises the following steps:

[0050] 1. Preparation before the experiment

[0051] like Figure 1 As shown, the experiment was conducted in an annular rotating tank 1 with a radius of 1.5 m. A "coast" was constructed using a transparent acrylic sheet 4. A diffuser 5 connected to the rear of the "coast" simulated an "estuary" (with a constant flow area). A sloped terrain 3 was added to simulate the continental shelf topography associated with estuarine plume conditions. Before each experiment, salt water (salinity controlled by the experimental parameter reduced gravity g') was injected into the annular rotating tank 1 until the water level reached the specified level.

[0052] Cameras 2 are installed above and on one side of the annular rotating tank 1 for taking color images during the experiment.

[0053] Dilute 30 mL of cherry red food dye to 40 L with deionized water to form dyed water. Empty calibration tank 6 (with a right-angled trapezoidal cross section) as follows: Figure 2 As shown, after adding dyed fresh water to a specific height, the calibration tank is fixed near the "river mouth" and fixed on the acrylic plate, as shown in Figure 2 As shown, this ensures that the water surface in the calibration tank is flush with the current brine level. This also prevents the dyed freshwater in the calibration tank from flowing out and mixing with the brine during the rotation of the rotating tank, potentially interfering with the experiment. Because the depth values ​​corresponding to each point in the calibration tank in the overhead image (the distance from the intersection of a vertical line with the water surface to the intersection of that vertical line with the hypotenuse of the trapezoidal cross-section) are difficult to obtain directly, they must be calculated using a geometric similarity formula. Figure 2 The gradient in b is intended to illustrate that the grayscale value and depth value in the calibration groove area in the top view are in direct proportion.

[0054] The color image of the plume evolution near the diffuser obtained by camera 2 is grayscaled using the MATLAB command "rgb2gray" (e.g. Figure 3a Based on the ratio of the grayscale value I of the dyed freshwater in the calibration tank to the grayscale value I0 of the corresponding pixel in the empty tank, i.e., the normalized grayscale value (eliminating background interference in the shooting area), and the corresponding normalized depth value h, a scatter plot of normalized grayscale and depth is drawn.

[0055] Based on the Lambert-Beer law, it is believed that the normalized grayscale and depth of the current plume experiment have the following exponential function relationship:

[0056]

[0057] Where I / I0 is the normalized grayscale value mentioned above; A, B, and D are coefficients to be determined. Since theoretically, when the normalized depth value h = 0, I / I0 = 1, and therefore D = 1-A, the original problem is transformed into a problem of solving A and B. This relationship converts image grayscale values ​​into fluid depth values.

[0058] Use the MATLAB app called 'Curve Fitting' to fit the exponential function curve (such as Figure 4 As shown in the figure, the essence is to use the trust region algorithm to solve the nonlinear least squares problem and obtain the grayscale-depth calibration curve. The subsequent series of images taken by the camera (mainly the top view) are used to inversely calculate the normalized grayscale value into the depth value according to the above exponential function curve (as shown in the figure). Figure 3b shown).

[0059] 2. Experimental Data Collection

[0060] After removing the calibration tank, the annular rotating tank 1 rotated for at least four hours to meet tempering requirements before conducting various operating condition experiments. A constant-flow pump controlled the inflow, continuously pumping dyed freshwater from the water supply tank to diffuser 5. Camera 2, a CCD camera, captured overhead and side-on images, which were then grayscaled as described in step 1. All images from each operating condition were normalized to the first image from that condition to obtain a normalized grayscale value to eliminate experimental background influences.

[0061] 3. Depth calculation in plume experiments

[0062] The normalized grayscale values ​​in the overhead image obtained in step 2 are back-calculated using the grayscale-depth calibration curve obtained in step 1 to obtain the depth value of each pixel. The first 2% of the average depth value is used as the maximum depth of the plume in the image (this value can be used to determine the contact relationship between the plume and the terrain). One-fifth of the maximum depth value is used as the boundary between the plume and the surrounding fluid. This empirical value was determined through multiple field measurements.

[0063] 4. Depth-based geometric characteristic parameter calculation

[0064] Based on the cutoff value in step 3, the plume profile (such as Figure 5a As shown), we can then get a binary image (as shown Figure 5b The binarized image can be used to determine parameters including the maximum width of the plume area.

[0065] Select the transverse section where the maximum depth value is located. Since the geometric relationship between the introduced slope terrain 3 and the experimental annular rotation trough 1 is known, it can be obtained by Figure 6 Observe whether the contour intersects the terrain, and then judge the contact situation of the plume obtained by inverting the normalized grayscale value with the help of the grayscale-depth calibration curve.

[0066] In this experiment, a GoPro camera was also set up to capture a side view, allowing real-time tracking of the plume's contact. This also provided the maximum depth point and the instantaneous horizontal distance from that point to the acrylic wall, which was used for comparison with the maximum depth of the depth field captured by the side-viewing camera. Furthermore, based on existing theoretical depth formulas, the depth values ​​obtained using the three different methods were cross-checked to verify the reliability of the depth field method of inverting the standardized grayscale using the grayscale-depth calibration curve.

[0067] 5. Verify freshwater flow conservation to determine the accuracy of the technology

[0068] "Freshwater flow conservation" refers to the inflow of dyed freshwater V in Equal to the plume volume V in the area captured by the CCD camera bulge and the coastal current transport outside the shooting area ∑Q′ fcc The sum of Δt, that is

[0069] V in =V bulge +∑Q′ fcc Δt (2)

[0070] Where, the plume volume V bulge According to the depth field calculation obtained above, it is the sum of the product of the depth value of all pixels within the contour determined by the binary image and the unit area; the coastal current transport volume per unit time Q′ fcc In actual calculation, it is necessary to Figure 3b A rectangular computational domain (e.g. Figure 3b The calculation formula is:

[0071]

[0072] Where α is an empirical coefficient in the range (0.5, 0.8), which is taken as 0.6 in this experiment; f is the Coriolis parameter; S0 is the salinity of the ambient water; and the reduced gravity g′ = Δρ / ρ ambient =(ρ ambient -ρ inflow ) / ρ ambient (ρ ambient and ρ inflow refers to the density of the ambient water body and the inflow water body respectively); β is the positive correlation coefficient between the density difference and salinity difference between the ambient water body and the inflow water body; h i yes Figure 3b The average longitudinal depth in the calculation domain, N is Figure 3b The number of horizontal pixels in the calculation domain. Figure 7 As shown, the conservation of freshwater flow is well verified, indicating that the current plume experiment has a high accuracy in depth measurement. In the figure, T represents a period, Q represents the estuary flow, and the slope of the single slope terrain is a fixed value.

Claims

1. A method for measuring depth in an estuarine plume dyeing experiment, characterized in that The method comprises the following steps: Step 1: Pour salt water into the annular rotating tank to the specified water level, place dyed fresh water into the calibration tank fixed on the acrylic plate, and use a camera to take a bird's-eye view of the calibration tank and convert the image into grayscale. According to the ratio of the gray value I of the dyed fresh water in the calibration tank to the gray value I0 of the empty calibration tank, as well as the corresponding depth value, a scatter plot of normalized grayscale and depth is drawn, and an exponential function is used for nonlinear fitting to obtain a grayscale-depth calibration curve; Step 2: Take out the calibration tank; After the annular rotating tank is fully tempered, dyed fresh water is continuously introduced, and the plume is photographed from above and from the side using a camera. The images captured by the camera are converted into grayscale images and normalized. Step 3: Based on the grayscale-depth calibration curve in step 1, inversely calculate the depth field of the plume in the normalized overhead image in step 2; Step 4: Based on the depth field obtained in step 3, a binary image is drawn to determine the plume contour and the geometric parameters of the maximum width of the plume area are calculated.

2. The depth measurement method in an estuarine plume dyeing experiment according to claim 1, characterized in that: In step 1, a transparent acrylic plate is used to build a "coast" in the annular rotating tank, a diffuser connected to the rear of the "coast" simulates an "estuary", and a slope terrain is used to simulate the continental shelf terrain of the "estuary" plume environment.

3. The depth measurement method in an estuarine plume dyeing experiment according to claim 1, characterized in that: In step 1, cameras are provided above and on one side of the annular rotating groove.

4. The depth measurement method in an estuarine plume dyeing experiment according to claim 1, characterized in that: In step 3, the average value of the first 2% of the depths is taken as the maximum depth value of the plume; and 1 / 5 of the maximum depth value is taken as the boundary value between the plume and the ambient fluid.

5. The depth measurement method in an estuarine plume dyeing experiment according to claim 1, characterized in that: In step 4, a GOPRO camera is set up to capture a side view for real-time tracking of the plume's contact, obtaining the maximum depth point and the instantaneous value of the horizontal distance from the depth point to the acrylic plate wall, and comparing these with the depth field of the image captured by the side camera and the maximum depth of the plume in the overhead view calculated inversely in step 3.

6. The depth measurement method in an estuarine plume dyeing experiment according to claim 1, characterized in that: The method also includes step 5, verifying the conservation of freshwater flow to determine the accuracy of the method, specifically: whether the inflow of dyed freshwater is equal to the plume volume V in the camera shooting area bulge and the coastal current transport outside the shooting area ∑Q′ fcc The sum of △t is used to verify, where Q′ fcc is the coastal current transport volume per unit time.

7. The depth measurement method in an estuarine plume dyeing experiment according to claim 6, characterized in that: The plume volume V bulge The sum of the product of the depth values ​​of all pixels within the contour determined by the binary image and the unit area.

8. The depth measurement method in an estuarine plume dyeing experiment according to claim 6, characterized in that: The coastal current transport volume per unit time Q' fcc The calculation formula is: Where α is the empirical coefficient in the interval (0.5, 0.8); f is the Coriolis parameter; S0 is the salinity of the ambient water; and the reduced gravity g′ = △ρ / ρ ambient =(ρ ambient -ρ inflow ) / ρ ambient ρ ambient and ρ inflow Refers to the density of the ambient water body and the inflow water body respectively; β is the positive correlation coefficient between the density difference and salinity difference between the ambient water body and the inflow water body; h i is the average longitudinal depth in the rectangular computational domain downstream of the plume, and N is the number of horizontal pixels in the computational domain.

Images