Irregular half-day tide estuary saline invasion unsteady state analysis method considering time effect

Abstract

The invention discloses an irregular half-day tide estuary brine invasion unsteady state analysis method considering a time effect, and the method comprises the steps: firstly constructing a flow velocity expression considering different tidal partial effects, carrying out the Fourier series expansion of salinity, substituting the flow velocity and the salinity into a convection diffusion equation, and simplifying the flow velocity and the salinity; then referring to a salinity spatial change expression under a saline intrusion steady-state analysis model, assuming that the average salinity of a tidal period is substituted into simplification calculation to obtain saline intrusion time-space process unsteady-state analysis; and replacing the data parameters which are difficult to obtain in the analytic expression with the data parameters which are easy to obtain. According to the method, Fourier series expansion is adopted, a salinity spatial change expression under a saline intrusion steady-state analytical model is adopted as a basis to assume the average salinity of an unsteady-state tidal period, and the like, so that the problem of non-linear solution difficulty brought to a convection diffusion equation by a time item is ingeniously solved, and a series of physical parameters which are easy to obtain in production and life are introduced; and theoretical support is provided for predicting and preventing salt tide disasters.

Description

Technical Field

[0001] This invention relates to the field of estuarine saltwater intrusion prediction, and in particular to a nonsteady-state analytical method for irregular semi-diurnal tidal estuarine saltwater intrusion that takes into account time effects. Background Technology

[0002] Analytical models of salinity convection-diffusion are an effective means of deeply analyzing the physical processes of brine intrusion. However, current theoretical analyses are based on convection-diffusion equations that neglect time effects to avoid the nonlinearity difficulties caused by the time term in the original equations. While this approach can explain the physical characteristics of brine intrusion at specific times (such as periods of rapid and recessive tidal rise), it has significant limitations in explaining the mechanisms of brine intrusion during tidal wave movements of different periods. Therefore, developing a solution method that considers time effects to analyze the unsteady-state analytical model of brine intrusion in irregular semi-diurnal tidal estuaries, to more realistically depict the spatiotemporal processes of brine intrusion in estuaries, and to further improve the analytical theory of brine intrusion dynamics, is one of the current challenges. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a non-steady-state analytical method for saltwater intrusion in irregular semi-diurnal tidal estuaries that takes into account time effects, which can analyze the saltwater intrusion mechanism during the movement of tidal waves of different periods.

[0004] Technical solution: The present invention provides a non-steady-state analysis method for irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects, comprising the following steps:

[0005] (1) Considering diurnal and semi-diurnal tides, establish an expression for the cross-sectional average velocity;

[0006] (2) The expression for the spatiotemporal variation of cross-sectional average salinity is obtained by performing Fourier series expansion of salinity;

[0007] (3) Substitute the expression for the average flow velocity of the cross section and the expression for the spatiotemporal variation of the average salinity of the cross section into the salinity convection-diffusion equation to obtain the salinity convection-diffusion equation set.

[0008] (4) Referring to the expression of salinity spatial variation under the steady-state analytical model of brine intrusion, assuming the tidal cycle average salinity, and substituting the tidal cycle average salinity into the salinity convection-diffusion equation set, the unsteady analytical expression of the spatiotemporal process of brine intrusion is obtained.

[0009] (5) Substitute the slope of the linear fit between salinity and distance, and the tidal range into the unsteady analytical expression of the spatiotemporal process of saltwater intrusion, to obtain a simplified unsteady analytical expression of the spatiotemporal process of saltwater intrusion.

[0010] Furthermore, in step (1), the diurnal and semi-diurnal tides are considered as the main tidal clusters, and the estuary cross-sectional area decreases exponentially. The expression for the average flow velocity of the cross-section is:

[0011]

[0012] Among them, u f Let υ1 represent the runoff velocity, and υ2 represent the velocity amplitudes of the diurnal and semi-diurnal tidal clusters, respectively. and ω represents the initial phase of the current velocity of the diurnal and semi-diurnal tidal clusters, and ω represents the angular velocity of the semi-diurnal tidal cluster.

[0013] Further, in step (2), the spatiotemporal variation expression of the cross-sectional average salinity is:

[0014]

[0015] in, The salinity value is the average salinity value during the tidal cycle, s 11 s 12 s 21 and s 22 All are coefficients of the Fourier series expansion.

[0016] Furthermore, in step (3), the salinity convection-diffusion equation is:

[0017]

[0018] Where x is the distance to the entrance, D is the longitudinal salinity diffusion coefficient, and a is the cross-sectional area convergence coefficient.

[0019] Substituting the expressions for the cross-sectional average velocity and the spatiotemporal variation of the cross-sectional average salinity into the salinity convection-diffusion equations, the resulting set of salinity convection-diffusion equations is as follows:

[0020]

[0021] Further, in step (4), the expression for the periodic average salinity is:

[0022]

[0023] in, The tidal periodic average salinity at the river mouth is denoted by m, which is the parameter to be solved; the coefficients of the Fourier series expansion are s. 11 s 12 s 21 and s 22 It also satisfies the same relation:

[0024]

[0025] Where i takes the values ​​1 and 2, and j takes the values ​​1 and 2;

[0026] Will and s ij Substituting the expression into the salinity convection-diffusion equations, the parameter s to be solved is obtained. 11 s 12 s 21 s 22 And m, the unsteady analytical expression of the spatiotemporal process of saltwater intrusion is obtained as follows:

[0027]

[0028] Among them, Q f A0 represents the runoff flow rate, and A0 represents the cross-sectional area at the outlet.

[0029] Further, in step (5), the tidal range is:

[0030]

[0031] Suppose that the tidal path E decreases exponentially along the shoreward direction, then:

[0032]

[0033] The slope obtained from the linear fit is:

[0034]

[0035] Where E0 is the tidal range at the river mouth, e is the tidal range attenuation coefficient, and s 0max and s 0min These represent the maximum and minimum salinity values ​​at the mouth, respectively.

[0036] Furthermore, in step (5), the simplified unsteady-state analytical expression for the spatiotemporal process of saltwater intrusion is:

[0037]

[0038] in, and , representing the initial phases of the diurnal and semi-diurnal tidal clusters at the mouth, respectively, where c is the wave velocity. c0 is the wave velocity at the river mouth, and d is the friction loss coefficient along the water depth.

[0039] The non-steady-state analysis system for irregular semi-diurnal tidal brine intrusion in the estuary, which considers time effects, as described in this invention, includes:

[0040] The cross-sectional average velocity modeling unit is used to establish the cross-sectional average velocity expression considering diurnal and semi-diurnal tides.

[0041] The cross-sectional average salinity modeling unit is used to perform Fourier series expansion of salinity to obtain the spatiotemporal variation expression of cross-sectional average salinity.

[0042] The modeling unit for the salinity convection-diffusion equations is used to substitute the expression for the cross-sectional average flow velocity and the expression for the spatiotemporal variation of the cross-sectional average salinity into the salinity convection-diffusion equations to obtain the salinity convection-diffusion equations.

[0043] The unsteady-state analytical equation solving unit for the spatiotemporal process of brine intrusion is used to refer to the expression of salinity spatial variation under the steady-state analytical model of brine intrusion, assume the average salinity of the tidal cycle, substitute the average salinity of the tidal cycle into the salinity convection and diffusion equation set, and obtain the unsteady-state analytical equation for the spatiotemporal process of brine intrusion.

[0044] A simplified unit for the unsteady analytical expression of the spatiotemporal process of brine intrusion is used to substitute the slope of the linear fitting between salinity and distance, as well as the tidal range, into the unsteady analytical expression of the spatiotemporal process of brine intrusion to obtain a simplified unsteady analytical expression of the spatiotemporal process of brine intrusion.

[0045] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the unsteady-state analysis method for irregular semi-diurnal tidal estuarine saltwater intrusion considering time effects.

[0046] The computer program product of the present invention includes a computer program that, when executed by a processor, implements the unsteady-state analysis method for irregular semi-diurnal tidal estuarine saltwater intrusion considering time effects.

[0047] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: (1) The present invention proposes an effective solution to the unsteady analytical model of irregular semi-diurnal tidal saltwater intrusion considering the time effect. By performing Fourier series expansion on salinity and assuming the average salinity of the unsteady tidal cycle based on the expression of salinity spatial variation under the steady analytical model of saltwater intrusion, the nonlinear solution difficulty brought by the time term to the convection-diffusion equation is cleverly solved, providing theoretical support for predicting and preventing saltwater intrusion disasters; (2) The unsteady analytical solution provided by the present invention breaks through the limitation of the traditional steady-state model that can only describe the equilibrium state at a specific moment. It can dynamically analyze the spatiotemporal evolution process of saltwater intrusion throughout the tidal cycle, which helps to reveal the influence mechanism of different dominant tidal constituents on the degree of intrusion in complex tidal dynamics; (3) The present invention introduces a series of physical parameters that are easy to obtain in production and life, replacing some parameters that are not easy to obtain, providing accuracy and convenience for the actual operation of predicting and preventing saltwater intrusion. Attached Figure Description

[0048] Figure 1 This is a flowchart of the unsteady-state analysis method for irregular semi-diurnal tidal estuary saltwater intrusion according to the present invention. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0050] like Figure 1 As shown, the method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries includes the following steps.

[0051] Step S1: Assuming the cross-sectional area of ​​the estuary decreases exponentially, and considering the effects of different tidal constituents, take the diurnal and semi-diurnal constituents as the main tidal clusters, and write the expression for the average cross-sectional velocity.

[0052] Assume the estuary cross-sectional area decreases exponentially as follows:

[0053]

[0054] Where A0 refers to the cross-sectional area at the entrance, x is the distance to the entrance, positive in the direction towards the shore, and a is the cross-sectional area convergence coefficient, which represents the longitudinal narrowing rate of the cross-sectional area.

[0055] Furthermore, the diurnal and semi-diurnal tides can be considered as the main tidal clusters, and the expression for the cross-sectional average velocity is:

[0056]

[0057] Among them, u f This represents the runoff velocity, which is negative in this embodiment because its direction is offshore. υ1 and υ2 represent the velocity amplitudes of the diurnal and semi-diurnal tidal clusters, respectively. and ω represents the initial phase of the current velocity of the diurnal and semi-diurnal tidal clusters, ω represents the angular velocity of the semi-diurnal tidal cluster, and t represents time.

[0058] Step S2: Perform a Fourier series expansion on the salinity to obtain the spatiotemporal variation expression of the cross-sectional average salinity:

[0059]

[0060] in, Represents the average salinity value during the tidal cycle, s 11 s 12 s 21 and s 22 These represent the different coefficients of the Fourier series expansion.

[0061] Step S3: Based on the average flow velocity expression described in Step S1 and the spatiotemporal variation expression of cross-sectional average salinity described in Step S2, rewrite the salinity convection-diffusion equation; and further divide the salinity convection-diffusion equation into a set of equations if corresponding terms are equal.

[0062] The expression for the salinity convection-diffusion equation is as follows:

[0063]

[0064] Where A is the cross-sectional area of ​​the estuary, s is the average salinity value of the cross-section, u is the flow velocity, and D is the longitudinal salinity diffusion coefficient. Furthermore, assuming the diffusion coefficient remains constant along the river's course, the above equation can be simplified to:

[0065]

[0066] Substituting equations (2) and (3) into equation (5), we can obtain the first term on the left side of equation (5) as follows:

[0067]

[0068] The convection term, i.e., the second term on the left side of equation (5), can be expressed as:

[0069]

[0070] The two terms on the right side of equation (5) represent the salinity diffusion term, which can be further simplified to:

[0071]

[0072] Furthermore, since the coefficients of corresponding terms on both sides of the equation are equal, the above massive equation can be simplified into a system of equations:

[0073]

[0074] Step S4: Referring to the salinity spatial variation expression under the steady-state analytical model of brine intrusion, assume the periodic average salinity. Substitute the equations from Step S3 into the equation set, simplify and solve for the parameters, and then write the unsteady-state analytical expression of the spatiotemporal process of brine intrusion considering the influence of different tidal constituents on the nearshore estuary of irregular semi-diurnal tides.

[0075] Referring to the salinity spatial variation expression under the steady-state analytical model of brine intrusion, it is assumed that the tidal period average salinity can be written as:

[0076]

[0077] in, is the average salinity value during the tidal cycle at the river mouth, and m is the parameter to be solved.

[0078] Similarly, the coefficients s of the Fourier series expansion 11 ,s 12 ,s 21 and s 22 It also satisfies the same relation:

[0079]

[0080] Where i takes the values ​​1 and 2, and j takes the values ​​1 and 2.

[0081] Substituting equations (10) and (11) into (9), the system of equations can be transformed into:

[0082]

[0083] After further rearranging equation (12), we get:

[0084]

[0085] Will Substituting into equation (13), we get:

[0086] And it satisfies:

[0087] Substituting equation (14) into equation (15), we get:

[0088]

[0089] Solving equation (15), we get P1, P2, and m as follows:

[0090] Substituting equations (17), (19), and (20) into equation (14) yields the correlation coefficient:

[0091]

[0092] Considering the influence of different tidal constituents on the nearshore of an irregular semi-diurnal estuary, the unsteady-state analysis of the spatiotemporal process of saltwater intrusion can be expressed as:

[0093]

[0094] Step S5: Introduce the tidal range E, and the linear correlation between the salinity-related physical quantity ln(s / s0) and the distance-related physical quantity exp(x / a). The slope k and other parameters obtained by linear fitting are used to further rewrite and simplify the unsteady analytical expression of the spatiotemporal process of brine intrusion described in step S4.

[0095] In equation (21), the cross-sectional average velocity of the runoff can be expressed as u through the relationship between the runoff flow rate and the cross-sectional area. f =Q f Substituting / A into equation (21), we get:

[0096]

[0097] Wherein, tidal length E can be regarded as "horizontal tidal range", that is, the distance that a water particle moves from the time of receding tide to the time of receding tide. Therefore, according to tidal fluid dynamics, tidal length can be estimated by equation (24):

[0098]

[0099] Therefore, equation (23) can be further simplified to:

[0100]

[0101] The salinity longitudinal diffusion coefficient D can be obtained by backfitting the mean salinity variation along the tidal cycle:

[0102]

[0103] Furthermore, a linear correlation exists between the salinity-related physical quantity ln(s / s0) and the distance-related physical quantity exp(x / a), and the slope k obtained from the linear fitting can be denoted as:

[0104]

[0105] Due to parameters D and Q f These can be combined into a single variable that is easier to calibrate, by introducing a new parameter here defined as the mixing coefficient:

[0106]

[0107] The mixing coefficient will change over time, but by combining the measured salinity with Equation (26) for fitting analysis, the estuarine mixing coefficient can be easily determined.

[0108] Assuming that the tidal path E decreases exponentially along the shoreward direction, then

[0109]

[0110] Where E0 is the tidal length at the estuary, and e is the tidal length attenuation coefficient. According to the definition, during periods of rising or falling tides, when the tidal velocity is 0, the salinity value reaches its maximum (maximum / minimum) value. Therefore, the tidal length at the estuary can be approximately estimated using equation (25):

[0111]

[0112] Among them, s 0max and s 0min These represent the maximum and minimum salinity values ​​at the mouth, respectively.

[0113] Assume the water depth decreases exponentially along the path:

[0114]

[0115] Where h0 represents the water depth at the inlet, and d is the friction loss coefficient of the water depth.

[0116] Using the classic wave propagation formula to describe the propagation of tidal waves in a river estuary, the tidal wave propagation speed can be expressed as:

[0117]

[0118] Where c is the wave velocity and h is the water depth. Substitute equation (31) into equation (32).

[0119] The attenuation of tidal wave velocity along the path is expressed as:

[0120]

[0121] Where c0 is the wave velocity at the mouth, and as can be seen from equation (33), the tidal wave velocity is assumed to decrease along the path.

[0122] Therefore, the unsteady analytical equation (23) for the spatiotemporal process of irregular semi-diurnal tidal saltwater intrusion in the estuary can be expressed as:

[0123]

[0124] in, and These represent the initial phases at the mouth of the diurnal and semi-diurnal tidal clusters, respectively.

[0125] The non-steady-state analysis system for irregular semi-diurnal tidal brine intrusion in the estuary, which considers time effects, as described in this invention, includes:

[0126] The cross-sectional average velocity modeling unit is used to establish the cross-sectional average velocity expression considering diurnal and semi-diurnal tides.

[0127] The cross-sectional average salinity modeling unit is used to perform Fourier series expansion of salinity to obtain the spatiotemporal variation expression of cross-sectional average salinity.

[0128] The modeling unit for the salinity convection-diffusion equations is used to substitute the expression for the cross-sectional average flow velocity and the expression for the spatiotemporal variation of the cross-sectional average salinity into the salinity convection-diffusion equations to obtain the salinity convection-diffusion equations.

[0129] The unsteady-state analytical equation solving unit for the spatiotemporal process of brine intrusion is used to refer to the expression of salinity spatial variation under the steady-state analytical model of brine intrusion, assume the average salinity of the tidal cycle, substitute the average salinity of the tidal cycle into the salinity convection and diffusion equation set, and obtain the unsteady-state analytical equation for the spatiotemporal process of brine intrusion.

[0130] A simplified unit for the unsteady analytical expression of the spatiotemporal process of brine intrusion is used to substitute the slope of the linear fitting between salinity and distance, as well as the tidal range, into the unsteady analytical expression of the spatiotemporal process of brine intrusion to obtain a simplified unsteady analytical expression of the spatiotemporal process of brine intrusion.

[0131] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the aforementioned unsteady-state analysis method for irregular semi-diurnal tidal estuarine brine intrusion considering time effects. The processor executes the computer program stored in the memory to implement the various steps of the methods described in the above embodiments.

[0132] The computer program product of the present invention includes a computer program that, when executed by a processor, implements the unsteady-state analysis method for irregular semi-diurnal tidal estuarine saltwater intrusion considering time effects.

Claims

1. A nonsteady-state analytical method for irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects, characterized in that, Includes the following steps: (1) Considering diurnal and semi-diurnal tides, establish an expression for the cross-sectional average velocity; (2) The expression for the spatiotemporal variation of cross-sectional average salinity is obtained by performing Fourier series expansion of salinity; (3) Substitute the expression for the average flow velocity of the cross section and the expression for the spatiotemporal variation of the average salinity of the cross section into the salinity convection-diffusion equation to obtain the salinity convection-diffusion equation set. (4) Referring to the expression of salinity spatial variation under the steady-state analytical model of brine intrusion, assuming the tidal cycle average salinity, and substituting the tidal cycle average salinity into the salinity convection-diffusion equation set, the unsteady analytical expression of the spatiotemporal process of brine intrusion is obtained. (5) Substitute the slope of the linear fit between salinity and distance, and the tidal range into the unsteady analytical expression of the spatiotemporal process of saltwater intrusion, to obtain a simplified unsteady analytical expression of the spatiotemporal process of saltwater intrusion.

2. The method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects according to claim 1, characterized in that, In step (1), the diurnal and semi-diurnal tides are considered as the main tidal clusters, and the estuary cross-sectional area decreases exponentially. The expression for the average flow velocity of the cross-section is: Among them, u f Let υ1 represent the runoff velocity, and υ2 represent the velocity amplitudes of the diurnal and semi-diurnal tidal clusters, respectively. and ω represents the initial phase of the current velocity for both diurnal and semidiurnal tidal clusters, and ω represents the angular velocity of the semidiurnal tidal cluster.

3. The method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects according to claim 2, characterized in that, In step (2), the spatiotemporal variation expression of the cross-sectional average salinity is: in, The salinity value is the average salinity value during the tidal cycle, s 11 s 12 s 21 and s 22 All are coefficients of the Fourier series expansion.

4. The method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects according to claim 3, characterized in that, In step (3), the salinity convection-diffusion equation is: Where x is the distance to the entrance, D is the longitudinal salinity diffusion coefficient, and a is the cross-sectional area convergence coefficient. Substituting the expressions for the average cross-sectional velocity and the spatiotemporal variation of the average cross-sectional salinity into the salinity convection-diffusion equations, the resulting set of salinity convection-diffusion equations is as follows:

5. The method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects according to claim 4, characterized in that, In step (4), the expression for the periodic average salinity is: in, The salinity is the tidal periodic average at the river mouth, where m is the parameter to be solved; the coefficients s in the Fourier series expansion are... 11 s 12 s 21 and s 22 It also satisfies the same relation: Where i takes the values ​​1 and 2, and j takes the values ​​1 and 2; Will and s ij Substituting the expression into the salinity convection-diffusion equations, the parameter s to be solved is obtained. 11 s 12 s 21 s 22 And m, the unsteady analytical expression of the spatiotemporal process of saltwater intrusion is obtained as follows: Among them, Q f A0 represents the runoff flow rate, and A0 represents the cross-sectional area at the outlet.

6. The method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects according to claim 5, characterized in that, In step (5), the tidal range is: Suppose that the tidal path E decreases exponentially along the shoreward direction, then: The slope obtained from the linear fit is: Where E0 is the tidal range at the river mouth, e is the tidal range attenuation coefficient, and s 0max and s 0min These represent the maximum and minimum salinity values ​​at the mouth, respectively.

7. The method for analyzing the unsteady state of irregular semi-diurnal tidal saltwater intrusion in estuaries considering time effects according to claim 6, characterized in that, In step (5), the simplified unsteady-state analytical expression of the saltwater intrusion spatiotemporal process is: in, and , representing the initial phases of the diurnal and semi-diurnal tidal clusters at the mouth, respectively, where c is the wave velocity. c0 is the wave velocity at the river mouth, and d is the friction loss coefficient along the water depth.

8. A non-steady-state analysis system for irregular semi-diurnal tidal brine intrusion considering time effects, characterized in that, include: The cross-sectional average velocity modeling unit is used to establish the cross-sectional average velocity expression considering diurnal and semi-diurnal tides. The cross-sectional average salinity modeling unit is used to perform Fourier series expansion of salinity to obtain the spatiotemporal variation expression of cross-sectional average salinity. The modeling unit for the salinity convection-diffusion equations is used to substitute the expression for the cross-sectional average flow velocity and the expression for the spatiotemporal variation of the cross-sectional average salinity into the salinity convection-diffusion equations to obtain the salinity convection-diffusion equations. The unsteady-state analytical equation solving unit for the spatiotemporal process of brine intrusion is used to refer to the expression of salinity spatial variation under the steady-state analytical model of brine intrusion, assume the average salinity of the tidal cycle, substitute the average salinity of the tidal cycle into the salinity convection and diffusion equation set, and obtain the unsteady-state analytical equation for the spatiotemporal process of brine intrusion. A simplified unit for the unsteady analytical expression of the spatiotemporal process of brine intrusion is used to substitute the slope of the linear fitting between salinity and distance, as well as the tidal range, into the unsteady analytical expression of the spatiotemporal process of brine intrusion to obtain a simplified unsteady analytical expression of the spatiotemporal process of brine intrusion.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the unsteady-state analysis method for irregular semi-diurnal tidal estuary saltwater intrusion considering time effects, as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the unsteady-state analysis method for irregular semi-diurnal tidal estuary saltwater intrusion considering time effects, as described in any one of claims 1-7.

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