Pith Number

pith:VPDD4AGZ

pith:2026:VPDD4AGZBOF3OP6I4OHR6C5OWX

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On the fundamental solution for viscous internal waves and Brinkman flows. Part 1. Two dimensions

Saikumar Bheemarasetty, Stefan G. Llewellyn Smith

The fundamental solutions for viscous internal waves and Brinkman flows are single integrals with logarithmic singularities.

arxiv:2605.15451 v1 · 2026-05-14 · physics.flu-dyn

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Claims

C1strongest claim

The viscous and diffusive fundamental solutions for monochromatic internal waves in a uniformly stratified medium and for anisotropic Brinkman flow take the form of single integrals with logarithmic singularities; for Pr ≳ O(1) a uniform asymptotic expansion of the wave field can be computed rigorously, with density diffusion attenuating amplitude as (1+Pr^{-1})^{-2/3} and broadening beam width as (1+Pr^{-1})^{1/3}.

C2weakest assumption

The derivation assumes a uniformly stratified medium with constant buoyancy frequency together with the validity of the linearized viscous and diffusive governing equations for monochromatic waves and the anisotropic Brinkman model; these enter when the fundamental solution is constructed via Fourier or integral-transform methods.

C3one line summary

Derives single-integral viscous fundamental solutions for internal waves and anisotropic Brinkman flows, with rigorous uniform asymptotics and Prandtl-number scaling for attenuation and beam broadening.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] M. Abramowitz and I. A. Stegun , title =

[2] P. G. Baines , title =. Deep-Sea Res. , year = 1973, volume = 20, pages = 1973

[3] 2001 , address = 2001

[4] Critical slope singularities in rotating and stratified fluids , author=. Phys. Rev. Fluids , volume=

[5] A. J. M. Davis and Llewellyn Smith, S. G. , title =. J. Fluid Mech. , year = 2010, volume = 656, pages = 2010

Receipt and verification

First computed	2026-05-20T00:00:59.322179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abc63e00d90b8bb73fc8e38f1f0baeb5ee3dc01955f41cda37b92245459d4bcb

Aliases

arxiv: 2605.15451 · arxiv_version: 2605.15451v1 · doi: 10.48550/arxiv.2605.15451 · pith_short_12: VPDD4AGZBOF3 · pith_short_16: VPDD4AGZBOF3OP6I · pith_short_8: VPDD4AGZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VPDD4AGZBOF3OP6I4OHR6C5OWX \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: abc63e00d90b8bb73fc8e38f1f0baeb5ee3dc01955f41cda37b92245459d4bcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b59a18edd63630914976c323c61766da7a229224de15d6921336b48965e68306",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2026-05-14T22:28:28Z",
    "title_canon_sha256": "4c4fb5691019694bda793ee7e2db1f73dca943d81e9aab5a0894d08a9a0de22e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15451",
    "kind": "arxiv",
    "version": 1
  }
}