Method for estimating turbulent kinetic energy dissipation rate, apparatus for estimating turbulent kinetic energy dissipation rate, program for estimating turbulent kinetic energy dissipation rate, and non-transitory computer-readable storage medium

Abstract

To provide a method for estimating a turbulent kinetic energy dissipation rate.SOLUTION: The method for estimating a turbulent kinetic energy dissipation rate includes the steps of: acquiring the wavenumber spectrum Φ(k) of a fluid; calculating k.Φ(k) by multiplying the wavenumber spectrum Φ(k) by a wavenumber k; calculating a frictional rate u* by using the k.Φ(k), an experience constant a, a Karman constant κ, and the expression (1); and calculating a turbulent kinetic energy dissipation rate ε by using a friction rate u*. Expression (1) is u*=a-1 / 2-κ1 / 3-(k.Φ(k))1 / 2.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for estimating the turbulent kinetic energy dissipation rate, an apparatus for estimating the turbulent kinetic energy dissipation rate, a program for estimating the turbulent kinetic energy dissipation rate, and a non-transitory readable storage medium for a computer.

Background Art

[0002] In the ocean, the turbulent motion of seawater is dominant in the vertical transport of heat, momentum, and dissolved chemical substances such as carbon dioxide. Therefore, it is important to grasp the strength of the on-site turbulence in order to understand the dynamics of the ocean, which is the basis of industry and social activities.

[0003] The strength of turbulence has traditionally been evaluated by an index called the turbulent kinetic energy dissipation rate. The turbulent kinetic energy dissipation rate indicates the rate at which the kinetic energy of turbulence is converted into heat by the viscosity of water per unit time and per unit weight. The turbulent kinetic energy dissipation rate can be measured in a carefully designed experimental water tank, but there has been no example of successful direct measurement in the ocean so far, and attempts have been made to obtain its estimated value within a theoretical framework such as the Osborn-Cox model.

[0004] The most standard method for obtaining an estimated value of the turbulent kinetic energy dissipation rate is a method using a free-falling profiler equipped with a shear probe. By freely dropping the profiler from the sea surface to an arbitrary water depth, fine flow velocity data is recorded by the shear probe during that time, the shear flow is calculated from this flow velocity data, and the turbulent kinetic energy dissipation rate is estimated using the high wave number band of the wave number spectrum of the shear flow, generally k>1 cpm.

[0005] Patent Document 1 discloses a particle image velocimetry device for measuring the velocity vector of a target flow field, and an arithmetic unit for calculating the shear stress based on the velocity fluctuation from the velocity vector. The arithmetic unit calculates the average velocity and velocity fluctuation of the flow field from the velocity vector, calculates all components of the Reynolds stress and the average velocity gradient based on the result, calculates the dissipation rate of turbulent energy from the Reynolds stress and the average velocity gradient, and calculates the shear stress based on the velocity fluctuation from the dissipation rate. It discloses a measuring device for the shear stress distribution of a flow field, characterized by the above.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] However, for a free-fall profiler, an operator on a ship for operating the measuring device always needs to operate the profiler. Therefore, it is difficult to observe the strength of turbulence at a certain point over a long period of time in a time series manner. In addition, there is a method of obtaining an estimated value of the turbulent kinetic energy dissipation rate from the flow velocity data obtained from an ultrasonic flow velocity sensor. However, at depths of more than 200 meters where there are few acoustic scatterers, the proportion of the flow velocity data measured by the ultrasonic flow velocity meter being rejected as an error becomes extremely large. Therefore, it is difficult to estimate the turbulent kinetic energy dissipation rate by an ultrasonic flow velocity meter in an environment with few acoustic scatterers.

[0008] Furthermore, Patent Document 1 has devised a method of obtaining the shear stress distribution by recording the fine flow velocity distribution as video data by Particle Image Velocimetry (PIV). However, since the device described in Patent Document 1 measures the phenomena in an experimental water tank, it is not suitable for field operation in the ocean.

[0009] The present invention has been made to solve the above problems, and an object thereof is to provide a method for estimating the turbulent kinetic energy dissipation rate.

Means for Solving the Problems

[0010] [1] A step of obtaining the wave number spectrum Φ(k) of the fluid, A step of calculating k·Φ(k) by multiplying the wave number k by the wave number spectrum Φ(k), Using the k·Φ(k), the empirical constant a, the von Kármán constant κ, and Equation (1) to calculate the friction velocity u * A step of calculating, Using the friction velocity u * A step of calculating the turbulent kinetic energy dissipation rate ε, comprising A method for estimating the turbulent kinetic energy dissipation rate, characterized in that. Equation (1) ··· u * = a -1 / 2 · κ 1 / 3 · (k·Φ(k)) 1 / 2 [2] The wave number spectrum Φ(k) is the wave number spectrum Φ(k) of the vertical flow of the fluid, In the step of calculating the turbulent kinetic energy dissipation rate ε, using the friction velocity u * And the height z from the seabed and Equation (2) to calculate the turbulent kinetic energy dissipation rate ε The method for estimating the turbulent kinetic energy dissipation rate according to [1], characterized in that. Equation (2) ··· ε = u * 3 · κ -1 · z -1 [3] Further, including a step of averaging the k·Φ(k) when k < 1 / 2 cpm The method for estimating the turbulent kinetic energy dissipation rate according to [1] or [2], characterized in that. [4] Obtaining the wave number spectrum Φ(k) using an ultrasonic flow velocity sensor The method for estimating the turbulent kinetic energy dissipation rate according to any one of [1] to [3], characterized in that. [5] An acquisition unit that acquires the wave number spectrum Φ(k) of the fluid, A k·Φ(k) calculation unit that calculates k·Φ(k) by multiplying the wave number k by the wave number spectrum Φ(k); Using the k·Φ(k), an empirical constant a, a Karman constant κ, and Equation (1), the friction velocity u * is calculated. The friction velocity u * calculation unit; The friction velocity u * is used to calculate the turbulent kinetic energy dissipation rate ε, and an estimation device for the turbulent kinetic energy dissipation rate is provided, comprising: This is an estimation device for the turbulent kinetic energy dissipation rate, characterized in that. Equation (1) ··· u * =a -1 / 2 ·κ 1 / 3 ·(k·Φ(k)) 1 / 2 [6] The wave number spectrum Φ(k) is the wave number spectrum Φ(k) of the vertical flow of the fluid, The dissipation rate calculation unit calculates the turbulent kinetic energy dissipation rate ε using the friction velocity u * and the height z from the seabed and Equation (2). This is an estimation device for the turbulent kinetic energy dissipation rate according to [5], characterized in that. Equation (2) ··· ε = u * 3 ·κ -1 ·z -1 [7] Further, it includes an averaging operation unit that averages the k·Φ(k) when k < 1 / 2 cpm. This is an estimation device for the turbulent kinetic energy dissipation rate according to [5] or [6], characterized in that. [8] A program for causing a computer to function as each part of the estimation device for the turbulent kinetic energy dissipation rate according to any one of [5] to [7]. [9] A non-temporary readable recording medium of a computer storing the program according to [8].

Advantages of the Invention

[0011] According to the present invention, a method for estimating the turbulent kinetic energy dissipation rate can be provided.

Brief Description of the Drawings

[0012]

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Embodiments for Carrying Out the Invention

[0013] Hereinafter, the present invention will be described through embodiments of the invention. However, the following embodiments do not limit the invention according to the claims. Also, not all combinations of features described in the embodiments are essential for the solution means of the invention. First, a method for estimating the turbulent kinetic energy dissipation rate according to an embodiment of the present invention will be described.

[0014] ≪Method for Estimating Turbulent Kinetic Energy Dissipation Rate≫ FIG. 1 is a flowchart showing a method for estimating the turbulent kinetic energy dissipation rate according to an embodiment of the present invention. As shown in FIG. 1, the method for estimating the turbulent kinetic energy dissipation rate according to an embodiment of the present invention includes (a) a step of obtaining a wave number spectrum Φ(k) of a fluid; (b) a step of calculating k·Φ(k) by multiplying the wave number spectrum Φ(k) by the wave number k; (c) using k·Φ(k), an empirical constant a, a von Kármán constant κ, and Equation (1) to calculate a friction velocity u * ; (d) a step of calculating a turbulent kinetic energy dissipation rate ε using the friction velocity u * . The method is characterized by comprising the above steps. Equation (1) ··· u * = a -1 / 2 · κ 1 / 3 · (k·Φ(k)) 1 / 2

[0015] <Step of obtaining the wave number spectrum Φ(k) of the fluid> In an embodiment of the present invention, the step of obtaining the wave number spectrum Φ(k) of the fluid is a step of obtaining data of the wave number spectrum Φ(k) of the fluid. The data of the wave number spectrum Φ(k) may be obtained by actually measuring the fluid, or may be obtained by simulation. The wave number spectrum Φ(k) obtained by actually measuring the fluid is not limited to that directly measured, and may be calculated from physical quantities obtained by actually measuring the fluid. The wave number spectrum Φ(k) obtained by simulation is a wave number spectrum Φ(k) calculated without using physical quantities obtained by actually measuring the fluid.

[0016] For the measurement of the wave number spectrum Φ(k), a known ultrasonic flow velocity sensor can be used. As a known ultrasonic flow velocity sensor, for example, the 3D point-type flow velocity meter Vector manufactured by Nortek AS can be mentioned.

[0017] A method for obtaining the wave number spectrum Φ(k) of a fluid may be received from, for example, a user terminal. The reception from the user terminal may be via a network.

[0018] <Step of multiplying the wave number k by the wave number spectrum Φ(k) to calculate k·Φ(k)> In an embodiment of the present invention, the step of multiplying the wave number k by the wave number spectrum Φ(k) to calculate k·Φ(k) is a step of multiplying the wave number k by the wave number spectrum Φ(k) corresponding to the aforementioned wave number k. By actually measuring the fluid, the wave number spectrum Φ(k) and the wave number k can be obtained. The wave number spectrum Φ(k) may be the wave number spectrum Φ(k) of the vertical flow of the fluid.

[0019] When analyzing all sizes of vortex fluctuations included in turbulent flow, numerical calculations may become difficult. On the other hand, in order to estimate the turbulent kinetic energy dissipation rate, it may not be necessary to analyze all sizes of vortex fluctuations included in turbulent flow. Therefore, without analyzing all sizes of vortex fluctuations included in turbulent flow, large vortex fluctuations above a certain threshold may be targeted for analysis, and the influence of small vortex fluctuations below a certain threshold may be expressed by a physical model that makes the calculation easier. As a method of expressing by a physical model that makes the calculation easier, for example, after calculating k·Φ(k), an averaging operation is performed on k·Φ(k) to calculate a representative value of k·Φ(k). The timing of performing the averaging operation on k·Φ(k) may be at any time as long as it is after calculating k·Φ(k).

[0020] The reason why the influence of small vortex fluctuations can be expressed by performing an averaging operation on k·Φ(k) to calculate a representative value of k·Φ(k) is as follows. Φ(k) has a downward-sloping right shoulder trend in which the energy decreases as the high wave number band increases in proportion to k, while k·Φ(k) compensates for this energy decay and provides a spectrum with a slope of zero (that is, a constant value is expected for any k). As a result, the representative value can be determined by averaging the values of k·Φ(k) in any wave number band (k1 < k < k2). -1 While having a downward-sloping right shoulder trend in which the energy decreases as the high wave number band increases in proportion to k, k·Φ(k) compensates for this energy decay and provides a spectrum with a slope of zero (that is, a constant value is expected for any k). As a result, the representative value can be determined by averaging the values of k·Φ(k) in any wave number band (k1 < k < k2).

[0021] A wider frequency band for performing the averaging operation can obtain a more accurate representative value. That is, ideally, the frequency band for performing the averaging operation is k1 = 0 and k2 = ∞. However, in reality, it is preferable to limit the frequency band for performing the averaging operation for various reasons. For example, an ultrasonic flow velocity sensor is generally installed near the deep seabed while being fixed to a platform. Since the physical size of the platform is usually <2 m, the frequency band is preferably set to be less than k2 = 1 / 2 cpm. By setting the frequency band for performing the averaging operation to be less than 1 / 2 cpm, the influence of artificial contamination such as turbulent flow caused by the platform itself can be prevented. Also, the influence of noise in the high-frequency band peculiar to acoustic devices can be avoided.

[0022] Also, it is preferable that the frequency band for performing the averaging operation is more than 1 / 7 cpm. Thereby, the turbulent kinetic energy dissipation rate can be accurately estimated, and the calculation can be simplified. When estimating the turbulent kinetic energy dissipation rate in the ocean, it is preferably more than 1 / h cpm. Thereby, the turbulent kinetic energy dissipation rate can be estimated more accurately. Here, h is the thickness of the bottom mixed layer.

[0023] <Using k·Φ(k), empirical constant a, von Kármán constant κ, and Equation (1) to calculate the friction velocity u * step> In an embodiment of the present invention, the step of calculating the friction velocity u using k·Φ(k), empirical constant a, von Kármán constant κ, and Equation (1) * is to substitute k·Φ(k), empirical constant a, and von Kármán constant κ into Equation (1) to calculate the friction velocity u * The empirical constant a and the von Kármán constant κ are known constants. Equation (1) ··· u * = a -1 / 2 · κ 1 / 3 · (k·Φ(k)) 1 / 2

[0024] In a situation sufficiently far from the interface, the wavenumber spectrum Φ(k) of the flow velocity (unit: m 2 s -2 cpm-1 ) and the turbulent kinetic energy dissipation rate ε (m 2 s -3 ) are related as expressed by the following equation (A). Equation (A) ··· Φ(k) = a · ε 2 / 3 · k -5 / 3

[0025] Here, a is an empirical constant (= 0.5) and k is the wave number (cpm). Since Φ(k) in Equation (A) can be actually measured, ε can be calculated by obtaining the slope (= a · ε 2 / 3 ) with respect to k of Φ(k) in a double logarithmic graph from the measured values.

[0026] On the other hand, in an environment affected by a boundary surface such as the seabed, the behavior of Φ(k) cannot be explained by Equation (A). The locations where human activities such as seabed resource exploration are carried out are generally layers closer to the seabed than the thickness h (m) of the seabed mixed layer, and it is necessary to obtain a general formula applicable to such environments. In the seabed mixed layer, ε is proportional to the cube of the friction velocity u * (m·s -1 ) (Equation (B)). Equation (B) ··· ε = u * 3 · κ -1 · z -1

[0027] At this time, κ is the von Kármán constant (= 0.41) and z is an arbitrary height (m) from the seabed (however, z < h). When substituting Equation (B) into ε in Equation (A) at this time, Φ(k) becomes a function of u * 2 in the seabed mixed layer (Equation (C)). Equation (C) ··· Φ(k) = a · (u * 3 · κ -1 · z -1 ) 2 / 3 · k -5 / 3 = a · κ -2 / 3 · u * 2 · z -2 / 3 · k -5 / 3

[0028] At this time, since the unit of k is cycles per meter (cpm = m -1 ), the wave number having the same length scale as z is k = z -1 . k = z -1 . By the relation of k = z, z in Equation (C) can be eliminated and rewritten as the following Equation (D). Equation (D) ··· Φ(k) = a · κ -2 / 3 · u * 2 · k -1

[0029] It has long been observed that in the mixed layer in contact with the boundary surface, the wave number spectrum of the flow velocity is proportional to the -1 power of the wave number (known literature: Katul & Chu 1998), and it can be confirmed that the assumption leading to the derivation of Equation (D) is reasonable.

[0030] Solving Equation (D) for u * yields the following Equation (1). Equation (1) ··· u * = a -1 / 2 · κ 1 / 3 · (k · Φ(k)) 1 / 2

[0031] (Step of calculating the turbulent kinetic energy dissipation rate ε using the friction velocity u * ) In an embodiment of the present invention, in the step of calculating the turbulent kinetic energy dissipation rate ε using the friction velocity u * , the friction velocity u * is substituted into the relational expression between the friction velocity u * and the turbulent kinetic energy dissipation rate ε to calculate the turbulent kinetic energy dissipation rate ε. As the relational expression between the friction velocity u * and the turbulent kinetic energy dissipation rate ε, Equation (2) may be used. Equation (2) ··· ε = u * 3 · κ -1 · z -1

[0032] Subsequently, an estimator of the turbulent kinetic energy dissipation rate according to another embodiment of the present invention will be described.

[0033] <<Estimation Device for Turbulent Motion Energy Dissipation Rate>> An estimation device for turbulent motion energy dissipation rate according to another embodiment of the present invention includes an acquisition unit that acquires a wave number spectrum Φ(k) of a fluid, a k·Φ(k) calculation unit that calculates k·Φ(k) by multiplying the wave number spectrum Φ(k) by the wave number k, and a dissipation rate calculation unit that calculates a dissipation rate ε of turbulent motion energy using the friction velocity u * and is characterized by comprising: Equation (1) ··· u * =a -1 / 2 ·κ 1 / 3 ·(k·Φ(k)) 1 / 2

[0034] An information providing system 100 including an estimation device for turbulent motion energy dissipation rate according to an embodiment of the present invention will be described. FIG. 2 is a diagram showing a configuration example of an information providing system 100 including an estimation device for turbulent motion energy dissipation rate according to an embodiment of the present invention. As shown in FIG. 2, the information providing system 100 includes an estimation device 200 and a terminal device 300. The estimation device 200 includes a control device 15, an arithmetic device 25, and a receiving device 35. The terminal device 300 is a specific example of a user terminal. The estimation device 200 and the terminal device 300 are communicably connected via a network 60. The network 60 may be configured by a wireless communication network, a wired communication network, or a combination of a wireless communication network and a wired communication network. The network 60 may be a wide area communication network, an in-house communication network, or a single cable. That is, the network 60 may be configured in any manner as long as it is a communication path capable of transmitting data.

[0035] The estimation device 200 receives at least data of the wave number spectrum Φ(k) and the wave number k via the network, calculates k·Φ(k) based on the wave number spectrum Φ(k) and the wave number k, and calculates the friction velocity u using k·Φ(k), the empirical constant a, the Karman constant κ, and Equation (1) * and calculates the friction velocity u *Using this, the dissipation rate ε of the turbulent kinetic energy is calculated. The wave number spectrum Φ(k) may be the wave number spectrum Φ(k) of the vertical flow of the fluid. Equation (1) ··· u * = a -1 / 2 · κ 1 / 3 · (k · Φ(k)) 1 / 2 Further, in the estimation device 200, the dissipation rate calculation unit may calculate the dissipation rate ε of the turbulent kinetic energy using the friction velocity u * the height z from the seabed, and Equation (2). Equation (2) ··· ε = u * 3 · κ -1 · z -1

[0036] The control device 15 is configured using an information processing device such as a Programmable Logic Controller (PLC), a single-board computer, or a personal computer. The control device 15 controls the arithmetic device 25 to perform arithmetic operations. The control device 15 controls the receiving device 35 to receive data.

[0037] The arithmetic device 25 performs arithmetic operations using the data received by the receiving device 35. The arithmetic device 25 is a specific example of a k · Φ(k) calculation unit, a friction velocity u * calculation unit, an averaging operation unit, and a dissipation rate calculation unit.

[0038] The receiving device 35 receives data from the terminal device 300. The data received includes, for example, flow velocity, wave number spectrum, frequency spectrum, and time series information thereof. The receiving device 35 is a specific example of an acquisition unit.

[0039] The terminal device 300 is configured using an information processing device such as a personal computer, a server device, or a dedicated device. When the terminal device 300 acquires a state value or a physical quantity, it records the acquired state value or physical quantity in the storage device in association with the date and time information in the storage device. The terminal device 300 transmits a predetermined value among the acquired state values and physical quantities to the estimation device 200 via the network 60. The values to be transmitted include, for example, flow velocity, wave number spectrum, frequency spectrum, and time series information thereof.

[0040] The terminal device 300 may include an input device and an output device. The input device is configured using existing input devices such as a keyboard, a pointing device (mouse, tablet, etc.), a button, or a touch panel. The input device may be configured using a microphone and a voice recognition device. In this case, the input device voice - recognizes the words spoken by the user and inputs the string information of the recognition result to the terminal device 300. The input device may be configured in any way as long as it can input the user's instructions to the terminal device 300. The output device may be configured using, for example, a device that outputs images or characters to a screen. For example, the output device can be configured using a CRT (Cathode Ray Tube), a liquid crystal display, an organic EL (Electro - Luminescent) display, etc. Also, the output device may be configured using a device that prints (prints) images or characters on a sheet. For example, the output device can be configured using an inkjet printer, a laser printer, etc. Also, the output device may be configured using a device that converts characters into voice and outputs them. In this case, the output device can be configured using a voice synthesis device and a voice output device (speaker). The output device may be configured using a light - emitting device such as an LED (Light Emitting Diode). In this case, the output device may cause the light - emitting device to emit light in a mode pre - associated with the information to be output, or may cause the light - emitting device at a position pre - associated with the information to be output to emit light.

[0041] The terminal device 300 acquires the values obtained by the user operating the input device. For example, the output device outputs each value input via the input device, the value of the estimation result by the estimation device 200, and the like.

[0042] Also, in the present embodiment, there is provided a turbulent kinetic energy dissipation rate estimation program for causing a computer to function as an estimation device for the turbulent kinetic energy dissipation rate, and a non-transitory readable recording medium of the computer storing the program. Examples of the non-transitory readable recording medium of the computer include magnetic tapes (such as digital data storage (DSS)), magnetic disks (such as hard disk drives (HDD), flexible disks (FD)), optical disks (such as compact disks (CD), digital versatile disks (DVD), Blu-ray disks (BD)), magneto-optical disks (MO), and flash memories (such as solid state drives (SSD), memory cards, USB memories).

Example

[0043] Hereinafter, the effects of the present invention will be described more specifically with reference to examples. The conditions in the examples are one example of the conditions adopted to confirm the feasibility and effects of the present invention, and the present invention is not limited to this one example of conditions. The present invention can adopt various conditions as long as it does not deviate from the gist of the present invention and achieves the object of the present invention.

[0044] Examples by the inventor are shown below, but differences in fine conditions are allowed as long as the essential part of the present invention is suppressed. At a point 1400 meters deep off the coast of Kumejima, Okinawa Prefecture, a commercially available ultrasonic flow velocity sensor ADV (Acoustic Doppler Velocimeter, manufactured by Nortek AS, Figure 3) was installed near the seabed. This point is a location where test drilling is being carried out for the purpose of seabed resource exploration. The ADV has an acoustic frequency of 6 MHz and a sampling volume of 2.65 cm 3It was installed on a low-profile platform manufactured by Environmental Comprehensive Technos Co., Ltd. in accordance with the specifications, with the sampling volume fixed upward so that it was located approximately 2 m from the seabed. A photograph of the exterior of the low-profile platform is shown in Fig. 4.

[0045] The ADV observed the flow velocities in three directions (two horizontal components and one vertical component) at 32 Hz for 90 seconds, and this was regarded as one burst observation. This burst observation was repeated every 5 minutes. That is, there was a blank period of 3 minutes and 30 seconds from the end of one burst observation until the start of the next burst observation, during which the flow velocity was not acquired.

[0046] Calculate the frequency spectrum of the vertical flow obtained in each burst observation. An example is shown in Fig. 5. Next, convert each frequency spectrum into a wavenumber spectrum Φ(k) based on the absolute flow velocity in the horizontal direction. This is shown in Fig. 6. Furthermore, multiply Φ(k) by the wavenumber k to obtain k·Φ(k). This is shown in Fig. 7.

[0047] Finally, for each burst observation, the representative value of k·Φ(k) is obtained by averaging in the range of k1 = 1 / 7 cpm and k2 = 1 / 2 cpm, and substituting it into Equation (1) to obtain u * The obtained u * By substituting it into Equation (B), ε can be obtained for any z. Here, in order to obtain the average ε in the water depth range corresponding to the wavenumber band (1 / 7 cpm < k < 1 / 2 cpm) where the averaging operation was performed, that is, 2 m < z < 7 m, ε was calculated for z = 2, 3, 4, 5, 6, 7 m, and an averaging operation was performed on them with respect to z. The time series of ε obtained in this way is shown as the solid line in Fig. 8. Since the burst observation was every 5 minutes, the values of ε were obtained at 5-minute intervals.

[0048] While the method disclosed by the present invention is theoretically justified, its usefulness has been verified from multiple perspectives by comparing it with the free-fall profiler, which is considered to obtain the most accurate estimated values currently. For this verification, a free-fall profiler VMP-X (Vertical Microstructure Profiler-X) manufactured by Rockland Scientific International was used. At the same location as this example, the VMP-X was freely dropped from the sea surface until the shear probe collided with the seabed, and the shear flow (du / dz)·(s -1 ) was recorded, and the estimated value of ε was obtained every second using the following formula (Equation (3)). Equation (3) ··· ε=(15 / 2)·v·<(du / dz) 2 >

[0049] At this time, ν is the kinematic viscosity coefficient (m 2 s -1 ), and <> represents the average operation. The VMP-X was dropped 8 times. For each drop, the estimated value of ε was obtained at intervals of approximately 0.5 meters vertically from the sea surface to the seabed. To compare with the present invention, for each drop, ε was averaged in the space of 2m < z < 7m, and these values were plotted as dots in Figure 8.

[0050] Figure 8 is a graph showing the turbulent kinetic energy dissipation rate ε plotted against time series. In Figure 8, the solid line represents the estimated value according to the present invention, and the white dots represent the estimated value by the prior art free-fall profiler. As shown in Figure 8, the method of this example enables continuous estimation of ε over a long period.

[0051] Figure 9 is a scatter plot of the turbulent kinetic energy dissipation rate according to this example and the turbulent kinetic energy according to the prior art. In Figure 9, the solid line shows the one-to-one relationship between the turbulent kinetic energy dissipation rate according to this example and the turbulent kinetic energy according to the prior art. Also, the two dashed lines respectively show the ranges of one order above and below the solid line. In Figure 9, the vertical axis represents the estimated value by the prior art free-fall profiler. As shown in Figure 9, according to the method of this example, a highly accurate estimated value can be obtained.

[0052] In the method of this embodiment, a commercially available ultrasonic flow velocity sensor was used. Further, the feature of the method of this embodiment lies in the post - processing of data. Therefore, according to this embodiment, fine variations of ε could be obtained while suppressing costs.

[0053] In this embodiment, a low - frequency band with little noise influence was used for calculation. Therefore, even in an environment with high noise at depths of 200 meters or more, ε could be estimated with little influence from noise.

[0054] Throughout the specification, when a certain part states that a certain component "has" or "comprises", this means that, unless otherwise stated to the contrary, it does not exclude other components and can further include other components.

[0055] Also, the term "… part" described in the specification means a unit that processes at least one function or operation, which may be embodied as hardware, software, or a combination of hardware and software.

[0056] In addition, within the scope not departing from the gist of the present invention, it is possible to appropriately replace the components in the above - mentioned embodiment with well - known components. Also, the above - mentioned modification examples may be appropriately combined.

Industrial Applicability

[0057] From the above, according to the present invention, a method for estimating the turbulent kinetic energy dissipation rate can be provided, so it has high industrial utility value.

Explanation of Signs

[0058] 15 Control device 25 Arithmetic device 35 Receiver 200 Estimation device

Claims

1. A step of obtaining a wave number spectrum Φ(k) of a fluid; A step of calculating k·Φ(k) by multiplying the wave number k by the wave number spectrum Φ(k); A step of calculating a friction velocity u by using the k·Φ(k), an empirical constant a, a Karman constant κ, and Equation (1); ＊ A step of calculating; The friction velocity u; ＊ A step of calculating a turbulent kinetic energy dissipation rate ε by using the friction velocity u; A method for estimating a turbulent kinetic energy dissipation rate, characterized by the above. Equation (1) ··· u ＊ = a －１／２ · κ １／３ · (k·Φ(k)) １／２

2. The wave number spectrum Φ(k) is a wave number spectrum Φ(k) of a vertical flow of the fluid, In the step of calculating the turbulent kinetic energy dissipation rate ε, the turbulent kinetic energy dissipation rate ε is calculated by using the friction velocity u, ＊ a height z from the seabed, and Equation (2); The method for estimating a turbulent kinetic energy dissipation rate according to Claim 1, characterized by the above. Equation (2) ··· ε = u ＊ ３ · κ －１ · z －１

3. Further including a step of averaging the k·Φ(k) when k < 1 / 2 cpm; The method for estimating a turbulent kinetic energy dissipation rate according to Claim 1 or 2, characterized by the above.

4. Obtaining the wave number spectrum Φ(k) by using an ultrasonic flow velocity sensor; The method for estimating a turbulent kinetic energy dissipation rate according to any one of Claims 1 to 3, characterized by the above.

5. An acquisition unit that acquires a wave number spectrum Φ(k) of a fluid; A k·Φ(k) calculation unit that multiplies the wave number k by the wave number spectrum Φ(k) to calculate k·Φ(k); Using the k·Φ(k), an empirical constant a, a Karman constant κ, and Equation (1), the friction velocity u ＊ is calculated for the friction velocity u ＊ calculation unit; Using the friction velocity u ＊ a dissipation rate calculation unit that calculates the turbulent kinetic energy dissipation rate ε, comprising An apparatus for estimating the turbulent kinetic energy dissipation rate, characterized in that. Equation (1)... u ＊ = a －１／２ ·κ １／３ ·(k·Φ(k)) １／２

6. The wave number spectrum Φ(k) is the wave number spectrum Φ(k) of the vertical flow of the fluid, The dissipation rate calculation unit uses the friction velocity u ＊ and the height z from the seabed and Equation (2) to calculate the turbulent kinetic energy dissipation rate ε The apparatus for estimating the turbulent kinetic energy dissipation rate according to claim 5, characterized in that. Equation (2)... ε = u ＊ ３ ·κ －１ ·z －１

7. Furthermore, it includes an averaging operation unit that averages the k·Φ(k) when k < 1 / 2 cpm The apparatus for estimating the turbulent kinetic energy dissipation rate according to claim 5 or 6, characterized in that.

8. A program for causing a computer to function as each part of the apparatus for estimating the turbulent kinetic energy dissipation rate according to any one of claims 5 to 7.

9. A non-transitory readable recording medium of a computer storing the program according to claim 8.

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