Mathematical Problems in Engineering

Volume 2016, Article ID 9812929, 9 pages

http://dx.doi.org/10.1155/2016/9812929

## Influence of Expendable Current Profiler Probe on Induced Electric Field of Ocean Currents

China University of Geosciences, Beijing 100083, China

Received 6 June 2016; Accepted 23 August 2016

Academic Editor: Nazrul Islam

Copyright © 2016 Qisheng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The expendable current profiler (XCP) is a new instrument that is internationally used to rapidly monitor ocean currents in marine environments. The most crucial part of this instrument is the XCP probe. Since the probe is of high electrical resistance, it acts almost like an insulator with respect to seawater. Placing it into the induced electric field (IEF) of seawater therefore yields a certain level of influence over the electric field. Therefore, in order to improve the accuracy of XCP measurements, the conditions associated with this influence can be used to guide the design of XCP probes; at the same time, these can also serve as reference points in order to provide technical support for the processing of XCP data on ocean currents. To this end, computer-based numerical simulations and laboratory-based physical simulations are used in this study. The results showed that after an XCP probe (diameter: 5 cm; length: 52 cm) was inserted into seawater, the voltage difference of ocean currents at both ends of the electric field sensor placed above the XCP probe increased by a factor of 1.85 (as compared to the case in which there is no influence from the probe).

#### 1. Introduction

The United States began researching expendable temperature and velocity profilers (XTVPs) as early as the 1970s and in 1978 successfully developed the first XTVP [1, 2]. Between 1979 and 1980, a research team led by Sanford and Sippican company made coproduction and sea trial of several hundred XTVP probes and obtained preliminary detection results [3, 4]. The company subsequently changed the name of this device from “XTVP” to “expendable current profiler” (XCP) and launched production of the instrument, which became widely used in marine surveys, scientific research, and national defense [4, 5]. The XCP is a type of expendable profiling instrument for marine environments and can obtain the profile information of ocean currents rapidly [6]. For the first time in China, we have conducted an in-depth study of various XCP technologies [7, 8]. After independent research and development, China’s first set of XCP equipment was manufactured using precision design [7]. Multiple marine tests indicated that placing the XCP probe into seawater changed the IEF of ocean currents. The XCP can be deployed through a probe launch or be manually cast from the carrying platform of ships, submarines, and aircraft. It can quickly measure ocean currents and temperature profiles while sinking and can calculate water depth based on the probe’s sinking velocity [9, 10]. Data are then transferred to the carrying platform through wired or wireless communication modes, and the real-time data of ocean currents and temperature variation with respect to water depth is obtained after data processing. To verify the accuracy of the XCP measurements, an acoustic Doppler current profiler (ADCP) is used for comparison. The used ADCP is an OS-75K from the RDI Company. The results of seawater experiments showed that the ocean current velocities measured by XCP and ADCP are very similar [7].

We found that placing this instrument in seawater led to changes in the induced electric field (IEF) that is generated by the movement of seawater. Hence, in-depth studies on the influence of XCP probes on the IEF of ocean currents are required in order to improve detection accuracy [11, 12]. In this study, computer-based numerical simulations and laboratory-based physical simulations were used to examine the influence of the XCP probe on the IEF of ocean currents and to obtain the corresponding coefficients of influence.

#### 2. Materials and Methods

##### 2.1. Integral Equation Method

The ellipsoidal probe was placed in homogeneous seawater with an electrical conductivity of . The probe itself has an electrical conductivity of , which is a function of . represents the radius vector. In addition, because the influence of magnetic permeability is usually minimal compared to that of electrical conductivity, it was assumed that .

It was assumed that the electric dipole source was located somewhere in space and that the time-harmonic factor was . We began with Maxwell’s equations for the frequency domain as follows:

The response of homogeneous seawater was defined as the primary field and was represented by the subscript “”; the primary field also satisfied the following Maxwell equations:

At this stage, the following equations were obtained by subtracting the formulas in (2) from the corresponding formulas in (1):where is the practical conductivity value of the model. The conductivity values inside and outside of the probe equal and , respectively.

At this stage, (4) can be rewritten as follows: If the difference between the total and primary field is considered to be the secondary field (represented by the subscript “”), then (5) can be simplified as follows:where the following equation holds:This is known as the scattered current, which would exist only within the probe.

Equation (3) can be similarly simplified:The secondary field can be treated as being caused by the scattered current . Because , the secondary field in the seawater can be calculated using the following equation:where and are the secondary vector potential and secondary scalar under Lorentz condition, respectively:In (10), is Green’s function for the scalar quantity of total space, which was derived from the following equation:where and .

When the probe is in half-space, an additional item must be added to (9) to reflect the influence of the interface. This additional item has been described by Hohman and Wannamaker et al. under the conditions of homogeneous and layered ground, respectively [13–15]. This leads to the following expression for the secondary field:

As described previously, the electromagnetic field is made up of two portions, the primary and secondary fields:Substituting (12), which represents the secondary field, into (13) yields the total electric field’s singular Fredholm integral equation of the second kind:where represents dyadic Green’s function. This function, which was required because the direction of the electric field at location would be different from that of the source current at location , can be derived using the following equation:where represents the derivative for the prime coordinate system and is the unit dyadic.

The probe was partitioned into cubic units, each of which had a length of [16]. The electric conductivity within each unit was constant. Because the scattered current within each unit would also be constant, the integral equation (3) can be approximated as follows:where and represent the electric conductivity and field of the th unit, respectively.

When is used to represent the integral term of (16), the latter can be written as follows:where is dyadic Green’s function for a small current integration. It is different from , which is dyadic Green’s function for a relatively infinitesimal current element.Under these conditions, the electric field at the centre of the th unit can be written as follows:After transposition, it can be written aswhere the following holds:Here, is a 3 × 3 unit matrix, and 0 is the zero tensor.

When every is expressed using (20), the following block matrix equation can be obtained:in the matrix , each element is itself a 3 × 3 matrix:Equation (22) can then be used to solve for the value of the electric field at the centre of each unit within the probe. At this stage, the electric field at any position outside the probe can be obtained using (16).

#### 3. Results and Discussion

##### 3.1. Numerical Simulations of the Probe’s Influence on Marine IEFs

###### 3.1.1. Theoretical Model

A theoretical model for the XCP probe (Figure 1(a)) was first established for conducting numerical simulations [17]. In the figure, AB and A′B′ refer to the electric dipoles. The used current was 1000 A, and the used frequencies were 0, 0.0001, and 1 Hz. The XCP probe was placed in an infinite amount of seawater with a resistivity of 0.33 Ωm. A Cartesian coordinate system was then established by assuming that seawater flow only occurs at the sea surface. The origin is located at the sea surface, while the -axis points in the direction of the ocean currents, and there are no ocean currents along the -axis. The - and -axes were both located at the sea surface, while the -axis pointed upward and was perpendicular to the sea surface. The -, -, and -axes conform to the right-hand rule. The conductivity of the probe was assumed to be 0 S/m, while the observation plane was located at = −1000 cm. The length of the probe’s minor axis was, respectively, at 1, 2, 4, 5, 6, 10, and 20 cm, while that of its major axis along the -direction was 52 cm. Mesh decomposition was carried out for the probe model [18], resulting in 40 × 40 × 52 grids (Figure 1(b)).