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Spectral analysis on the component characteristics of wake systems generated by the submerged body

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Abstract

The flow physics around the underwater target and its direct interaction with the flexible free surface are the important prerequisite to non-acoustic detection technology, such as Synthetic Aperture Radar (SAR), optical measurement methods or infrared detection. How the structure of wake pattern changes over frequency in the spectral domain is the objective that can promote the applications of these new approaches and it plays a crucial role in better understanding of the relationship between free surface disturbances and the motion state of the submerged body. The existing data of wave height from Computational Fluid Dynamics (CFD) is transferred to a series of discrete nodes with evenly spaced increments through the data interpolation. Based on a joint analysis of 2D Fast Fourier Transform (FFT) and the dispersion relation, the X-shaped representation of submerged body wakes are identified in the wavenumber space, together with the curves of the dispersion relation so as to validate the correctness of the computational procedures. Then a decomposition of the wake system is performed, including the contribution of the near-field Bernoulli hump and far-field Kelvin wave, these two components can be separately reconstructed in the spatial domain using the Inverse Fast Fourier Transform (IFFT). The distance between the first two maximum peaks of the Bernoulli hump is given and the relationship with the Froude number (Fn) is also discussed. Finally, the 1D-Power Spectral Density (PSD) is available to describe the frequency components and proportion of the components. The results lead to a further understanding of the roles of wake components and the motion state of underwater target.

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Data availability

The authors will supply the relevant data in response to reasonable requests.

Abbreviations

SAR:

Synthetic aperture radar

CFD:

Computational fluid dynamics

EFD:

Experimental fluid dynamics

FFT:

Fast Fourier transform

IFFT:

Inverse fast Fourier transform

PSD:

Power spectral density

RANS:

Reynolds averaged Navier Stokes

VOF:

Volume of fluid

h :

Depth of the submerged body

L :

Length of the submerged body

D :

Maximum diameter of the submerged body

k :

Turbulence kinetic energy

h*:

Non-dimensional depth

U :

Velocity of the freestream

kc :

Cutoff wavenumber

Fn:

Length Froude number

Fr:

Depth Froude number

C T :

Normalized resistance force

e :

Base size of the meshes

Re:

Reynolds number

Δt:

Time step

Δx, Δy:

Sample interval in x and y directions

M, N :

Sample number in x and y directions

Cp:

Pressure coefficient

ε :

Dissipation rate

q*:

Normalized amplitude of 2D-FFT

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Funding

This work is financially supported by the National Natural Science Foundation of China (Grand No. 62181275, 62171245), Shandong Provincial Natural Science Foundation (Grand No. ZR2020QA045, Grant No. ZR2021MD106), Laoshan Laboratory Science and Technology Innovation Project (Grant No. LSKJ202204704).

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Authors and Affiliations

  1. Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao, 26600, China

    Dong Li, Zhen Wang, Chuanlin He, Yan Xu & Yi Zheng

  2. School of Ocean Technology Sciences, Qilu University of Technology (Shandong Academy of Sciences), Qingdao, 26600, China

    Dong Li, Zhen Wang, Chuanlin He, Yan Xu & Yi Zheng

  3. Pilot National Laboratory for Marine Science and Technology, Qingdao, 266000, China

    Zhen Wang & Chuanlin He

Authors
  1. Dong Li
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  2. Zhen Wang
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  3. Chuanlin He
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  4. Yan Xu
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  5. Yi Zheng
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Contributions

DL: investigation, writing-original draft, software. ZW: software, data curation, funding acquisition. CH: writing–review & editing, Funding acquisition. YX: FFT program, Interpolation. YZ: post-processing, revision.

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Correspondence to Dong Li.

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Li, D., Wang, Z., He, C. et al. Spectral analysis on the component characteristics of wake systems generated by the submerged body. J Mar Sci Technol 28, 583–596 (2023). https://doi.org/10.1007/s00773-023-00942-9

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  • DOI: https://doi.org/10.1007/s00773-023-00942-9

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